UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Turbulent transfer characteristics over a suburban surface Roth, Matthias 1991

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1991_A1 R67.pdf [ 14.93MB ]
Metadata
JSON: 831-1.0100669.json
JSON-LD: 831-1.0100669-ld.json
RDF/XML (Pretty): 831-1.0100669-rdf.xml
RDF/JSON: 831-1.0100669-rdf.json
Turtle: 831-1.0100669-turtle.txt
N-Triples: 831-1.0100669-rdf-ntriples.txt
Original Record: 831-1.0100669-source.json
Full Text
831-1.0100669-fulltext.txt
Citation
831-1.0100669.ris

Full Text

TURBULENT TRANSFER CHARACTERISTICS OVER A SUBURBAN SURFACE By Matthias Roth Dipl. Natw., The Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, 1985 M.Sc, The University of British Columbia, 1988 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 May, 1991 © Matthias Roth, 1991 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 The University of British Columbia Vancouver, Canada Date A f c ^ 2, DE-6 (2/88) ABSTRACT The main motive f o r studying t u r b u l e n t flow i n an urban environment i s to understand the processes governing momentum, heat and mass exchange between the atmosphere and a very inhomogeneous and aerodynamically rough su r f a c e . This exchange regulates the microclimate wherein about 40% of the c u r r e n t world p o p u l a t i o n l i v e s . An understanding of i t s mechanisms i s e s s e n t i a l f o r a v a r i e t y of reasons and a p p l i c a t i o n s . The s t r u c t u r e of the atmosphere c l o s e to t h i s i r r e g u l a r surface i s not homogeneous and there i s reason f o r concern that t r a d i t i o n a l micrometeorological t h e o r i e s are inadequate to d e s c r i b e the turbu l e n t t r a n s f e r i n t h i s environment. The main o b j e c t i v e of the present study i s to i n v e s t i g a t e the tu r b u l e n t t r a n s f e r mechanism and the a p p l i c a b i l i t y of the Monin Obukhov s i m i l a r i t y framework i n an unstable suburban atmosphere. In a d d i t i o n the f i r s t f u l l set of energy balance data i n c l u d i n g longer term dir e c t l y - m e a s u r e d s e n s i b l e and l a t e n t heat f l u x e s i s presented. The r e s u l t s suggest that the (co)spectra i n respect to shape and l o c a t i o n of the peaks are r e l a t i v e l y i n s e n s i t i v e to sur f a c e f e a t u r e s . They g e n e r a l l y agree w e l l w i t h homogeneous surface l a y e r data w i t h the exceptions of u, T, uw and p o s s i b l y q which a l l e x h i b i t s l i g h t anomalies which may be a t t r i b u t e d to p a r t i c u l a r s urface f e a t u r e s . The non-dimensional d i s s i p a t i o n f u n c t i o n s and most of the i n t e g r a l s t a t i s t i c s r e s u l t s f o l l o w the trends p r e d i c t e d by s i m i l a r i t y theory ( i . e . they are a f u n c t i o n of s t a b i l i t y ) , however, the magnitudes are o f t e n s m a l l e r . i i i Analysis of the correlation coefficients shows that under near neutral and slightly unstable conditions the transfers of momentum and heat are most efficient (and enhanced compared to the homogeneous surface layer) whereas the transfer efficiency of moisture is generally least eff i c i e n t . This results in a dissimilar behaviour of heat and moisture. It is shown that the humidity statistics not only depend on surface boundary conditions but are also influenced by the entire PBL. Observational support in this respect is obtained from a. time series analysis of humidity signals which shows the sporadic occurrence of strong, dry downdrafts (under mainly cloudy conditions) which result in positive contributions to the moisture flux. There is evidence that the present observation levels are sometimes within the roughness sub-layer. At around noon and in the early afternoon the Bowen ratio measured using the gradient approach was often larger than the Bowen ratio obtained from directly measured fluxes. This affects the turbulent fluxes derived from the Bowen ratio-energy balance approach. It is suggested that beside the inequality of the transfer efficiencies sampling problems affect the gradient measurements. The average diurnal energy balance is in general agreement with previous summertime observations from the same site. The results indicate that the storage heat flux, obtained as the energy balance residual using directly measured turbulent fluxes, peaks slightly earlier than predicted by the objective hysteresis model. iv ABSTRACT i i TABLE OF CONTENTS iv L I S T OF TABLES v i i i L I S T OF FIGURES ix L I S T OF SYMBOLS AND ABBREVIATIONS. .' xv ACKNOWLEDGEMENTS xxi i P A R T I : IN T R O D U C T I O N CHAPTER 1: RESEARCH CONTEXT, CONCEPTS AND THEORY. 2 1.1 Rationale . . 2 1.2 The surface layer over urban terrain 5 1.3 Monin-Obukhov similarity theory and definitions 12 1.3. 1 General. 12 1.3.2 (Co)spectral representation 16 1.3.3 Further definitions 22 1.4 Study objectives 24 CHAPTER 2 : REVIEW OF URBAN TURBULENCE AND FLUX MEASUREMENTS 26 2.1 Urban turbulence measurements 26 .2.1.1 Introduction 26 2.1.2 (Co)spectra over urban terrain 28 2.1.3 Integral s t a t i s t i c s over urban terrain 33 2.1.4 Discussion 39 2.2 Urban energy balance measurements 41 2.2.1 Introduction 41 2.2.2 Considerations in evaluating the urban energy balance components 44 V 2.2.3 Observations of urban energy balances 49 C H A P T E R 3: M E A S U R E M E N T P R O G R A M M E A N D I N S T R U M E N T A T I O N 56 3.1 Observation site 56 3.2 Measurement considerations 60 3.3 Instrumentation 63 3.3.1 Mount ing arrangement . 63 3.3.2 Fast response sensors ..66 3.3.2.1 Sonic anemometer/thermometer ....66 3.3.2.2 Three-dimensional sonic anemometer 70 3.3.2.3 Lyman-alpha/Krypton hygrometers 71 3.3.3 Slow response sensors. . . . 75 3.4 Observation programme 77 3.5 Data acquisition and processing 79 P A R T II : T U R B U L E N T T R A N S F E R C H A R A C T E R I S T I C S C H A P T E R 4: T I M E S E R I E S R E P R E S E N T A T I O N O F T U R B U L E N T F L U C T U A T I O N S 83 4.1 Introduction 83 4.2 Results .84 4.2.1 Run 18 (clear skies) : 84 4.2.2 Run 17 (cloudy skies) • 93 4.3 Discussion 98 C H A P T E R 5: S P E C T R A L C H A R A C T E R I S T I C S 106 5.1 Normalized with (co)variance 106 5.1.1 Spectra 109 5.1.2 Cospectra 118 v i 5.2 S p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s , coherence and phase angle s p e c t r a 125 5.3 Normalized w i t h i n the Monin-Obukhov s i m i l a r i t y framework 131 5 .3 .1 Non-dimensional d i s s i p a t i o n and n o r m a l i z a t i o n r a t e s 134 5 .3 .2 S p e c t r a 140 5 . 3 . 3 Cospectra 148 5 .3 .4 S p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s . . . . . . . . . . 152 5.4 Summary and d i s c u s s i o n of ( co )spec t ra l r e s u l t s 159 5 .4 .1 Summary.. 159 5 . 4 . 1 . 1 Normalized with (co)variance 159 5 . 4 . 1 . 2 Non-dimensional d i s s i p a t i o n and n o r m a l i z a t i o n r a t e s 162 5 . 4 . 1 . 3 Normalized w i t h i n the Monin-Obukhov s i m i l a r i t y framework 163 5 . 4 . 1 . 4 S p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s 165 5 .4 .2 D i s c u s s i o n 166 CHAPTER 6: TURBULENCE STATISTICS 172 6.1 I n t e g r a l s t a t i s t i c s 172 .6 .1 .1 Standard d e v i a t i o n s of v e l o c i t y 174 6 .1 .2 Standard d e v i a t i o n s of temperature 182 6 .1 .3 Standard d e v i a t i o n s of humidity 184 6 .1 .4 Covariances 186 6.2 C o r r e l a t i o n c o e f f i c i e n t s 188 6 .2 .1 Momentum t r a n s f e r c o r r e l a t i o n c o e f f i c i e n t s 188 6 .2 .2 Heat t r a n s f e r c o r r e l a t i o n c o e f f i c i e n t s 190 6 .2 .3 Mois ture t r a n s f e r c o r r e l a t i o n c o e f f i c i e n t s 191 6 .2 .4 Temperature-humidity c o r r e l a t i o n c o e f f i c i e n t s 191 v i i 6.2.5 Comparison of correlation coefficients 193 6.3 Summary and discussion 198 6.3.1 Summary 198 6.3.2 Discussion 201 P A R T III : E N E R G Y B A L A N C E M E A S U R E M E N T S CHAPTER 7: URBAN ENERGY BALANCE RESULTS 211 7.1 Introduction. 211 7.2 Comparison of turbulent fluxes from two levels 213 7.3 Average energy balance and two case studies........ 220 7.4 Comparison of residual and parameterized storage heat fluxes 229 7.5 Comparison of Bowen ratios (and fluxes) measured using the eddy correlation systems and the gradient approach... 233 7.6 Summary and discussion 243 7.6.1 Summary 243 7.6.2 Discussion 245 CHAPTER 8: OVEARALL SUMMARY, DISCUSSION AND CONCLUSIONS 249 8.1 Overall summary 249 8.2 General discussion 255 8.3 Summary of conclusions 263 REFERENCES 268 APPENDIX A : CALIBRATION AND CORRECTION OF FAST RESPONSE SENSORS 279 A. 1 Kaijo-Denki sonic anemometer corrections 279 A.2 Lyman-alpha/Krypton hygrometer calibrations and corrections 282 APPENDIX B: (CO)SPECTRAL RESULTS FROM THE 1986 F I E LD STUDY. 288 LIST OF TABLES 1.1 Table summarizing z* values (measured from ground) from observations (o) and wind tunnel studies (w). D = inter-element spacing, H = height of roughness obstacle, Z Q = roughness length, d = zero-plane displacement height 9 2.1 Summary of s p e c t r a l peak frequencies (f ) from d i f f e r e n t m studies. The r u r a l reference data are f o r unstable c o n d i t i o n s as are a l l other s t u d i e s with the exception of Hogstrom et al. (1982) which i s from near neutral s t a b i l i t y . The values f o r Clarke et al. (1982) are based on t h e i r . suburban s i t e . The small numbers are the corresponding peak length s c a l e s (A ) where z' i s the height above d. * From Schmitt et al. (1979) 34 2.2 Comparison of reviewed standard deviations of wind v e l o c i t y normalized by the f r i c t i o n v e l o c i t y f o r neutral s t a b i l i t y , z' denotes the height above the top of the b u i l d i n g s 36 3.1 Summary of v a r i a b l e s measured, the instrumentation used and i t s p o s i t i o n on the tower. The code i s the same as used i n Figure 3.8 68 3.2 Dates, times and relevant c h a r a c t e r i s t i c s of turbulence measurement runs. As = A l t o s t r a t u s , Ac = Altocumulus, Cu = Cumulus. LAT = Local Apparant Time, YD = Y u l i a n Day, q = absolute humidity, T = temperature, U = wind speed and cp = wind d i r e c t i o n 78 LIST OF FIGURES 1.1 Schematic concept ion of the surface layer s t r u c t u r e over an urban surface . Q = s e n s i b l e heat f l u x ( a f t e r Oke et al. , H 1989) 6 2.1 V e r t i c a l v e l o c i t y (a) and temperature (b) s p e c t r a v s . f f o r three s t a b i l i t y c a t e g o r i e s from the suburban s i t e of the RAPS programme i n S t . L o u i s , MO. Dashed l i n e s are the Kaimal et al. (1972) l i m i t s f o r z ' / L = 0. S o l i d l i n e s above and below are the Kaimal s p e c t r a f o r z ' / L = -2 and 1, r e s p e c t i v e l y ( a f t e r C l a r k e et al. , 1982) 30 2.2 L o n g i t u d i n a l (a) and l a t e r a l (b) v e l o c i t y s p e c t r a v s . f f o r three s t a b i l i t y c a t e g o r i e s from the suburban s i t e of the RAPS programme i n S t . L o u i s , MO. Dashed and s o l i d l i n e s are as i n d i c a t e d i n F i g u r e 2 .1 . The upper dashed l i n e f o r u n s t a b l e c o n d i t i o n s i s an e x c l u s i v e zone ( a f t e r C l a r k e et al., 1982) 31 2 .3 Normalized v e l o c i t y s tandard d e v i a t i o n s v s . z ' / L f o r the i n d u s t r i a l ( l e f t ) and the suburban ( r i g h t ) s i t e s of the RAPS programme i n S t . L o u i s , MO. The s o l i d l i n e i s an e m p i r i c a l f i t to r u r a l data by Panofsky et al. , 1977 (eq. 6.1) ( a f t e r C l a r k e et al. , 1982) 38 2.4 Same as F igure 2.3 but f o r temperature. The s o l i d l i n e f o r the i n d u s t r i a l s i t e i s an e m p i r i c a l f i t to r u r a l data by Wyngaard et al., 1971 (eq. 6.2) ( a f te r C l a r k e et al., 1982) 38 2 .5 Schematic of the urban canopy volume and the f l u x e s i n v o l v e d i n the energy balance ( a f t e r Oke, 1987) 43 2.6 Average energy balances of r u r a l (a), suburban (b) areas and t h e i r d i f f e r e n c e (c ) . The data are 30 day ensemble averages ( a f t e r Cleugh and Oke, 1986) 51 3.1 The l o c a t i o n of the Sunset suburban f i e l d s i t e i n the Vancouver area and the surrounding land-uses 58 3.2 Photographic view from the top of the tower l o o k i n g to the south west 59 3 .3 Photographic view of the Sunset tower taken from the south west 59 3 .4 Photographic view of the Sunset tower from the west 64 3 .5 Photographic c l o s e - u p view of the two measurement l e v e l s 64 3.6 Photographic c l o s e - u p view of the 3-D K a i j o Denki anemometer (on the l e f t ) and the SAT/Lyman-alpha hygrometer combination X (on the right) 65 3.7 Photographic close-up view of the 3-D Kaijo Denki anemometer (on the right) and the SAT/Krypton hygrometer combination (on the l e f t ) . An identical combination was used at the lower level 65 3.8 Schematic of the Sunset tower and instrument locations. The code and level numbers are the same as in Table 3.1 67 4.1 Time series traces (60 min) for Run 18 of w' (a-d), v' (e) and u' (f). c) is measured at the lower level. The number in brackets refers to the sensor used (e.g. Table 3.1). KD = Kaijo Denki 86 4.2 Time series traces (60 min) for Run 18 of T' from SAT (a-c) and Kaijo Denki (d). c) is measured at the lower level 87 4.3 Time series traces (60 min) for Run 18 of q' (a-c) and the associated covariances w'q' from SAT/hygrometer combinations (d-f). c) and f) are measured at the lower level. LYERC = Lyman-alpha hygrometer. (The units of the covariances are a composition of the units of the corresponding S.D.). 89 4.4 Time series traces (60 min) for Run 18 of w'T' covariances from SAT (a-c) and Kaijo Denki (d). (The units of the covariances are a composition of the units of the corresponding S.D. ) 90 4.5 Time series traces (60 min) for Run 18 of u'w' (a), u'T' (b) (both from Kaijo Denki) and T'q' from SAT/hygrometer combinations (c-e). e) is measured at the lower level. (The units of the covariances are a composition of the units of the corresponding S.D.) 92 4.6 Time series traces (60 min) for Run 17 of w' from SAT (a), v' from Kaijo Denki (b), u' from Kaijo Denki (c), T' from SAT (d) and q' from Lyman-alpha' hygrometer (e). (The units of the covariances are a composition of the units of the corresponding S.D.) , 94 4.7 Time series traces (60 min) for Run 17 of w'T' from SAT (a), w'q' from SAT/Lyman-alpha hygrometer combination (b), u'w' from Kaijo Denki (c), u'T' from Kaijo Denki (d) and T'q' from SAT/Lyman-alpha hygrometer combination (e). (The units of the covariances are a composition of the units of the corresponding S.D.) 96 4.8 Normalized humidity spectrum for Run 18 (a) and Run 17 (b) vs. f on a log-log plot 97 5.1 Normalized composite spectra of w vs f on log-log plot; this study (symbols) compared with 1986 results (dashed line) and a model developed by Hojstrup, 1981 (solid line). Vertical xi lines are +/- 1 cr 110 5.2 Normalized composite spectra of u (a) and v (b) vs f on a log-log plot; this study (symbols) compared with Anderson and Verma, 1985 (dotted line) and the 1986 results (dashed line). Vertical lines are +/- 1 <r 112 m 5.3 Same as Figure 5.2 but for T (a) and q (b) 114 5.4 Same as Figure 5.2 but for uw (a) and uT (b) 119 5.5 Same as Figure 5.2 but for wT (a) and wq (b) 121 5.6 Normalized composite spectra of Tq vs f on log-log plot from the present study (symbols). Vertical lines are +/- 1 cr 124 m 5.7 Composite spectral correlation coefficients ( l e f t ) , composite coherence spectra (middle) and composite phase angle spectra (right) vs log f for uw (a), wT (b) and uT (c), a l l using the KD system .127 5.8 Same as Figure 5.7 but for wT (a), wq (b) and Tq (c) using the three SAT systems. 130 5.9 Non-dimensional dissipation rates for turbulent kinetic energy (a), heat (b) and moisture (c) vs. z'/L . The solid V line i s the rural reference (Kaimal et al. , 1972). The dashed line in (a) is from the St. Louis study for the suburban site (Clarke et al., 1982) 135 5.10 Normalization functions for the fluxes of momentum (a), heat (b) and moisture (c) vs. z'/L . The solid line at unity is V the rural reference (Kaimal et al. , 1972) 138 5.11 Composite spectra of w from upper (a) and lower (b) level for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively. The dotted line is from Hogstrom et al. (1982). .• .141 5.12 Same as Figure 5.11 but for u (a) and v (b) from upper level. The lower dashed line marks an excluded zone (see text) 143 5.13 Composite spectra of T from upper (a) and lower (b) level for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively 145 5.14 Same as Figure 5.13 but for q 147 5.15 Composite cospectra of uw from the upper level for three s t a b i l i t y classes. The solid line i s the neutral limit on x i i the stable side and the upper and lower dashed lines approximate the upper and lower unstable limits from /Caimal et al. (1972) 149 5.16 Composite cospectra of wT from upper (a) and lower (b) level for four s t a b i l i t y classes. Dashed and solid lines are as indicated on Figure 5.15 151 5.17 Same as Figure 5.16 but for wq 153 5.18 Composite spectral correlation coefficients of uw from the upper level for three s t a b i l i t y classes 155 5.19 Composite spectral correlation coefficients of wT from upper (a) and lower (b) level for four s t a b i l i t y classes .156 5.20 Same as Figure 5.19 but for wq . . . 158 5.21 Same as Figure 5.19 but for Tq 160 6.1 Plot of u„ vs U. The dashed line i s a linear f i t from Clarke et al., 1982 for their suburban site (z' = 25 m). 173 6.2 Turbulence intensity vs. z'/L for u and v (a) and w (b) 175 6.3 Normalized standard deviations of u and v vs. z'/L compared V with an empirical f i t by Clarke et al., 1982 (dashed line) for their industrial site (a) and on log-log plot (b) 177 6.4 Normalized standard deviations of w vs. z'/L compared with V empirical f i t s to rural data by Panofsky et al., 1977 (solid line) and urban data by Clarke et al., 1982 (dashed line) for their suburban site (a) and on log-log plot (b) 179 6.5 Normalized standard deviations of w vs. w compared with a m linear f i t by Clarke et al. , 1982 (dashed line) for their industrial and suburban sites 181 6.6 Normalized standard deviations of T vs. z'/L compared with V an empirical f i t by Wyngaard et al. , 1971 (solid line) (a) and on log-log plot (b) 183 6.7 Normalized standard deviations of q vs. z'/L compared with V an empirical f i t by Hogstrom and Smedman-Hogstrom, 1974 (solid line) (a) and on log-log plot (b). 185 6.8 Ratios of horizontal and vertical components of heat flux compared with an empirical f i t by Wyngaard et al. , 1971 (solid line) 187 6.9 Correlation coefficients vs. z'/L for momentum transfer (a) V x i i i and heat t r a n s f e r (b) . The s o l i d l i n e i n (a) i n an e m p i r i c a l . f i t by McBean (1970) to r u r a l data and the s o l i d l i n e i n (b) represents a f r e e convect ion p r e d i c t i o n (see text) 189 6.10 C o r r e l a t i o n c o e f f i c i e n t s vs . z ' / L f o r moisture t r a n s f e r (a) V and Tq (b). The s o l i d l i n e i n (a) represents a f r e e c o n v e c t i o n p r e d i c t i o n (see text) 192 6.11 Comparison of wq and Tq c o r r e l a t i o n c o e f f i c i e n t s 194 6.12 R a t i o of c o r r e l a t i o n c o e f f i c i e n t s v s . z ' / L of heat t r a n s f e r (a) and moisture t r a n s f e r (b) to those of momentum t r a n s f e r . T h e s o l i d l i n e s i n (a) and (b) are e m p i r i c a l f i t s by McBean and Miyake (1972) and McBean (1970). The dashed l i n e i n (a) i s K / K from Businger et al. , 1971 195 H M 6.13 R a t i o of c o r r e l a t i o n c o e f f i c i e n t s v s . z ' / L (a) and r (b) v Tq f o r heat and moisture t r a n s f e r . . 197 7.1 Comparison of h o u r l y Q measured at the upper l e v e l H (SAT(1127)) vs . that at the lower l e v e l (SAT(1126)) ( c rosses ) . A l s o comparison w i t h an a d d i t i o n a l sensor (SAT(1130)) at the upper l e v e l ( s tars ) 214 7.2 Comparison of h o u r l y Q £ measured at the upper l e v e l (KH1016) v s . that at the lower l e v e l (KH1011) ( c rosses ) . A l s o comparison with an a d d i t i o n a l sensor (Ly-alpha) at the upper l e v e l ( s tars ) 214 7.3 D i u r n a l v a r i a t i o n of 20 min values of c o r r e c t e d and u n c o r r e c t e d la tent - heat f l u x e s w i t h a s s o c i a t e d oxygen and d e n s i t y c o r r e c t i o n terms f o r YD 195. 217 7.4 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 (a) and l a t e n t (b) heat f l u x e s measured at the upper and lower l e v e l . The numbers i n (a) i n d i c a t e the number of values used i n the averaging 218 7.5 Average energy balance at the Sunset s i t e (a) and average Bowen r a t i o (0) (b) f o r YD 187 - 196 221 7.6 D i u r n a l v a r i a t i o n of energy balance components (a) and the r a t i o s of 6 and AQ / Q * (b) f o r YD 192 222 S,SP 7.7 D i u r n a l v a r i a t i o n of energy balance components (a) and the r a t i o s of 8 and AQ / Q * (b) f o r YD 195 223 S,SP 7.8 D i u r n a l v a r i a t i o n of the average r a t i o s A = A Q g / Q * (a) and x = Q / Q * (b) from t h i s and other s t u d i e s 227 H xiv 7.9 Hourly residual (AQ ) vs. parameterized (AQ ) storage heat s SP fluxes (a) and comparison of storage heat fluxes obtained as the average residual, parameterized using (7.3) and the residual using (8.2) (AQ ) (b) 230 SHB 7.10 Hysteresis loop relation between residual (AQs), parameterized (AQ ) and residual using (8.2) (AQ ) SP SHB storage heat fluxes and net radiation. Numbers on plot indicate time (LAT) 232 7.11 Average Bowen ratio determined using the fluxes measured by. the eddy correlation, £ (solid line), and RTDMS sensors, /3 F G (dashed line). The numbers in (a) indicate the number of values used in the averaging 236 7.12 Comparison of hourly sensible (a) and latent (b) heat fluxes determined using the eddy correlation (Q ) and Bowen H, E ratio-energy balance (Q ) approaches 238 HB, EB 7.13 Comparison of average sensible (a) and latent (b) heat fluxes determined using the eddy correlation (Q ) and H, E Bowen ratio-energy balance (Q ) approaches ....240 HB,EB ,EHB A.1 Lyman-alpha hygrometer calibration curve. June 1 and 2, 1989 and Sept. 12, 1989 correspond to the calibrations performed before and after the measurement programme 283 A. 2 Krypton hygrometer calibration curve for S/N 1011 as obtained from Campbell Scienti f i c 283 B. 1 Composite spectra of w (a) and T (b) from the 1986 study for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively 290 B.2 Same as Figure B. 1 but for u (a) and wT (b). The solid line is the neutral limit on the stable side and the upper and lower dashed lines approximate the upper and lower unstable lmits from Kaimal et al. (1972) 292 XV LIST OF SYMBOLS AND ABBREVIATIONS Note: Symbols only related to the appendices are not l i s t e d here. Abbreviations A/D analogue to d i g i t a l AFCRL Air Force Cambridge Research Laboratories BOMEX Barbados Oceanographic and Meteorological Experiment KD . . Kaijo Denki KH Krypton hygrometer LAT Local Apparent Time Ly-a Lyman-alpha hygrometer MO Minnesota MOS Monin-Obukhov similarity PBL Planetary Boundary layer PC personal computer RAPS Regional Air Pollution Study F.R.G. Federal Republic of a United Germany RMSD root mean squared difference RTDMS reversing temperature difference measurement system SAT Sonic anemometer/thermometer S/N se r i a l number TKE turbulent kinetic energy YD Yulian Day xvi Roman letters Ai i n e r t i a l subrange constant (Kolmogorov constant) for vertical and lateral wind velocity A 2 i n e r t i a l subrange constant (Kolmogorov constant) for longitudinal wind velocity Ac Altocumulus As Altostratus a empirical constant (Chapter 6) B T i n e r t i a l subrange constant for temperature B i n e r t i a l subrange constant for humidity C characteristic of the turbulence C empirical constants (eq. 2.3) Cm non-dimensional group 2 -1 —1 —3 Co cospectral density (m s , m K, m g kg and m g m for momentum, sensible heat and moisture (using specific and absolute humidity), respectively) Coh coherence spectrum Cu Cumulus °C degree Centigrade c empirical constant (Chapter 7) c specific heat of air at constant pressure (J kg"1 K _ 1) p D horizontal spacing of roughness elements (m) d zero-plane displacement height (m) d i path length of sonic anemometer (m) index of agreement E height of embankment (Figure 3.8) (m) x v i i e vapour pressure (Pa) F 'a function o f f non-dimensional frequency f Nyquist frequency (s *) N Gtz'/L^) normalization function for momentum flux cospectrum g acceleration of gravity (m s"2) H height of roughness elements (m) H(z'/L ) normalization function for sensible heat flux cospect V I energy density, current (eq. 3.1) (ma) K E 2 —1 eddy d i f f u s i v i t y for moisture (m s ) K : H 2 -j eddy d i f f u s i v i t y for heat (m s ) K M 2 -1 eddy d i f f u s i v i t y for momentum (m s ) k von Karman constant k 1 wavenumber in longitudinal wind direction (m_1) k i absorption coefficient of i-th gas (eq. 3.1) (mm-1) k 0 absorption coefficient for oxygen (m g ) k w 2 —1 absorption coefficient for water vapour (m g ) L V v i r t u a l Monin-Obukhov length (m) M number of (co)spectral runs N* 2 —1 dissipation rate of temperature variance (K s ) n natural frequency (s - 1) NP number of (co)spectral densities in frequency band P barometric pressure (Pa) Ph phase-angle spectrum (degree) Q quadrature spectrum Q(z'/L ) V normalization function for moisture flux cospectrum dir e c t l y measure latent heat flux density (W m ) x v i i i anthropogenic heat flux density (W m ) direct l y measured sensible heat flux density (W m~2) latent heat flux density from Bowen ratio-energy balance approach (W m ) latent heat flux density from eq. 7.1 (W m~2) sensible heat flux density from Bowen ratio-energy balance approach (W m~2) net all-wave radiation flux density (W m~2) -3 absolute humidity (g m ) specific humidity (g kg"1) surface layer humidity scale (g kg"1 or g m"3) spectral correlation coefficient (linear) correlation coefficient aerodynamic resistance (s m"1) canopy resistance (s m"1) i •» . . . , 2 -1 „2 -1 2 , - 2 - 1 2 -6 -1 „ spectral density (m s , K s , g kg s and g m s for wind, temperature, specific and absolute humidity, respectively) slope of saturation vapour pressure curve (Pa °C _ 1) absolute temperature (K) dry-bulb temperature (°C) free convection temperature scale (K) absolute vi r t u a l temperature (K) wet-bulb temperature (°C) surface layer temperature scale (K) turbulence intensity mean wind velocity (m s 1) longitudinal wind velocity (m s - 1) xix u free convection velocity scale (m s - 1) f um f r i c t i o n velocity (m s - 1) v transverse wind velocity (m s"1) w vertical wind velocity (m s"1) w combined velocity scale (Chapter 6) (m s - 1) ro x distance between hygrometer sensors (mm) z height above ground (m) •z^ height of planetary boundary layer (m) Z Q aerodynamic roughness length (m) z' effective height of measurement (m) z' height above top of buildings (m) z* depth of roughness sub-layer (m) Greek letters 0 Bowen ratio using directly measured fluxes 0 Bowen ratio using RTDMS sensors r dry adiabatic lapse rate (K m"1) y psychrometric constant (Pa C ) 7* dissipation rate for humidity variance (g kg s or g m s 1 for specific and absolute humidity, respectively) AQ net heat advection (W m ) A AQg 'measured' storage heat flux density (W m ) AQgp parameterized storage heat flux density (W m~2) A0-cUt> storage heat flux density from eq. 7.2 (W m~2) SHB AT dry-bulb temperature difference (°C) d AT wet-bulb temperature difference (°C) X X spacing of RTDMS sensors (m) non-dimensional cospectral constant for moisture 2 —3 dissipation rate for turbulent kinetic energy (m s ) non-dimensional cospectral constant for momentum latent heat of vapourization (J kg 1) - wavelength (m) - AQ /Q* (Chapter 7) s non-dimensional cospectral constant for sensible heat mathematical constant (3.14159...) density of i - t h gas (eq. 3.1) (g m ) -1 -1 -3 standard deviation (m s , K, g kg and g m for wind, temperature, specific and absolute humidity, respectively) modified standard deviation (Chapter 5) non-dimensional temperature profile non-dimensional wind profile non-dimensional dissipation rate for temperature variance non-dimensional humidity profile non-dimensional dissipation rate for humidity variance non-dimensional dissipation rate for turbulent kinetic energy Q /Q* (Chapter 7) H McNaughton and Jarvis' omega factor f i n i t e difference ratio of molecular masses of water vapour to dry a i r wind direction (degrees from north) X X 1 S u b s c r i p t s l j uw, wT, wq or Tq m a s s o c i a t e d with a maximum q absolute humidity q s p e c i f i c humidity s T absolute temperature t time Tq kinematic temperature-absolute humidity Tq kinematic temperature -spec i f i c humidity s u l o n g i t u d i n a l wind v e l o c i t y uw kinematic momentum f l u x v l a t e r a l wind v e l o c i t y w v e r t i c a l wind v e l o c i t y wq kinematic moisture f l u x s WT kinematic temperature f l u x evaluated at standard pressure and temperature S u p e r s c r i p t s time average f l u x e s averaged over two l e v e l s (Chapter 7) ' instantaneous from mean x x i i ACKNOWLEDGEMENTS I wish to express my gratitude to those who assisted in the realization of the present study. Although many people contributed in different ways I naturally remain responsible for any remaining errors. I am deeply indebted to my research supervisor, Dr. Timothy R. Oke, for his encouragement, guidance and generosity throughout my graduate studies. He offered a research environment wherein I could pursue my own ideas. His role as mentor and teacher are greatly appreciated. Special thanks are owed to Dr. Douw G. Steyn who was always available with an attentive ear and provided invaluable advise on numerous occasions. I am also very grateful to Dr. Gordon A. McBean for his constructive comments which were instrumental especially for the f i n a l draft of this thesis. I would like to thank Dr. Ian S. Gartshore for taking time to serve on my supervisory committee. A l l of above deserve special thanks for the prompt reading of this thesis. My colleagues and former graduate students Drs. Sue Grimmond and HaPe Schmid as well as Jamie Voogt provided many useful discussions and were always a source of helpful, practical information. Gabor Fricska's help in the f i e l is greatly appreciated, as is the excellent technical support by Jan Skapski and Henryk Kozlow. Mark Roseberry wrote the PC data acquisition software. Funding for this research has been provided to Dr. T. R. Oke by the Natural Science and Engineering Research Council of Canada and the Atmospheric Environment Service of Environment Canada. The f i e l d s i t e was made available by the B.C. Hydro and Power Authority. While working on this thesis I was supported by University of B r i t i s h Columbia Graduate Fellowships and Research and Teaching Assistanships in the Department of Geography. I wish to thank my family and friends at 'Home' for their continued support. Also very appreciated are my house-mates and friends over the last three years: Michelle, Dawn, Tom, Dan, Andrea and Madeleine. They provided a different outlook on l i f e and a much needed source of distraction. This particular effort during the last few months would not have been possible without those regular 'Friday-night-phone-calls' - thank you Helen for your support. 1 P A R T I : INTRODUCTION 2 CHAPTER 1: RESEARCH CONTEXT, CONCEPTS AND THEORY This chapter presents the background to this research, followed by a discussion of the surface layer over the urban surface and a brief introduction to the Monin-Obukhov similarity (MOS) theory. It ends with a statement of the study objectives. 1.1 R a t i o n a l e Turbulent processes are well understood in the atmospheric surface layer (the lower part of the planetary boundary layer, PBL, which i s characterized by almost 'constant' fluxes with height and wherein horizontal advection due to changes in the upwind surface character are negligible) over 'ideal' (low roughness, unlimited fetch) terrain but less so over very rough or inhomogeneous surfaces. Some progress has been made in the description and parameterization of turbulence in horizontally homogeneous but rough environments such as the surface layer over forests (e.g. Raupach, 1979, Garratt, 1980, Baldocchi and Meyers, 1988, Gao et al. , 1989) and t a l l crops (Raupach and Thorn, 1981). These studies reinforce the idea that the surface layer over a very rough surface must be considered in two parts: the upper, usually referred to as the in e r t i a l sub-layer (Tennekes, 1973) or 'constant' flux layer and the lower, the roughness sub-layer (Raupach, 1979) or transition layer. In the 'constant' flux layer standard micrometeorological theory has been shown to apply (e.g. Kaimal et al. , 1972) and turbulent fluxes and st a t i s t i c s can be evaluated using approaches such as the aerodynamic, 3 Bowen ratio-energy balance and MOS theory. However, the applicability of these frameworks must be questioned when applied to the roughness sub-layer because several of the assumptions underlying their derivation are probably invalid. In contrast to the progress that has been made over forests, boundary layers over inhomogeneous and rough terrain in general are not very well understood. One reason for this weakness is the lack of appropriate experimental data which could be used to develop a consistent theoretical or conceptual framework for turbulent transfer in the roughness sub-layer. The absence of an appropriate framework raises several problems for the measurement and analysis of turbulent fluxes and s t a t i s t i c s close to a rough surface. Points of concern include the sampling strategy to be employed (in space and time), the height of measurement, the representativeness of measurements etc. Considering the fact that most boundary layers of interest to the human population occur over inhomogeneous and rough surfaces (e.g. forests, crops and urbanized areas) the lack of experimental data and understanding of roughness sub-layer processes is both surprising and unfortunate. Sci e n t i f i c interest in the turbulent transfer processes and energy exchanges over heterogeneous surfaces is of course j u s t i f i e d in i t s own right. In this thesis the structure of turbulence over one such surface, a built-up area, is investigated. There are several reasons for choosing this environment. 4 F i r s t l y , the study of turbulence is basic to understanding and predicting the structure of the planetary boundary layer and i t s climates. Turbulent transfer is responsible for much of the heat and vi r t u a l l y a l l of the mass (e.g. water, gaseous and particulates) and momentum exchanges at the surface and throughout the PBL. Further, the turbulent transfer of sensible and latent heat are fluxes in the surface energy balance which is fundamental to an understanding of the climatology of any site. Secondly, comprehension of turbulent transfer characteristics is central to methods of determining fluxes. In the case of urban areas very few experimental results from surface energy balance measurements exist (for a review see Oke, 1988). With the exception of a short-term study by Ching et al. (1983) the direct evaluation of a l l turbulent flux components and reliable closure of the energy balance has not been achieved. This i s because the methods used to measure the turbulent fluxes have sought to relate the turbulent fluxes in terms of mean gradients of related properties. This approach is especially open to errors produced by the spatial and temporal var i a b i l i t y that is common in the urban environment. Thirdly, the determination of the storage heat flux is especially d i f f i c u l t in the urban case. This is frustrating because the storage heat flux is thought to be one of the driving forces behind the formation and evolution of the nocturnal heat island (Oke, 1982). Because of the complex geometry and the variety of different surface materials, i t is almost impossible to directly measure this flux but heat storage can be 5 estimated as the residual of the energy balance i f a l l other terms are measured. Of these the turbulent energy fluxes are most open to error so their accurate assessement becomes especially important. Fourthly, there are several practical applications of importance. The dispersion and diffusion of pollutants are strongly influenced and conditioned by the turbulent state of the atmosphere. In particular the transfer characteristics in an urban environment may be different from those in a homogeneous surface layer and deserve close scrutiny i f we are to improve urban air pollution dispersion modelling. . In wind engineering i t i s of interest that buffeting and failure of structures such as roofs, towers and bridges is not only due to strong average winds, but also to the intensity of the wind fluctuations, and these are increased over rough urban terrain (e.g. Clarke et al. , 1982). 1 . 2 The surface layer over urban terrain As mentioned, the surface layer over inhomogeneous and rough surfaces has to be considered in two parts, namely the roughness sub-layer and the 'constant' flux layer. This concept can also be applied to an urban surface (Figure 1.1) where the large physical dimensions of the urban roughness elements and the spatial inhomogeneity of the surface create practical d i f f i c u l t i e s in the use of the traditional surface ('constant' flux) layer approaches. Figure 1.1 shows that every surface facet at the urban-atmosphere interface has i t s own exchange of heat. Furthermore, the sources and sinks of this entity are arranged at different levels and in different geometric configurations. In addition the flow f i e l d s are 6 F i g u r e 1 .1 : Schematic c o n c e p t i o n of the surface l a y e r s t r u c t u r e over an urban s u r f a c e . Q = s e n s i b l e heat f l u x ( a f t e r Oke et al., H .. 1989). 7 a f f e c t e d by d i r e c t i n t e r a c t i o n with i n d i v i d u a l and/or a combination of roughness elements. E f f e c t s include l o c a l pressure g r a d i e n t s r e l a t e d to form drag on the roughness obstacles and wake product ion . A l l of t h i s r e s u l t s i n m i c r o - s c a l e f l u x f i e l d s w i t h i n and j u s t above the urban canopy which are h i g h l y v a r i a b l e i n space and time. Although F i g u r e 1.1 l i m i t s i t s e l f to the s e n s i b l e heat f l u x , the same i s true f o r mass (e .g . water vapour, carbon dioxide) and momentum exchanges. The a c t i o n of turbulent mixing 'smears' these d i f f e r e n c e s i n the roughness s u b - l a y e r above the roughness elements so that at some height (z*) the h o r i z o n t a l v a r i a b i l i t y disappears ( i n the time average) and a ' c o n s t a n t ' f l u x layer i s present . It f o l l o w s that , al though turbulent processes above z * may be treated as h o r i z o n t a l l y uniform i n time and space, the turbulent f i e l d below z* must be considered t h r e e - d i m e n s i o n a l . In p r a c t i c a l a p p l i c a t i o n s , sensor l o c a t i o n s f o r measuring turbulence parameters must be located above z* to be considered f u l l y s p a t i a l l y r e p r e s e n t a t i v e of the under lying t e r r a i n and to be able to make use of standard micrometeorological approaches. The v e r t i c a l extent of the ' c o n s t a n t ' f l u x layer on the other hand i s determined by the development of an i n t e r n a l boundary layer which responds to meso-scale land-use changes i n the upwind surface c h a r a c t e r i s t i c s . Consider ing the f a c t that a f u l l y adjusted boundary layer develops only s lowly i n the d i r e c t i o n of the mean wind and given the large roughness elements and surface patches t y p i c a l of an urban area, i t i s p o s s i b l e that the roughness s u b - l a y e r exceeds the v e r t i c a l range of the ' constant ' f l u x layer ( t y p i c a l l y 10% of the PBL depth) , so that one-dimensional surface layer s c a l i n g becomes 8 inappropriate (Oke et al. , 1989). The depth of the roughness sub-layer (z*) is the subject of current debate. Table 1.1 summarizes relationships to estimate z* values from the literature. Some are derived from observations over forests whereas others are obtained from wind tunnel studies. No such estimates exist from urban measurements. It appears that the length scales relevant to z* are the horizontal spacing of the dominant roughness elements (D), their height (H) and the roughness length ( Z Q ) . The values in Table 1.1 are obtained from gradient and eddy correlation measurements (ideally observed simultaneously) and the subsequent evaluation of the flux-gradient relationships. The criterion for an observed roughness sub-layer effect is a deviation of the measured non-dimensional vertical profile function from that derived over 'ideal' terrain (e.g. Dyer, 1974). Although the relations given in Table 1.1 yield a range of different values for z*, i t is generally accepted that the inter-element spacing (D) plays a crucial role (e.g. Garratt, 1980). Most authors conclude that the heat transfer is affected more strongly than i s momentum. Raupach and Legg (1984) for instance do not observe a change for momentum transfer in their wind tunnel study. The observations also show that the vertical extent of the roughness sub-layer increases with increasing atmospheric instability. The mechanism leading to the observed enhancement of eddy d i f f u s i v i t i e s is explained through wake diffusion: wakes generated by individual roughness elements promote intense turbulent mixing, thereby 9 Reference z* Comments Tennekes (1973) (o) Townsend (1976) (o) 50-lOOz o for log-profile Pasquill (1974) (o) 2.5H region of wake effects Mulhearn and Finnigan (1978) (w) D 2D wind (neutral) momentum (neutral) Garratt (1978a) (o) 4.5H 3H momentum (neutral) sensible heat (neutral) Raupach et al. (1980) (w) H+1.5D wind (neutral) Garratt (1980) (o) 3D+d wind (unstable) Garratt (1980) (o) 150z +d 0 35z +d 0 lOOz +d 0 Z q= 0.4 m (wind, unstable) z = 0.9 m (wind, unstable) 0 temperature (unstable) Raupach and Legg (1984)(w) lOH+d sensible heat (neutral) Fazu and Schwerdtfeger (1989) (o) 4.5D momentum (neutral) Table 1.1; Table summarizing z* values (measured from ground) from observations (o) and wind tunnel studies (w). D inter-element spacing, H = height of roughness obstacle, Z Q = roughness length, d = zero-plane displacement height. 10 reducing the vertical gradients. The observed dissimilarities between momentum and temperature (moisture is usually assumed to behave like temperature) has been explored by Raupach (1979) and Raupach et al. (1980). They postulate that mechanical as well as thermal horizontal inhomogeneities are important. They confirm that the roughness sub-layer is always a region of horizontal inhomogeneity combined with a strong wake diffusion effect. This latter point may be especially important in the urban context. Due to the extreme patchiness introduced by the irregular arrangement of a variety of surface materials the roughness sub-layer over an urban surface can be highly inhomogeneous in the horizontal. Furthermore, because of the irregular source and sink distributions for heat and moisture there is reason to doubt the equality of the respective eddy d i f f u s i v i t i e s although this has yet to be shown. Unfortunately these points have not gained much attention in urban meteorology. Using the values of H, D, d and Z q for the present study site (see below), which are of similar magnitude as found in other urban residential terrain, Table 1.1 yields z* values between 20 and 100 m. This range encompasses the height of most meteorological towers in urbanised areas including that used in the present study (23 m). This tower has been used in the past in a number of energy balance studies which used the Bowen ratio-energy balance approach in determining the turbulent fluxes (e.g. Kalanda et al., 1980; Cleugh and Oke, 1986; Grimmond, 1988). Considering the complex structure of the surface layer and the height of towers i t follows that there is no guarantee that past 11 observations were conducted in a 'constant' flux layer where MOS w i l l apply. Therefore there exists considerable interest in a more detailed study of the turbulent transfer close to the ground, particularly at the site used in the present study. A priori i t cannot be assumed that MOS and the Bowen ratio-energy balance technique apply in the urban surface/roughness sub-layer. MOS does not include a length scale, such as z^, characteristic of the surface texture or roughness. Considering the nature of turbulence very near the ground we would expect the characteristic length of the turbulent eddies to be influenced by the surface structure. As the height above ground, z, becomes larger this effect should fade away and f i n a l l y become unimportant. Wyngaard (1973) points out, that in dropping Z q from the governing parameter group the application of MOS is restricted to cases where z/z >> 1. o The complex structure of the urban surface has also implications for the determination of the energy balance components. Besides the turbulent fluxes of sensible heat and moisture, whose determination may be affected by possible roughness sub-layer effects, the storage heat flux has been the center of attention and controversy. This term is easily measured in the case of simple and homogeneous surfaces but i t s direct determination in the complex urban system is exceedingly d i f f i c u l t (Oke, 1988). As a result, the storage heat flux is usually obtained through parameterization on the basis of measured net radiation and surface description. The parameterization, however, adds another potential error source to the indirect determination of the moisture flux using e.g. the 12 Bowen ratio-energy balance approach. The obvious alternative approach is to measure a l l the other terms (including the latent heat flux) in the energy balance and have the storage as a residual. But given that the latent heat flux i s both variable and large, unless a reliable estimate of this flux is available i t is d i f f i c u l t to achieve reliable closure of the energy balance. 1.3 Monin-Obukhov similarity theory and definitions 1.3.1 General The understanding of the turbulent atmospheric 'constant' flux layer is largely based upon MOS theory (for a detailed discussion of this scaling scheme see e.g. Arya, 1988, p. 157ff). For a stationary and horizontally-homogeneous surface layer Monin and Obukhov (1954) postulated that the characteristics of turbulence depend on only a few physical parameters. Above the direct influence of the bottom boundary the important parameters are the height z, the surface fluxes of momentum and heat and the buoyancy parameter g/T (acceleration of gravity divided by mean absolute virtual temperature, T = T(l + 0.61q ), where T i s the V s mean absolute temperature and q is the mean specific humidity. From these four governing parameters a velocity, a temperature and a length scale can be formed, defined as: u # = (u'w ,2 + v'w' ) 2.1/4 (1.1) T» = -w'T'/u* (1.2) 13 L = -u 3 T / g k :wrT' (1.3) V w V V where u # is the f r i c t i o n velocity (taking into account the pos s i b i l i t y that the stress tensor may not be aligned with the mean wind); u'w' and v'w' are the kinematic momentum fluxes in the longitudinal and transverse wind directions, respectively; is the surface layer temperature scale ( f r i c t i o n temperature); w'T ' is the kinematic virtual temperature flux V defined as w'T ' = vPT' + 0.61T w'q ' with w'q ' as the kinematic V s s moisture flux; L is the Monin-Obukhov st a b i l i t y length (including the moisture effect) and k is the von Karman constant (here taken to be 0.40). It should be noted that the choice of u^, T^, L and z was somewhat arbitrary and two other scales could be defined based on above four governing parameters: u = (g/f vPT"' z ) 1 / 3 (1.4) f V V T = w T ' / u (1.5) f V f where u^ and T are the free convection velocity and temperature scales, respectively. Dimensional analysis predicts that a suitable dependent variable, after non-dimensionalization with these scales is a function of z/L only. Therefore, for any given characteristic of the turbulence or structure of the flow, say C, a non-dimensional grouping of u #, T^, g/T and z can be found, say C¥, so that: C/C. = F(z/L ) (1.6) where F denotes 'a function o f . McBean (1986) points out that this is s t r i c t l y a postulate, however, the main advantage of the Monin-Obukhov 14 framework is the insight i t gives into how data should be interpreted. The ratio z/L is a measure of the relative importance of convective V or buoyant production of turbulent kinetic energy to that of purely mechanical production and hence is a measure of the s t a b i l i t y of the atmosphere. In the neutral case, where the sensible heat flux-goes to zero, z/L approaches 0 (L -> ± oo). Under unstable conditions with a V V positive sensible heat flux z/L becomes negative (L < 0) and for stable V V conditions the opposite holds (L > 0). V Equation (1.6) is a powerful prediction. It follows that every characteristic of the turbulence in the 'ideal* surface layer, regardless of surface conditions, height, wind speed, time of day, temperature etc. becomes a universal function of z/L when properly normalized. MOS applied to the standard deviations (cr) of turbulent fluctuations suggests the following relationships: <r /u- = F (z/L ) (1.7) u,v,w u>v,w V <r /T- = F (z/L ) (1.8) T * T v <r /q* = F (z/L ) (1.9) q q v s where the subscripts u, v, w, T and q refer to the longitudinal, s transverse and vertical wind, temperature and specific humidity, respectively. The surface layer humidity scale q # is defined as -w'qs'/uj|f. Experimental evidence supports these relationships for w and T and, to some extent, q . The horizontal wind components u and v, however, s seem to scale better with z., the depth of the daytime PBL. In the 15 following, standard deviations of turbulent fluctuations scaled according to (1.7) - (1.9) w i l l be refered to as the normalized standard deviations. Under neutral conditions the buoyant production disappears and i t can be shown that F = F(0) = constant, therefore: u,v,w cr Ai- = constant (1.10) u,v,w Under these conditions cr and T # should go to zero. However, because of horizontal inhomogeneities and electrical noise the former w i l l l i k e l y remain nonzero and as a result c /Tm becomes large. In the limit of free convection when most turbulent motion arise due to buoyancy, the vertical wind shear becomes very small and u w does not seem to be an important scaling parameter anymore. In these circumstances i t seems appropriate to choose the free convection scaling parameters in the normalizations and i t can be shown that cr /u and cr /T are constant. w f T f Since the preferred method of presentation is in terms of z/L these ratios can be written as: cr /u* w * c r / 1 * and in analogy: q s which is reasonably well confirmed by observations. . For extremely stable stratification the turbulent eddies are very F (-z/L ) W V 1/3 F (-z/L ) T v -1/3 F (-z/L ) q v -1/3 (1.11) (1.12) (1.13) 16 small, suggesting that z loses is importance as a relevant parameter. The predictions are then: cr /u~ = const.; cr/T» = const.; cr /a* = const. (1.14) w * T * q s In addition to the normalized standard deviations the turbulence intensity, t^, is an often computed descriptor of turbulence and is defined as: t = cr /U (1.15) u,v,w u,v,w where U is the mean wind speed. Both, the normalized standard deviations and the turbulent intensities are part of the integral s t a t i s t i c s ; integral because the standard deviations of interest are integrated over a frequency range which, i f possible, encompasses the entire range of energy containing eddies. 1.3.2 (Co)spectral representation MOS applied to (co)spectra introduces the natural frequency n (in Hz) which leads to a further non-dimensional group: f = nz/U (1.16) After proper normalization spectra follow the relation: S /C- = F(f,z/L ) (1.17) C * v where S c is the spectrum of a variable C. The representation of spectra is based on the Kolmogorov-Obukhov 17 hypotheses (e.g. Champagne et al., 1977). According to the second Kolmogorov Hypothesis for the inertial subrange (between the production and dissipation scales) the spectral density (S) of velocity components are given by: S (k ) = A e 2 / 3k " 5 / 3 (1.18) u,v,w 1 1,2 1 where k is the wavenumber in the longitudinal wind direction, e is the dissipation rate of turbulent kinetic energy and A is a universal 1,2 constant for the inertial subrange (Kolmogorov constant). Since the in e r t i a l subrange spectral levels for v and w are higher than those for u by a factor of 4/3 predicted by isotropy, the corresponding Kolmogorov constants d i f f e r by the same ratio. In the present study Ai (for v and w) and A 2 (for u) were set to 0.68 and 0.5, respectively (Panofsky and Dutton, 1984). Similarly, for the temperature and humidity fluctuations, the one-dimensional spectra can be represented as: S (k ) = B e 1/3N*k " 5 / 3 (1.19) T I T 1 S (k ) = B c V k (1.20) q 1 q 1 where N* and j* are the rates of destruction by molecular conductivity of T' /2 and q ' /2, respectively. B are constants analogous to A in s T,q 1,2 (1.18). The actual value of B , however, are not as well established as T,q' for A . Many studies observe a constant close to 0.8 for both the 1,2 temperature and humidity (e.g. Paquin and Pond, 1971, Dyer and Hicks, 1982). In the present study the value recommended by Panofsky and Dutton (1984) of B = B = 0.78 is used for both variables. T q 18 The spectral densities in (1.18) - (1.20) relate to wavenumbers. We measure frequency, not wavenumber and the conversion from one to the other i s made through the use of Taylor's frozen turbulence hypothesis: k = 2rcn/U (1.21) By using (1.21), equations (1.18) - (1.20) can be rewritten as (e.g. Kaimal et al., 1972): nS (n) = A e 2 / 3(27rn/U)" 2 / 3 (1.22) u,v,w 1,2 nS (n) = B e" 1 / 3 N*(27rn/U)"2/3 (1.23) T T nS (n) = B e" 1 / 3y*(27in/U)" 2 / 3 (1.24) q q s The dissipation rates for turbulent energy, temperature and humidity can now be obtained through: e = (27rn/U) (nS (n)/A ) 3 / 2 (1.25) u,v,w 1,2 N* = (27rn/U)2/3 (nS (n)/B ) e 1 / 3 (1.26) T T = (27in/U)2/3 (nS (n)/B ) e 1 / 3 (1.27) q q s where the spectral densities are evaluated at a frequency n within the in e r t i a l subrange. The dissipation rates e, N* and y* are often replaced by non-dimensional dissipation rates defined as: <Pe = ekz/u*3 (1.28) C6n = ^kz/u^T* 2 (1.29) </> = y*kz/u^qmZ (1.30) 0 19 Subsituting (1.16) and (1.28) - (1.30) into (1.22)-(1.24) leads to: nS (n)/u* 2 = A (2Trk)" 2 / 30 2 / 3 f " 2 / 3 (1.31) u,v,w * 1,2 e nS (n)/T 2 = B (27rk)~ 2 / 30 "1/3<6 f " 2 / 3 (1.32) T * T E N nS (n)/q 2 = B (27rk)"2/30 ~W3<f> f " 2 / 3 (1.33) q q G Tf s where the spectral density is in units of velocity (1.31), temperature (1.32) and specific humidity (1.33) squared per unit frequency. (1.31) - (1.33) are consistent with Monin-Obukhov scaling, which implies that spectral characteristics are only a function of f and z/L^ (note that the non-dimensional dissipation rates depend on z/L^). If we now include <b , c6.. and <p in the normalization of the spectra (i.e. e N y divide the left-hand-sides of (1.31) - (1.33) by these quantities) we remove the z/L dependence in their equations. This brings a l l spectra into coincidence in the inertial subrange whereas the low frequency parts spread out as a function of stability. This is the normalization applied to the spectra presented herein. The representation of cospectra follows Wyngaard and Cote (1972). They proposed a model which assumes that the cospectra between the vertical velocity and another variable at high frequencies is proportional to the vertical gradient of that variable. The cospectra further depend only on e and k , with constants which are s t a b i l i t y dependent. Dimensional analysis then requires for the cospectra of momentum, heat and water vapour: 20 Co (k ) = -< dU/dz e 1 / 3 k„ 7 / 3 (1.34) uw 1 1 1 Co (k ) = -fx aT /5z e 1 / 3 k.,~7/3 (1.35) wT 1 ^1 v 1 Co (k ) = -5 dq /dz e 1 / 3 k.,"7'3 (1.36) wq 1 I s 1 s where c^, n^and 8^ are the non-dimensional cospectral constants. (Note that the original paper by Wyngaard and Cote does not include the humidity cospectrum. Here i t is assumed that humidity behaves in a similar manner to temperature). Unlike the spectra the cospectra f a l l off more rapidly with a -7/3 slope (compared to -5/3) because of increasing isotropy with increasing wavenumber. With the use of (1.16) and (1.21) we obtain the more typical forms of: nCo (n) = -C 3U/3z e 1 / 3 ( Z / 2 T T ) 4 / 3 f " 4 / 3 (1.37) uw 1 nCo (n) = - / i 9T /dz e 1 / 3 (Z/2T T) 4 / 3 f " 4 / 3 (1.38) wT 1 v nCo (n) = -5 3q /3z e 1 / 3 (Z / 2 J I ) 4 / 3 f " 4 / 3 (1.39) wq I s s By using (1.28) and the equations for the non-dimensional wind, temperature and humidity gradients: <t> = (kz/u*) (SU/dz) (1.40) <t> = (kz/T.) (aT /az) (i.4i) h * v 0 = (kz/q*) O q V a z ) (1.42) equations (1.37) - (1.39) can be put into the usual Monin-Obukhov form: 21 nCo (n)/u 2 = -(27rk) 4 / 3 < 0 0 1 / 3 f 4 / 3 (1.43) uw * 1 me nCo (nJ/u-T. = - (27rk)" 4 / 3 n <f> 0 1 / 3 f " 4 / 3 (1.44) wT * * 1 h e nCo (n)/u ,q» = - (27 ik) " 4 / 3 S 0 0 1 / 3 f " 4 / 3 (1.45) wq * * 1 q E s 1/3 1/3 1/3 The combinations £ 0 0 , fx 0 <j> and 5 0 0 depend on z/L only l m G l h e l q G v and can be determined directly from measurements of cospectra in the ine r t i a l subrange and z/L without going through the separate functions. This was done by Kaimal et al. (1972). Panofsky and Dutton (1984) relate these separate functions to the normalization functions used by the Kaimal study, which are for momentum, heat and water vapour, respectively: G(z/L ) = « <f> <f> 1 / 3)/0.56 v 1 mC = -nCo (n) (27rk) 4 / 3 f 4 / 3/(u„ 20.56) (1.46) uw H(z/L ) = (fx <t> <t> 1 / 3)/1.62 v l h e = -nCowT(n) (2?rk) 4 / 3 f 4 / 3 / ( T » u , 1 . 6 2 ) (1.47) Q(z/L ) = (6 0 0 1 / 3)/1.62 v 1 q e = -nCo (n) (27rk) 4 / 3 f 4 / 3 /(q,u l l.1 .62) (1.48) wq s The equations (1.46) - (1.48) differ slightly from the corresponding ones in Kaimal et al. (1972) and Wyngaard and Cote (1972). In the combination (27rk)4/3, these two references omit the von Karman constant. To make the results from the present study f u l l y comparable with the Kansas experiment (Kaimal et al. , 1972) k wil l be omitted. To bring the 22 cospectra i n t o coincidence i n the -7/3 (-4/3) region we d i v i d e (1.43) -(1.45) by G ( z / L ), H ( z / L ) and Q ( z / L ) which again, as f o r the spec t ra , V V V separates the low frequency end according to s t a b i l i t y . The f o l l o w i n g are the n o r m a l i z a t i o n s used f o r the presenta t ion of the cospectra i n the present study: -nCo (n) / u 2 G ( z / L ) =0 .56 ( 2 T T ) " 4 / 3 f " 4 / 3 (1.49) -nCo (n) / u - T - H ( z / L ) = 1.62 (2n)~i/3 f 4 / 3 (1.50) wT * * v -nCo (n) / u - q - Q ( z / L ) = 1.62 (2n) f (1.51) wq v s 1 . 3 . 3 Further definitions The f o l l o w i n g d e f i n i t i o n s introduce several other q u a n t i t i e s and terms which w i l l be used i n the presenta t ion of the r e s u l t s of t h i s t h e s i s . The c o r r e l a t i o n c o e f f i c i e n t s are def ined as: r = u'w' / (cr cr ) (1.52) UW u w r = w'T ' / (cr cr ) (1.53) wT w T r = w'q ' / (<r <r ) (1.54) wq s w q s s r = T ' q ' / (cr cr ) (1.55) Tq T q s s The c o r r e l a t i o n c o e f f i c i e n t s can be looked at as a measure of the o v e r a l l e f f i c i e n c y of the t r a n s f e r , regardless of s c a l e . In the l i t e r a t u r e i t i s 23 more common to investigate the exchange coefficients (K) or eddy d i f f u s i v i t i e s : K = u- / (au/sz) K = u.T* / OT/az + D K e = u^q* / (aqg/az) (1.56) (1.57) (1.58) where M, H and E stand for momentum, heat and moisture, respectively and T is the dry adiabatic lapse rate. The ratios of eddy d i f f u s i v i t i e s are closely related to the ratios of correlation coefficients since: wT K H M cr /OU/3z) cr /(3T/3Z + D T (1.59) wq K K cr /(au/az) u M L q cr /(aq /3z) (1.60) wT wq K cr /(3q /3z) q s s cr /OT/3z + D T (1.61) When examining the transfer mechanisms the spectral correlation coefficients: Co (f) R (f) = ^ (1.62) U [S^f) s ^ f } ] 1 ' 2 [ 24 are of special importance, where i j is any of uw, wT, wq or Tq. The coherence spectra are defined as follows: [Co 2 ( f ) + Q 2 ( f ) ] 1 / 2 Coh (f) = i i l-i (1.63) ; i ( f ) S j . i J [S. f)  ( f ) ] 1 / 2 where Q are the quadrature spectra. The phase angle spectra are given by: -i Q i , ( f ) Ph (f) = tan l-i (1.64) Co i j (f) 1.4 Study objectives The central goal of this thesis is to study the turbulent transfer characteristics over a suburb as an example of a rough, heterogeneous surface. A l l the standard measures (wind components, temperature, humidity, and the fluxes of momentum, sensible heat and moisture) w i l l be investigated. Part II of the thesis w i l l concentrate on the analysis of above variables using the MOS framework. By use of observations from 2 levels i t i s possible to assess the degree to which these characteristics conform to 'ideal' conditions and to possibly conclude whether z > z* at the present study site. The 'ideal' conditions w i l l be represented by observations from Kaimal et al. (1972) based on the 1968 Kansas AFCRL measurement programme. Throughout the thesis these results w i l l be referred to as the 'Kaimal reference' or 'Kaimal data'. The objectives for Part II can be summarized as follows: 25 1) To evaluate the spectral characteristics including (co)spectra coherence and phase-angle spectra. 2) To compute the non-dimensional dissipation and normalization functions. 3) To examine the turbulent transfer mechanism through the analysis of spectral correlation coefficients. 4) To investigate the integral statistics. 5) To determine the transfer f a c i l i t y of the fluxes. 6) To assess whether z > z*. 7) To compare the findings from the present study in (1) - (5) with the 'ideal' rural case and assess the applicability of similarity theory. Since these are the f i r s t f u l l set of data including (a) the direct evaluation of the latent heat flux and (b) the direct simultaneous evaluation of both sensible and latent heat flux for an urban area i t is valuable to explore the following objectives in Part III of this thesis: 8) To evaluate the role of the turbulent fluxes in the complete energy balance. 9) To assess the size of the storage heat flux and compare the residual estimates with those using the parameterization approach. 10) To compare the directly measured Bowen ratios with the ones obtained from the profile approach. 26 CHAPTER 2: REVIEW OF URBAN TURBULENCE AND FLUX MEASUREMENTS 2.1 U rban t u r b u l e n c e measurements 2.1.1 I n t r o d u c t i o n The literature identifies three major features which affect the turbulence structure of the urban boundary layer: 1) The presence of large roughness elements, 2) a 'heat island' that arises from the combination of canyon geometry, increased thermal admittance, the apparent lack of significant evapotranspiration and anthropogenic heat sources and 3) the injection of water vapour as well as gaseous and particulate air pollutants into the atmosphere. The relative importance of these factors can be qualitatively assessed and in general the above liste d effects lead to: an increase in the atmospheric mixing layer depth (doming above the city) less stable thermal stratification within the urban surface layer - an increase (decrease) in wind speeds during light (strong) wind conditions above roof level (with a threshold at approximately 4 m s"1) an increase in the intensity of turbulence In addition, i t i s possible that preferential frequencies are generated in turbulent fluctuations due to the regular, formalized geometry of ci t i e s and also pressure effects may be important in the momentum 27 transfer. Before proceeding with a review of the (co)spectral measurements over the very complex terrain of an urban area, i t seems worthwhile to b r i e f l y discuss results from less complex but s t i l l not 'ideal' surfaces. This may help in the interpretation of any unusual features observed. Panofsky et al., (1982) compare spectra (velocity only) from several studies over complex terrain and gauge them against well-established 'reference' spectra over 'ideal' terrain. They observe that downwind of an increase in surface roughness, spectral densities are affected only in the internal boundary layer. Based on these observations Panofsky et al. propose the following: - high frequencies (wavelength much less than the fetch over the changed terrain) respond rapidly to changes imposed on the flow by surface geometry. Thus, high-frequency turbulence is always in a state of quasi-equilibrium and the spectral shape conforms to that over uniform terrain. - vertical velocity spectra over complex terrain closely resemble those over uniform terrain. This arises because vertical velocity spectra, in contrast to those of the horizontal components, have most of their energy at relatively high frequencies. - the low frequencies of the spectra of the horizontal components are affected by the upstream terrain characteristics. The following sections provide a review of the relatively few studies 28 of turbulence within urban environments. Most lack a complete- set of parameters for the evaluation of the similarity functions for presentation within the MOS framework. Notable exceptions in this respect are the observations by Clarke et al. (1982) from the Regional Air Pollution Study (RAPS) programme in St. Louis, MO. and Hogstrom et al. (1982). Usually the (co)spectra are normalized by the respective (co)variances. Intercomparison between the various studies is made d i f f i c u l t because the nature of the underlying surface changes from one site to the other. Although the land-use is always classified as urban or suburban, surface descriptors such as Z q , d, H, amount of green space etc. can be quite different. Some degree of similarity is to be found in the studies of Coppin (1979), Clarke et al. (1982), Steyn (1982) and Roth et al. (1989) which a l l involve measurement programmes which are similar concerning measuring heights, instruments and nature of the surface. It should be noted that the results from most studies rely on observations made below recommended z* values (Table 1.1). 2.1.2 (Co)spectra over urban terrain For the vertical velocity component under unstable to near neutral s t r a t i f i c a t i o n Ramsdell (1975) (6.7 m above roof tops in a central business d i s t r i c t ) , Coppin (1979) (z' = 24 m, where z' is the height above d), Steyn (1982) (z' = 20.5 m), Clarke et al. (1982) (z' = 25 m) (Figure 2.1a) and Hogstrom et al. (1982) (z' = 5 m at their central city site) measured more energy at lower frequencies than the reference spectra, with an associated slight shift of the peak towards the lower frequencies. The spectra by Roth et al. (1989) (z' = 19 m; same site as 29 Steyn (1982) and the present study) are different in that they agree with the Kaimal results. Clarke et al. (1982) report more low frequency energy of the vertical component for stable and neutral conditions (Figure 2.la). Steyn (1982) and Hogstrom et al. (1982; only for the v component) under unstable conditions again report more low frequency energy in the horizontal wind components. On the other hand Coppin (1979), Clarke et al. (1982) (Figure 2.2) and Roth et al. (1989) show agreement (or even underestimation in the case of the u component) compared with the spectral densities measured by Kaimal. As for the vertical component, Clarke et al. (1982) measure more low frequency energy in the horizontal components under neutral and stable conditions (Figure 2.2) which is due to the development of a secondary peak at low frequencies which they attribute to meso-scale processes. There is some correspondence between the few available observations of scalar spectra and the rural reference data. Coppin (1979) observed a s t a b i l i t y dependence of the low frequency end in the temperature spectra (increase of low frequency energy with increasing i n s t a b i l i t y ) . The stable and near neutral temperature spectra measured by Clarke et al. (1982) (Figure 2.1b) indicate a shift of the peak towards lower frequencies. Their unstable temperature spectra have a broad peak and suggest slightly less energy input at low frequencies than the corresponding rural reference (Figure 2.1b). This is similar to the temperature spectra measured by Roth et al. (1989). The only humidity spectrum is presented by Coppin (1979), however, instrumental problems 30 10- 3 1 0 - 2 10" 1 1 10 1 0 ' 3 1 0 * 2 1 10 f = nz'/U f " nz'/U Figure 2.1: Vertical velocity (a) and temperature (b) spectra vs. f for three s t a b i l i t y categories from the suburban site of the RAPS programme in St. Louis, MO. Dashed lines are the Kaimal et al. (1972) limits for z'/L = 0. Solid lines above and below are the Kaimal spectra for z'/L = -2 and 1, respectively (after Clarke et al. , 1982). 31 Figure 2.2: Longitudinal (a) and lateral (b) velocity spectra vs. f for three s t a b i l i t y categories from the suburban site of the RAPS programme in St. Louis, MO. Dashed and solid lines are as indicated in Figure 2.1. The upper dashed line for unstable conditions i s an exclusive zone (after Clarke et al., 1982). 32 allowed only for a limited analysis. This spectrum shows a strong adherence to the -2/3 law at high frequencies. The stress cospectra reported by Bowne and Ball (1970) (z = 54 m) exhibit more low frequency energy and a larger amount of high frequency variablity than is observed in the Kaimal .reference, whereas Coppin's (1979) observations agree with i t well. The momentum flux cospectra measured by Roth et al. (1989) show slightly lower density values in between the energy containing region and the ine r t i a l subrange and a large amount of scatter at the high frequency end. Otherwise the overall shape follows the reference data. The heat flux cospectra measured by Coppin (1979) clearly show higher energy densities at the low frequency end which increase with increasing instability. The heat flux cospectra by Roth et al. (1989) agree very well with rural observations. Similar to their momentum flux cospectra a relatively fast r o l l - o f f was observed at the low frequency end. The one moisture flux cospectrum shown in Coppin (1979) cannot be regarded as being representative. Coppin points out that the location of the peak is the same as found in rural reference data. The one study reporting on the Tq cospectrum (Medeiros Filho et al., 1988) shows a clear -5/3 slope at the high frequency end. It is generally agreed (e.g. Brook, 1972, z = 17-29 m; Jackson, 1978, z = 10-70 m) that the spectral length scale, as derived from the peak frequency, increases with height of measurement as seen in data observed over 'ideal' sites. Ramsdell (1975) does not measure such an increase for the horizontal wind components. Jackson (1978), on the other hand, showed that the length scale for u suddenly dropped to relatively low values at 33 measuring heights of the order of (and below) the height of the upwind buildings. He concluded that this reflects the smaller-scale turbulence generated in the wake of the buildings upstream. The s t a b i l i t y dependence of the vertical length scale conforms with similarity theory because of i t s inverse relationship with stability. For convective conditions Wamser and Miiller, 1977 (z = 50 and 250 m) observe a decrease in the vertical length scale with increasing roughness. This could not be confirmed by Clarke et al. (1982). Their spectral length scale for the vertical component was generally larger when compared with reference data and no dependence on surface roughness could be established. This latter result is in agreement with similarity theory. Table 2.1 summarizes (co)spectral peak frequencies (f ) and m corresponding peak length scales (A = z'/f , where z' = z - d) from the m m studies discussed above. Included are also the results from the present study. Note that, although only one number is usually associated with each f value i t would be appropriate to give a range of values because the peaks are often rather f l a t and therefore not very well defined. 2.1 .3 I n t e g r a l s t a t i s t i c s o ve r u r b a n t e r r a i n A l l authors who report on turbulence intensities agree on the fact that this ratio is dependent on wind speed, wind direction (roughness) and height of measurement. In general the intensity of turbulence is up to two times larger (especially close to the buildings), over urban areas compared to the adjacent rural terrain. The vertical component is the most affected. It is concluded that the increased turbulence intensities 34 Study V a r i a b l e u V w T UW wT wq R u r a l reference : Kaimal et al. (0.005 (0.002 0.2 0.02 (0.01 (0.02 (0.02 (1972) -0.02) -0.03) -0.1) -0 .2) - 0 . 1 ) * Coppin (1979) 0.025 40z' 0.2 5z' 0.04 25z' 0.03 33z' 0. 1 10z' Steyn (1980) 0.017 60z' 0.01 100z' 0.1 10z' Hogstrom et al. (1982) 0.05 20z' 0.4 2. 5z' C l a r k e et al. (0.007 (0.005 (0. 1 (0.006 (1982) -0.03) -0.02) -0.3) -0.04) Roth et al. (1989) 0.017 60z' 0.2 5z' 0.023 43z' 0.04 25z' 0.05 20z' Present study 0.021 48z' 0.013 77z' 0.2 5z' 0.04 25z' 0.03 33z' 0.04 25z' 0.03 33z' Table 2 .1 : Summary of s p e c t r a l peak frequencies (f ) from d i f f e r e n t m s t u d i e s . The r u r a l reference data are f o r unstable c o n d i t i o n s as are a l l other s tudies with the exception of Hogstrom et al. (1982) which i s from near neutra l s t a b i l i t y . The values f o r Clarke et al. (1982) are based on t h e i r suburban s i t e . The small numbers are the corresponding peak length s c a l e s (A ) m where z ' i s the height above d. * From Schmitt et al. (1979). 35 are due to form drag and associated mechanical shear production near the roughness elements which results in a decrease in wind speed. Since the standard deviations of the turbulent fluctuations remain essentially the same over urban and rural areas this leads to increased intensities. Of the few studies reporting on the s t a b i l i t y dependence of the turbulence intensity four studies could not observe any relationship (Brook, 1972; Ramsdell, 1975 for -2.5 < z/L < 0.17; Hogstrom et al., 1982 for -0.2 < z'/L < 0.2; Rotach, 1990, -0.3 < z'/L < -0.004, 10 m above roof tops in a high density urban area), whereas Clarke et al. (1982) observe increasing values with increasing instability (-1.6 < z'/L < 0.8) and increasing roughness. A lot of attention has been paid to the velocity standard deviations normalized by u # in the neutral limit. Under these conditions similarity theory predicts these ratios to be a constant (see eq. 1.10). Table 2.2 l i s t s the values from the studies reviewed here and the present study. The rural reference values are from a review by Counihan (1975). It should be noted that the values for the longitudinal and vertical velocity components are well established in the rural case, but not for the lateral component which shows considerable varia b i l i t y . Table 2.2 demonstrates that no systematic differences exist between the rural and urban observations. The cr /u» ratios agree well between themselves and u the rural reference with the possible exception of three studies (Jackson, 1978; Steyn, 1982; Rotach, 1990) which report lower values. Similar to the rural case the urban lateral component exhibits some var i a b i l i t y . The normalized urban vertical velocity standard deviations 36 Study cr A u cr Al* cr /u» U V w Commments Counihan (1975) 2.5 1.9 1.3 Rural reference Bowne and Ball (1970) 2.5 1.5 1.3 z = 53.5 m slightly unstable Ramsdell (1975) 2.5 2.0 1.5 urban residential Jackson (1978) 2.1 1.7 1.3 Averages from z = 10 - 70 m Coppin (1979) 2.5 - 1.1 w extrapolated to neutrality Steyn (1982) 2.2 1.8 1.4 Near neutral Clarke et al. (1982) 2.4 1.8 1.3 Averages over a l l data Hogstrom et al. (1982) 2.5 2.2 1.5 2.6 2.3 1.4 Uplandia, z' = 5 m Granby, z = 50 m Yersel and Goble (1986) 2.7 2.2 1.2 Averages over a l l data Rotach (1990) 2.2 1.5 1.0 Near neutral z' = 10 m Present study 2.3 1.7 1.2 Near neutral Table 2.2: Comparison of reviewed standard deviations of wind velocity normalized by the f r i c t i o n velocity for neutral st a b i l i t y , z' denotes the height above the top of the buildings. 37 also correspond to the rural value with the possible exception of the Coppin (1979) and Rotach (1990) studies. Similarity theory predicts the normalized standard deviations to be a function of sta b i l i t y . Ramsdell (1975), however, measured only a very weak dependence in the st a b i l i t y range of -2.5 < z/L < 0.17. Coppin (1979) could not establish a trend with s t a b i l i t y for cr Au, unlike the <r Ai* ratios which increased with increasing in s t a b i l i t y (-1.04 < z/L < w * -0.27). Coppin concluded that the horizontal component probably would have scaled better with z^. Steyn (1982) measured an increase of the normalized standard deviations with increasing in s t a b i l i t y (up to z'/L = -70) for a l l three velocity components. However, he was unable to choose between z or z^ as the better scaling variable. Clarke et al. (1982) concluded, that to the extent MOS can be applied to the normalized standard deviations (wind and temperature) the theory holds for their data obtained in the urban environment. However, as shown in Figure 2.3, the empirical forms of the relationships d i f f e r in the case of w. For any z'/L (z'/L up to -4) the ratios were generally larger for the rural reference compared to the urban sites (especially for small negative values of z'/L). The horizontal wind components seemed to scale better with z^/L, however, Clarke et al. s t i l l observed a z'/L dependence for v. The normalized temperature standard deviations from the same study agree well with the reference curve (Figure 2.4). No obvious trend of the normalized standard deviations versus s t a b i l i t y in the range -0.2 < z'/L < 0.2 could be measured by Hogstrom et al. (1982) and Rotach (1990) for -0.3 < z'/L < -0.004. 38 z'/L z'/L Figure 2.3: Normalized velocity standard deviations vs. z'/L for the. industrial (left) and the suburban (right) sites of the RAPS programme in St. Louis, MO. The solid line i s an empirical f i t to rural data by Panofsky et al. , 1977 (eq. 6.1) (after Clarke et al., 1982). Figure 2.4: Same as Figure 2.3 but for temperature. The solid line for the industrial site is an empirical f i t to rural data by Wyngaard et al. , 1971 (eq. 6.2) (after Clarke et al. , 1982). 39 Clarke et al. (1982) (w more affected than u) as well as Yersel and Goble (1986) (u more affected than w) found an inverse relationship between normalized standard deviations and roughness length. This is in disagreement with MOS which does not include Z q as a governing parameter. 2.1.4 Discussion The spectral results indicate that MOS might apply in the atmospheric layer close to the urban surface. The shape of the spectra of a l l components is preserved, but minor changes in the peak frequencies and in the amount of low frequency energy compared with rural reference spectra are reported to occur. At the high frequency end of the velocity spectra the 4/3 ratio required for isotropy often cannot be confirmed (e.g. Ramsdell, 1975) or only at very high frequencies, f > 5 (e.g. Hogstrom et al. (1982) at their 50m tower site with urban fetch). Kaimal et al. (1972) observe an onset of local isotropy at f as small as one. On the other hand McBean and E l l i o t (1978) conclude from measurements over a sli g h t l y undulating surface that locally isotropic turbulence cannot begin until f > 8 because the velocity-pressure gradient term in the variance budget for the longitudinal velocity component was nonzero for f < 8. The conclusion that MOS appears to apply to some extent for some variables and turbulence statistics is surprising, at least for those measurements which obviously were made within the roughness sub-layer where the individual roughness elements are assumed to influence the characteristics of turbulence. For instance the observations by Ramsdell 40 (1975), Hogstrom et al. (1982) and in part by Rotach (1990) are taken in the immediate v i c i n i t y of buildings (6 to 10 m above roof tops) yet this does not seem to affect either the general shape of the spectra or the normalized standard deviations of the velocity components. Few studies attempt to explain the observed departures from reference data. Clarke et al. (1982) suggest that i t may be possible to describe a physical basis for these differences and provide the following explanation for their measured 'anomalies'. For neutral conditions they suggest that the existence of a longer spectral length scale above the urban surface raises the possibility that the non-dimensional wind shear may be less than unity and may account in part for the lower values of cr (observed for very small negative z'/L values) at their suburban sites. The data reported in their study were obtained at heights of 20 to 50 ZQ which is below the value of 50 - 100 Z q suggested by Tennekes (1973) for the validity of the logarithmic wind profile. Below that height, in the immediate vic i n i t y of roughness elements, departure from the logarithmic wind profile has been shown to occur resulting in a non-dimensional wind shear which is indeed less than unity (Garratt, 1978a and b). The analysis of the turbulent kinetic energy (TKE) budget by Clarke et al. (1987) also shows that for unstable conditions, the ratio of the buoyant production of turbulence relative to the shear production was roughly the same at a l l their sites. However, the dissipation was larger at their rural site and the residual term in the TKE budget was significantly larger at the urban sites. This larger residual component 41 is suggested to be due to vertical advection, flux divergence and pressure transport. In the case of neutral s t a b i l i t y the shear production of turbulence was approximately in balance with the dissipation at a l l sites. Smaller non-dimensional dissipation constants compared to reference data were also observed by Roth (1990). To conclude this review i t should be pointed out that despite the fact that the Monin-Obukhov framework seems to apply to some extent over a rough urban surface, the small body of available observations is not sufficient to warrant firm conclusions. In addition, the presentation of the results often lacks the proper scaling within the surface layer s i m i l i a r i t y framework. It is also unfortunate that there are only very few observations of the turbulent fluxes of momentum, heat and moisture despite their importance in driving the urban energy balance. So far no results of the turbulent fluxes presented within the MOS framework have been reported. In addition, information concerning coherence and phase-angle spectra as well as spectral correlation coefficients, which are important descriptors of the turbulent transfer processes, are completely lacking. 2 . 2 U rban e n e r g y b a l a n c e measurements 2.2.1 I n t r o d u c t i o n Urbanization produces radical changes in the nature of the urban surface and properties of the atmosphere above i t . Alterations involve the transformation of the radiative, thermal, moisture and aerodynamic 42 characteristics (Oke, 1987) with associated changes in the natural radiation, energy and hydrological balances. Well documented effects include 1) the increase of air pollution thereby affecting the radiative transfer, 2) removal of transpiring vegetation and i t s replacement by largely impervious materials (so called 'waterproofing' of the surface) and 3) the use of dense building materials with thermal properties which make them good conductors and storers of heat. The surface energy budget as a special case of the principle of conservation of thermal energy is of great u t i l i t y in characterizing various surfaces and is used as a framework for studying these effects. A special feature and probably the most fundamental d i f f i c u l t y in evaluating the urban surface energy balance is the definition of the 'surface' i t s e l f . The complex three-dimensional structure of the surface makes i t almost impossible to assign a surface datum for meteorological purposes. A useful appproach in dealing with urban energy balances was introduced by Oke (1988). Here the energy balance applies to the top of a volume which extends from above roof-level to the depth of zero vertical heat flux over a time period chosen (Figure 2.5). This approach limits the interpretation of results to dimensions equal to, or greater than, those of the volume. Using this building-air volume approach the energy balance of the volume can be written as: Q* + Q = Q + Q + AQ_ + AQ (2.1) F n E S A where Q* is the net all-wave radiation flux density, Q i s the F anthropogenic heat flux density due to combustion, Q , Q are the 43 Figure 2.5: Schematic of the urban canopy volume and the fluxes involved in the energy balance (after Oke, 1987). 44 turbulent flux densities of sensible and latent heat respectively, AQ G is the net heat storage (in the air, buildings, ground and vegetation) and AQ a is the net horizontal heat advection. The following section considers the evaluation of these energy balance components. 2 . 2 . 2 Considerations in evaluating the urban energy balance components The anthropogenic heat flux is a source of energy in the urban environment which is not usually encountered in other systems and arises from fuel combustion (domestic heating, transportation, industry and metabolism). This term is often ignored in urban energy balance studies, however, as shown by Oke (1987) i t can be substantial and even surpass the radiative energy input for some urban areas in winter. At midday on a typical summer day Yap (1973) and Grimmond (1988) suggest Q = 15 W m for the Sunset area. Based on the diurnal variation F shown by Grimmond (1988) values of 11 W m~2 for 0600 - 2300 LAT (Local Apparent Time) and 7 W m"2 for 2300 - 0600 LAT were chosen for the present study. During nighttime space heating is the dominant contributor to Q whereas during the day and in the evening heating and t r a f f i c contribute almost equally. To ensure that the sensors measure the integrated effects of the entire underlying surface and are representative of the suburban area turbulent flux measurements should be performed in the surface layer (i.e. above z*). Based on results presented below there is some evidence that the sensors were sometimes located in the roughness sub-layer. This 45 has i m p l i c a t i o n s f o r the clos u r e of the energy balance and the rep r e s e n t a t i v e n e s s of the turbulent f l u x measurements (see a l s o 3.2). To help demonstrate the p o s s i b l e e f f e c t s that surface inhomogeneities can have on the s p a t i a l v a r i a b i l i t y of the r a d i a t i v e and s e n s i b l e heat f l u x e s r e s u l t s from previous s t u d i e s w i l l be presented. These r e l y on data which used synchronous measurements from four mobile s i t e s i n the general Sunset area i n a d d i t i o n to the main Sunset s i t e . Cleugh (1990) and Schmid et al. (1991) report that the s p a t i a l d i f f e r e n c e s i n hourl y net r a d i a t i o n i n the Sunset area are r e l a t i v e l y s m a l l . The systematic e r r o r was l e s s than 5% of the mean net r a d i a t i o n and the o v e r a l l root mean squared d i f f e r e n c e (RMSD) from the fou r mobile _2 s i t e s was 24 W m . This f i g u r e 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 c a l i b r a t i o n performed at the Sunset s i t e y i e l d i n g a RMSD of -2 12 W m . Cleugh (1990) concludes that t h i s c o nservative behaviour means that a p o i n t observation 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 Sunset area. Comparison of s e n s i b l e heat f l u x measurements at the Sunset s i t e and the mobile s i t e s show a systematic d i f f e r e n c e i n that the former are higher (Schmid, 1988; using the same data set as Cleugh, 1990). The mean -2 -2 values f o r the measurement p e r i o d were 130 W m (Sunset) and 100 W m (mobile s i t e s ) r e s u l t i n g i n an overestimation of about 25%. Cleugh (1990) -2 -2 c a l c u l a t e s a RMSD of 45 W m f o r the mobile s i t e s compared to 13 W m from an i n t e r - s e n s o r c a l i b r a t i o n performed at the Sunset s i t e . A p o s s i b l e e x p l a n a t i o n i s given by Schmid (1988) a t t r i b u t i n g the higher values at the Sunset s i t e to the f a c t that the immediate surroundings of the Sunset 46 tower, which consist of the non-vegetated and dry transformer substation to the west and north-west and a major road intersection and associated commercial buildings to the south-east, preferentially influence the Sunset heat flux measurements. No similar spatial variability estimates are available for the latent heat flux. Considering the uneven source/sink distribution for moisture (which is similar in i t s irregularity to that for heat) some spatial inhomogeneity is to be expected. However, given the fact that the moisture flux under certain conditions may be additionally influenced by boundary layer processes and that the Tq correlation, which affects the wq correlation, is less than unity (see below) a simple analogy with the spatial v a r i a b i l i t y of the sensible heat flux observations is not warranted. On a larger scale, variability of the turbulent fluxes in the urban boundary layer was demonstrated in the aircraft study of Ching (1985) in St. Louis, MO. It shows spatial variations of about 75% for Q£ and 30% for Q . H The practical problems associated with the determination of the storage heat flux have been pointed out earlier (e.g. in 1.2). There are two direct methods to obtain 'measured' values of AQs. F i r s t l y , one could measure the heat storage for each individual surface type and combine them with an appropriate weighting scheme. This requires a large sampling effort and there have only been studies for individual surface types (Yap, 1973; Taesler, 1978 and Doll et al. 1985). For short term studies Kerschgens and Hacker (1985) and Kerschgens and Kraus (1990) combined measurements from a paved and grassed area and weighted them according to 47 the fraction of impervious and green cover in the upwind region to yield AQS-Secondly, the storage heat flux can be obtained as the residual of the energy balance (2.1) i f a l l other terms are measured: AQ = Q* + Q - Q ~ Q ~ AQ (2.2) S F H E A Because AQ is the residual i t contains the cummulative errors of a l l s other measurements. To avoid having to measure a l l other fluxes a model approach can be used relating the storage heat flux to the net radiation. Oke et al. (1981) proposed an objective linear regression model which combines linear regression equations between Q* and AQg for a number of surfaces and weighs them according to their proportional area in the study region. Oke and Cleugh (1987) observe a hysteresis pattern in measurements of Q* and AQ which is not unlike those seen in observations over bare s o i l , s Incorporating this hysteresis loop based on a relationship by Camuffo and Bernardi (1982), Oke and Cleugh (1987) develop a hysteresis model for the determination of AQ . s Oke and Cleugh (1987) note that the model coefficients of their hysteresis model only relate to the specific site and weather conditions of the study from which i t was derived and subsequently Cleugh (1990) combines a Camuffo and Bernardi (1982) type hysteresis equation from data for individual surface types with an Oke et al. (1981) type areal weighting scheme to create an objective hysteresis model applicable to 48 any urban site. This model is described and evaluated in Grimmond et al. (1991). The determination of the model specific empirical coefficients needs a surface description involving the determination of the plan area of greenspace and paved surfaces and the three-dimensional area of buildings (i.e. area of roofs and walls). The four areas are determined as percentages of the total active area (active area i s the plan area plus the area of the walls and the roofs). These percentages are used to weight the empirical coefficients for each of the surface types and to arrive at the coefficients for the combination equation. The following is the form of the objective hysteresis model: 3(Q* + Q ) A Q S P = C i ( Q * + Q F ) + C 2 + C 3 ( 2 , 3 ) dt with d(Q* + Q J (Q* + Q ) - (Q* + Q ) , — = L ± ± _ (2.4) at 2 where the subscript p stands for parameterized, C , C_ and are the empirical coefficients and t is time. The second term in (2.3) is the hysteresis loop departure from the linear relation. Based on a site survey by Grimmond (1988) the following are the empirical coefficients for the Sunset site used in the present study: C = 0.38, = 0.27 hr and C 3 = -29.3 W m~2. Grimmond et al. ("1991) note that for hours when (Q* + Q ) is negative a separate equation of the form AQ = Q* + Q leads to F S F an even better performance of the objective hysteresis model. This equality i s inappropriate when calculating nocturnal values of Q and HB Q from the Bowen ratios (eq. 3.4 and 3.5 below) since i t would result EB in the two turbulent fluxes equalling zero. Instead a separate 49 combination equation of the form (2.3) is used when Q* + Q f < 0 with the following coefficients (Grimmond et al. , 1991): C = 0.98, = 0.004 hr and C = 2.5 W m~2. 3 The advection term in (2.1) is due to the horizontal transfer of sensible and latent heat through the sides of the building-air volume (Figure 2.5). This term has to be taken into account i f the volume is not surrounded by similar land-uses. By choosing sites with sufficient horizontal homogeneity local or meso-scale advection can be avoided. Using data from the Sunset site, Steyn (1985) demonstrated that the residuals necessary to close the energy balance were random and completely independent of wind direction. This was taken as evidence of site surface homogeneity. If any advective effects are present in the present study they w i l l show up as a contribution to the storage heat flux since a l l possible errors are accumulated in this residual term. Advective effects have been demonstrated on a number of scales. Oke (1979), within the canopy of the urban system, shows that the energy used in evapotranspiration by an irrigated suburban lawn can exceed i t s net radiation budget. This is possible due to advection of heat energy from surrounding dry surfaces. On a larger scale aircraft measurements over St. Louis, MO. by Ching et al. (1983) reveal spatial heat flux patterns at a height of 150 m which they attribute to the presence of an urban heat island and/or meso scale land-use features. 2.2.3 Observations of urban energy balances It i s only within the last decade that reliable urban energy balance 50 results have become available. In the following, a few of these studies w i l l be introduced to demonstrate the effect urbanization has on the energy partitioning at the surface. These data can be compared against the results from the present study in Part III of this thesis. Differences between the surface energy budget components of urban and rural sites are usually used to assess the impact of urban development, although this approach is known to be flawed (Lowry, 1977). Ideally the urban observations should be compared with pre-urban results from the same location, s t r a t i f i e d according to weather conditions, a requirement, however, which is hard to attain. A typical diurnal variation of the energy balance components averaged over 30 summer days following a wet early summer in 1983 is given in Figure 2.6. Q* and Q were directly measured, AQ was computed using the H S objective linear regression model and Q e was obtained as the residual. The results from an extensive grassland (Figure 2.6a) are considered to be typical of rural conditions. The three most important fluxes are a l l in-phase and exhibit a variation which is approximately symmetric about noon. Only the storage heat flux is slightly different because of i t s relatively late peak. The corresponding suburban results from the Sunset site (Figure 2.6b) show that Q is the primary means of dissipating the H daytime net radiation surplus. The relatively high values of Q show that E water i s s t i l l readily available for evapotranspiration despite the water proofing effects of urban development. Heat storage i s considerable during daytime. The in-phase relationship with Q* is forced by the linear relation used in the parameterization for AQ G. This suppresses any temporal trends (hysteresis effects) which may have been present in the 51 Figure 2.6: Average energy balances of rural (a), suburban (b) areas and their difference (c). The data are 30 day ensemble averages (after Cleugh and Oke, 1986). 52 data set. Q becomes increasingly important in the late afternoon and H remains positive until after the sign reversal of Q*. Yap and Oke (1974) explain the delay in the decline of Q with the release of the daytime H heat storage from some urban surfaces prior to sunset. This occurs in response to extensive and abrupt shading experienced within the canopy at relatively low Sun angles. The relatively high Q£ values in the morning are hypothesized to be due to the water (from irrigation) being freely available at the surface (Cleugh and Oke, 1986). At night with light winds there is almost a balance with the net radiation drain being supplied almost entirely from storage. The suburban-rural energy differences are shown in Figure 2.6c. Throughout the daytime the net radiation input is slightly higher at the suburban site which can be attributed to the lower albedo of the urban area. The heat i s mainly put into storage in the urban fabric in the morning and released as turbulent sensible heat to the atmosphere in the late afternoon and evening. The average Bowen ratio values for this particualar data set were 0.46 and 1.28 for the rural and suburban sites, respectively. Substantial evapotranspiration rates_ in urban environments have been observed by Oke and McCaughey (1983). They report measurements from the Sunset area when the surface was very moist, almost saturated (following a wet early summer) and which are suddenly exposed to a high radiation input. Under these circumstances the suburban Q values exceed Q and the E H former were even larger than those measured at the rural control site. The average suburban Bowen ratio for the 19 day period in 1980 was 0.16 53 compared to 0.67 measured at the rural site. The explanation forwarded by Oke and McCaughey (1983) suggests advective interaction between the very dry and wet surfaces in suburbia which results in increased evapotranspiration rates through the 'oasis'-type advection mechanism demonstrated by Oke (1979). Although the circumstances leading to these small Bowen ratio values are not typical the Oke and McCaughey study clearly demonstrates the potential for large Q £ values. Probably the most extensive energy balance data set spanning several seasons is presented by Grimmond (1988). It shows that Q at the Sunset E site is an important term in the energy balance in a l l months from January to June, 1987. In particular Q is the dominant output flux in E the January/February period. The three output fluxes (Q , Q and AQ ) H E S from the January to June period are very similar before noon which is slig h t l y different from the suburban energy balance reported by Cleugh and Oke (1986) (Figure 2.6b). This is probably due to the inclusion of the improved hysteresis type storage heat flux function by Grimmond (1988). The ensemble plots of Grimmond (1988) are similar to those of Cleugh and Oke (1986) in the afternoon and show that Q h is the largest flux followed by Q £ and AQG. The average Bowen ratio for the month of June was 1.47. The average diurnal energy balance at Sunset presented by Cleugh (1990) for a relatively dry period during April - September in 1986 shows that the latent heat flux is the largest energy flux density in the early morning but is overtaken by the sensible and storage heat fluxes in mid-morning. From the mid-afternoon onwards Q and Q dominate. The 54 average Bowen ratio for the Cleugh study was about 2.15. Long term va r i a b i l i t y in the suburban energy balances were studied by Cleugh and Oke (1986) using the 1983 Sunset data set. Their Bowen ratio results show large day-to-day variability and some sharp peaks suggesting an abrupt change in either surface or atmospheric control on energy partitioning. No such variability was observed at their rural site. Similar suburban Bowen ratio variability has been observed before. Kalanda et al. (1981) and Grimmond and Oke (1986) demonstrate a close correlation between irrigation habits and evapotranspiration. Cleugh and Oke (1986) note that the correlation of the daily Bowen ratio v a r i a b i l i t y with wind direction, cloudiness and a suppressed water vapour d e f i c i t i s suggestive of synoptic-scale control rather than due to local advection caused by spatial surface inhomogeneities. DeBruin (1983) and McNaughton and Spriggs (1986) in the context of regional evapotranspiration modelling point out that the role of the entire PBL has to be considered in analysing the energy, mass and momentum exchanges at the surface. For example Q controls the rate of H growth of the PBL and the downward entrainment of usually drier and warmer air. This in turn modifies the saturation d e f i c i t of the PBL, thereby controlling Q , which i t s e l f is inversely related to Q via the E H surface energy balance (Cleugh and Oke, 1986). In the urban environment the turbulent surface and mixed layer are closely coupled because of the low aerodynamic resistance over the rough terrain. The increased turbulence intensities and mixing present over urban surfaces result in a strong coupling of the surface moisture and thermal properties in the 55 surface layer with the entire PBL. The intensified mixing is also responsible for enhanced entrainment at the top of the PBL. This has been demonstrated by Hildebrand and Ackerman (1984) who show the entrainment of warm, dry air into the PBL over St. Louis, MO. to be larger and more variable than that in surrounding rural areas. On the other hand, the turbulent surface layer over grassed and other low roughness surfaces i s poorly coupled to the mixed layer. This explains the low Bowen ratio v a r i a b i l i t y observed by Cleugh and Oke (1986) at their rural site. 56 CHAPTER 3: MEASUREMENT PROGRAMME AND INSTRUMENTATION 3.1 O b s e r v a t i o n s i t e The observational programme for the present study was conducted in a suburban area of Vancouver, British Columbia, Canada. The same site has been used in a number of urban climate and micrometeorology projects before (e.g. Kalanda, 1979; Steyn, 1982; Oke and McCaughey, 1983; Cleugh and Oke, 1986; Grimmond, 1988; Schmid, 1988; Roth et al. , 1989; Cleugh, 1990). Because of the research experience at this site much of the groundwork with respect to site selection and surface description has already been completed (Kalanda, 1979 and Steyn, 1980) and can be transferred to the present study. In the following a brief synopsis of the general setting of the study area and the specific characteristics of the site are presented. Vancouver is located at the mouth of the Lower Fraser Valley which extends from the Strait of Georgia in the west to the Fraser canyon in the east. The valley is bounded by mountains reaching heights of 1500 m. The general climatology of the region is discussed in Hay and Oke (1976). Briefly, the large scale flow is predominately from the west. The summers are dominated by persistent high pressure systems with occasional weak frontal disturbances from the north. Several physical features of the landscape combine to produce local climate variations. Chief among these are the influences of orography, 57 proximity to water bodies and urbanization. Steyn and Faulkner (1986) show that both land/sea and mountain/valley circulations occur. The effect of the land/sea breeze is to cause mainly westerly winds during daytime and weaker easterly flow during the night. Due to the sea breeze and the associated advection of air, the height of the PBL is reduced typically to only 500 m (Steyn and Oke, 1982; Steyn and McKendry, 1988). The suburban study site (called Sunset) is located in south Vancouver (Figure 3.1) and consists mainly of single family residential housing. Figure 3.2 provides a view from the top of the tower towards south west the direction of the prevailing daytime winds. The 1-2 storey houses have a mean height of 8.5 m with an inter-element spacing of about 23 m. A site survey by Cleugh (1988) shows that the total active area (horizontal and vertical surfaces) is 1.5 times the plan area. Within a 2 km radius c i r c l e centered on the site about 43% of the active area i s greenspace, 13% i s roof, 11% is paved and 33% is walls (or canyon). The aerodynamic roughness length of the area surrounding the site i s assessed by Steyn (1980) to range from 0.4 to 0.7 m with a mean of 0.52 m using Lettau's (1969) land-use/roughness element analysis over sixteen sectors. This indicates reasonable surface homogeneity. Steyn (1980) computes a zero-plane displacement length in the western sector of approximately 3.5 m based on estimations from land-use analysis. The instruments used in the present study were mounted on a triangular-section, steel lattice, free standing tower (27.5 m high) erected in the south-east corner of a transformer substation (Figures 3.3 58 Figure 3.1: The location of the Sunset suburban f i e l d site in the Vancouver area and the surrounding land-uses. F i g u r e 3 .3 : Photographic view of the Sunset tower taken from the south west. 60 and 3.4). Steyn (1980) calculated a shadow fraction of 0.14 for the upper section of the tower. A tra i l e r at the base of the tower housed the recording equipment. 3.2 Measurement c o n s i d e r a t i o n s The main objective of the present study is to research the turbulence structure of the roughness sub-layer/surface layer. As pointed out earlier z* values for urban areas are not available; however, Table 1.1 provides some guidelines regarding the possible vertical extent of the roughness sub-layer. Using the site specific values of Z q , d, H and D, the relations in Table 1.1 yield z* values ranging from 20 to 100 m (measured above ground). The last four references cited in Table 1.1 give rather large values (with the exception of Garratt (1980) for wind when Z q = 0.9 m), whereas the z* estimates from the remaining sources are between 20 and 40 m. The effective height of the tower used in this study is 27.5 - 5 = 22.5 m (since the base of the tower i s below an escarpment of height E = 5 m, Figures 3.4 and 3.8) and is therefore at the low end of z* estimates. It seems likely that the sensors mounted on the tower (especially those below the top) are affected by roughness sub-layer effects. Due to practical constraints i t was not possible to extend the height of the tower in order to ensure that the top sensors would probe the homogeneous surface layer. This prompts the need to review the methodology used in determining the turbulent fluxes in the energy budget (which should represent the integrated effects of the .surface types characterizing the land-use) and budget closure. The existence of different source areas for radiative and turbulent fluxes raises problems for budget closure. Oke et al. (1989) point out, that the comparison of flux components with different source areas in a balance equation is methodologically incorrect since the system is inconsistent. Each component of the balance refers to a different system. The question of representativeness of sensible heat flux measurement has been addressed by Schmid (1988). The upwind, downwind and lateral boundaries of the so called source area contributing to the flux sensed at a certain height depend on the characteristics of the flow and on the boundary layer development between the surface and the sensor level. The area tends towards an e l l i p t i c a l shape aligned along the prevailing wind (Pasquill, 1972, Schmid and Oke, 1990). The dimensions of the turbulent source area can be calculated using the Source Area Model developed by Schmid (1988) and described in Schmid and Oke (1990). Naturally the location and shape of this area is continually shifting with the wind and st a b i l i t y . The magnitude of the spatial variability for the present study area is demonstrated by Schmid et al. (1991). In the case of sensible heat flux comparison at two spatially separate sites, differences of up to 25% are possible within the same land-use zone in certain conditions. However, i t can be shown (Schmid, 1988) that with larger source areas, the spatial averaging of the flux contributions increases and thus the measurements become both more spatially representative and temporally less variable. In this case, the different source areas are at least s t a t i s t i c a l l y compatible and closure of the energy balance should be 62 possible. Oke et al. (1989) conclude that despite the physical problems presented by the nature of the surface i t is possible to obtain valid areally-averaged fluxes from fixed point observations provided that careful site selection, height of measurement and temporal sampling procedures are followed. Associated with increasing height of measurement i s a need for longer averaging times, because the dominant eddy scale in the streamwise direction increases with height and so does the integral time scale. Wyngaard (1973) demonstrates how the required averaging time for second moments depends on the variables involved and the state of the atmospheric stability. Under unstable conditions Wyngaard's equations yield averaging times of about 19 min (second moments of vertical wind speed and temperature) and 56 min (sensible heat flux) using z' = 19 m, a typical mean wind speed of 3 m s 1 and a degree of uncertainty of 15%. As one approaches neutrality these averaging times increase for the sensible heat flux. At time scales larger than about one hour or so non-stationary processes begin to affect the flow f i e l d . Roth et al. (1989) compared averaging times for heat fluxes computed over 60 min with the mean of those over four 15 min periods and find no significant under- or overestimation over the range 5 to 300 W m"2. In the present study an averaging time of 60 min was chosen for a l l turbulence quantities and fluxes measured by the fast response sensors. 63 3.3 Instrumentation 3.3.1 Mounting arrangement Turbulence sensors were mounted at two levels on the tower (Figures 3.4, 3.5 and 3.8). After allowing for d, the effective measuring heights were z' = 11.0 and 18.9 m , respectively ( Z ' / Z q = 21 and 36). To ensure that the turbulence measurements would not be affected by tower effects on the wind f i e l d the sensors at the upper level were mounted on a rotatable boom attached to a retractable support arm connected to the tower. The end of this support arm, when f u l l y extended, was about 2 m from the tower structure. The position of the boom was rotated to ensure that the sensors always faced into the approaching mean wind at the beginning of each turbulence run. This could be done from the base of the tower. A similar arrangement was used for the sensors on the lower level. The turbulent variables u' , v' , w' , T' and q' were measured at the upper level (Figures 3.6 and 3.7) and w', T' and q' at the lower level. To obtain the w'q' covariance two different instruments were combined. This required that the separation between the two sensors be as small as possible so as to be able to measure the small-scale eddies but large enough not to risk any flow interference or wake effects from one instrument onto the other. The horizontal distance between the two instruments was about 0.11 m and the humidity sensor was set back by an additional 20 mm roughly (Figures 3.6 and 3.7). Apart from the fast response sensors an array of slow response F i g u r e 3.4: Photographic view of the Sunset tower from the west. F i g u r e 3.5: Photographic c lose-up view of the two measurement l e v e l s . 65 F i g u r e 3.6: Photographic close-up view of the 3-D K a i j o Denki anemometer (on the l e f t ) and the SAT/Lyman-alpha hygrometer combination (on the r i g h t ) . F i g u r e 3.7: Photographic close-up view of the 3-D K a i j o Denki anemometer (on the r i g h t ) and the SAT/Krypton hygrometer combination (on the l e f t ) . An i d e n t i c a l combination was used at the lower l e v e l . 66 instruments was employed to measure net radiation, wind speed and wind direction. They were mounted on a separate boom at the upper level and an additional wind speed sensor was placed at the lower level (Figure 3.5). Further, a reversing psychrometer system to measure the Bowen ratio was installed with i t s upper and lower sensor level approximately identical to the upper and lower boom positions. The reversing sensors can be identified just to the right of the tower structure in Figure 3.5. Figure 3.8 presents a schematic of the Sunset tower and instrument locations. Table 3.1 summarizes a l l the instruments used, the variables measured and their heights on the tower. In the following the nature of the fast and slow response sensors are presented separately. 3 . 3 . 2 F a s t r e s p o n s e s e n s o r s 3 . 3 . 2 . 1 S o n i c anemometer/thermometer The turbulent fluctuations of w and T and therefore the covariance w'T' were measured with a sonic anemometer and fine-wire thermocouple, SAT (Campbell Scientific, Model CA27T) (sensor at the very l e f t in e.g. Figure 3.7). The theory of a one-dimensional sonic system was discussed in detail by Kaimal and Businger (1963). The original form of the anemometer part of the SAT as used in this study was f i r s t introduced by Campbell and Unsworth (1979) who discuss the following main characteristics of the instrument: 1) The wind speed resolution i s better than 10 mm s 2) the d r i f t at zero wind speed is less than 3 mm s - 1 K - 1 and 3) the calibration is 1 m s Volt . The cosine response has errors of less than ± 10% over the range of -30° to +30° from the 67 > 0> D -a o u SW NE > o x: 0) QO 4) & > w ja N (0 -H O as oo Figure 3.8: Schematic of the Sunset tower and instrument locations. The code and level numbers are the same as in Table 3.1. 68 Variables Instruments Effective height, z' Level Code T , T d w McCaughey RTDMS upper cart lower cart 17.01 m 10.05 3 1 A A 2 l U cup anemometer upper level lower level 19.50 11.03 5 2 B B 2 l Q* net pyrradiometer 18.90 4 G f> wind vane 19.50 5 •H w'J'.q' SAT (1126) / Krypton hygrometer (1011) 11.03 2 C u' ,v' ,w' ,V 3-D Kaijo Denki 18.90 4 E w'.T'.q' SAT (1127) / Krypton hygrometer (1016) 18.90 4 D w'.T'.q' SAT (1130) / Lyman-alpha hygrometer 18.90 4 F Table 3.1: Summary of variables measured, the instrumentation used and i t s position on the tower. The code is the same as used in Figure 3.8. 69 horizontal. McBean (1972) shows that this range of angles accounts for almost a l l eddy flux transfer even in unstable conditions. The electronic frequency response is up to 40 Hz but the path length of 0.1 m determines the eddy response. According to Mitsuta (1966), the signal amplitude is reduced by 10% at a frequency of 0.26 U/d^ where d i is the path length. In this case with d i being 0.1 m the 90% cut-off frequency (in Hz) would be at 2.6 U (where U is in m s Y A fine wire thermocouple probe (diameter 12.7 micrometer) is mounted within the sonic anemometer's vertical axis and 20 to 30 mm from the sonic path. The frequency response of the junction exceeds 30 Hz (Biltoft o -1 and Gaynor, 1987) and the calibration is 4 C Volt . The probe is referenced to the thermal mass of the mounting base. Temperature variance is computed as the differential between the ambient temperature and that of the slowly varying thermal mass. According to Tanner et al. (1985) the reference junction time constant is about 20 min. This could not be confirmed by B i l t o f t and Gaynor (1987) who compared high frequency temperature measurements from a SAT system with temperature readings from fast-response platinum wire temperature probes. They conclude that the time constant may be considerably less than 20 min. Comparison of temperature signals from the SAT with those from a three-dimensional sonic anemometer, which are not affected by this problem, shows very good agreement between the two different sensors (e.g. Figure 4.2). It is concluded that the apparently relatively short reference junction time constant of the SAT system was not a problem in the present study. 70 3 . 3 . 2 . 2 T h r e e - d i m e n s i o n a l s o n i c anemometer A three-dimensional sonic anemometer (Kaijo Denki, model: DAT-310, probe: TR-61C) with two orthogonal axes in the horizontal plane and one vertical axis (Figure 3.6) was used to measure the turbulent fluctuations of u, v, w, and T and their respective covariances for the derivation of the momentum and heat fluxes. The principle of operation is discussed in Kaimal (1980). The sensor spacing of this instrument is 0.2 m, the - l ° resolution of the wind speed measurement is 5 mm s and 0.025 C for temperature with a frequency response of 10 Hz. The sonic-derived temperature is affected by both humidity and velocity fluctuations (Kaimal and Businger, 1963). In the present study the temperature s t a t i s t i c s and the sensible heat flux were corrected for these effects using a procedure by Schotanus et al. (1983). Inevitably the bulky array of the sensor arrangement causes distortion of the velocity f i e l d being measured. The two main sources of error are: 1) shadowing in the wake of the transducers which results in an attenuation of the measured wind and 2) flow distortion by the whole sensor array and mounting structures which alters the local flow at the instrument location. As shown by Hanafusa et al. (1982) and Schotanus et al. (1983) these error sources cannot be neglected. They obtain errors in the wind speed or individual wind components of up to 20% for some directions relative to the axis of the transducer array. Grant and Watkins (1989) measure maximum errors in mean wind speed and standard deviations of the horizontal wind components of 10 to 20%. The consequences of both error sources on turbulent s t a t i s t i c s have been 71 treated theoretically by Wyngaard (1981), Wyngaard and Zhang (1985) and Wyngaard et al. (1985). In the present study the Kaijo Denki measurements are corrected for above error sources based on a wind tunnel calibration by Rotach and Calanca (1989; personal communication) using Wyngaard's findings. The corrections applied are outlined in Appendix Al. A bi-directional inclinometer was installed on the mounting plate of the anemometer to measure the deviation from the horizontal plane. Unfortunately the inclinometer measurements were contaminated by el e c t r i c a l noise, therefore only allowing for an approximate estimate of the ' t i l t ' angle. This angle was usually less than ±2° and predominately negative (i.e. the sensors were leaning 'forward'). The deviation from a hypothetical plane with mean vertical velocity w = 0 was less and in the o — order of ±1 . A t i l t correction to force w to zero was applied to a few runs; however, the 'corrected' u'w' covariances did not change by more than 5%. It was decided not to apply any correction. Furthermore, such a t i l t correction is only acceptable i f the instrument has a reliable zero wind speed calibration. 3.3.2.3 Lyman-alpha/Krypton hygrometers The water vapour fluctuations q' were measured with a Lyman-alpha and two Krypton hygrometers (Figures 3.6 and 3.7). The derivation of the humidity fluctuations is based on the energy absorption due to humidity (and other absorbers in the atmosphere) according to Beer's law. For a system consisting of a collimated source of radiation and a detector separated by a distance x and operating at a single wavelength, the 72 energy remaining is given by (Tillmann, 1965): I = I exp • -x k p 3 3 + (3.1) where I = received energy density, I = emitted energy density, = absorption coefficient of i-th gas, p = density of i-th gas, p density of i-th gas at standard temperature and pressure and i = subscript identifying gases such as 1 -) water vapour, 2 -> oxygen etc. The terms I and I may be replaced by their sensed voltage equivalents. The Lyman-alpha humidiometer used in this study (ERC, model BLR, modification Fl) consists of a hydrogen uranium lamp which emits Lyman-alpha ultraviolet radiation of 121.56 nanometer wavelength across a sampling path, and a n i t r i c oxide detector tube. The principles of operation are described in e.g. Tillmann (1965) and Buck (1985). The Lyman-alpha radiation ionizes the n i t r i c oxide in the detector, causing a current I. The source and detector tubes are both equipped with magnesium fluoride windows which pass the Lyman-aplha wavelength but are opaque to most other radiation. The main advantage of the Lyman-alpha emission line is high absorption for water vapour but uniquely low absorption for oxygen. For the particular sensor used in the present study the source-detector spacing was 7.8 mm and the output current was set to 0.22 ma. Since the current generated by small movements of the di e l e c t r i c in the cable leading to the detector tube is comparable in magnitude to the desired output from the detector tube, every effort was made not to l o 73 subject this cable to even slight vibrations. Note that the mounting arrangement for the sensor and detector tubes was custom made (Figure 3.6). The mounting arms were designed to create least possible flow interference and were attached to the base (thermal mass) of the sonic anemometer. Since the magnesium fluoride windows are prone to degradation (aging) and to remove any dirt particles which might affect the transmission of the light, the windows were periodically cleaned with d i s t i l l e d water (after about 10 hours of use). A calibration relating a known humidity to the voltage output was performed before and after the measurement programme. The calibration curves, typical calibration coefficients and the operational equations to derive q' are presented in Appendix A2. The high reactivity of hydrogen in the excited state leads to some d i f f i c u l t i e s in the application of the Lyman-alpha hygrometer: failure to maintain stable calibration, non-linearity in the log output vs. vapour concentration relationship and a relatively short lifetime of the source tube (which can be extended by using a uranium hydrogen mixture). In response Campbell and Tanner (1985) developed an alternative to the Lyman-alpha sensor based on the same principle of operation but using a Krypton source with emissions at 116.49 and 123.58 nanometers. Campbell and Tanner point out that the shorter wavelength is strongly attenuated by the magnesium fluoride windows but is s t i l l present in the detected signal. The main disadvantage, however, is the far greater sensitivity of the Krypton line to oxygen compared to the Lyman-alpha line. At the shorter 74 wave length Krypton line, i t is 8.3 times worse than Lyman-alpha while at the longer wavelength, which is four times as intense, i t is 62.5 times worse than Lyman-alpha (Tillmann, 1988). Tanner and Green (1989) present a procedure to correct for the additional oxygen absorption of the Krypton hygrometer. The measurements in the present study were corrected for this effect as outlined in Appendix A.2. The Krypton hygrometers used in the present study are produced by Campbell Scientific (model KH20). The sensor spacings were 7.95 and 8.03 mm for the two instruments used (S/N 1016 and S/N 1011). The frequency response of this instrument is given as 100 Hz (Tanner et al. , 1985). As for the Lyman-alpha hygrometer the windows were periodically cleaned. The manufacturer's calibration curve was accepted for the Krypton hygrometers because the water vapour absorption coefficients, k , show a w strong linear relationship with the water vapour density and the same coefficients apply for a large range of different absolute humidities (Figure A. 2) (note that the slope of the calibration curves in Figures A. 1 and A.2 is proportional to the calibration coefficient). In the case of the Lyman-alpha hygrometer no calibration curve was available from the manufacturer. Furthermore, the non-linear relationship between the sensor output and the water vapour density (Figure A.l) and the probability of failure to maintain stable calibration prompted for a calibration before and after the measurement programme. However, as shown in Figure A.l the slopes of the calibration curve remained about the same between the two calibration periods. A vapour flux correction due to density effects because of the vapour 75 transport by a small vertical wind ('Webb' - correction) (Appendix A.2) was applied to the Lyman-alpha and Krypton measurements. 3.3.3 Slow response sensors For a summary of the slow response sensors and their positioning on the tower see Table 3.1 and Figures 3.5 and 3.8. The net all-wave radiation was measured with a net pyrradiometer (Swissteco S-l). The polyethyl domes were kept inflated and free of internal condensation by air pumped through granulated s i l i c a desiccant. Typical measurement errors for net pyrradiometers are 3 - 4 % (Latimer, 1972). The wind speed sensor (Met One) was a 3-cup anemometer with a start-up speed of 0.5 m s 1. The wind direction sensor (Met One) was a light weight, a i r - f o i l vane producing a potentiometer output which is proportional to wind direction. The atmospheric presssure data for this study were collected at the Vancouver International Airport Climate Station (see Figure 3.1). The fluxes of sensible heat (Q ) and moisture (Q ) were HB EB additionally measured with a reversing temperature difference measurement system (RTDMS) which was similar to the one used by McCaughey et al. (1987). The aspirated wet- and dry-bulb thermocouples (10 junction copper/constantan thermopiles) were mounted within radiation shields on two carts which move up and down on a trackway (Figure 3.5). The carts at the end of their run are separated by Az = 6.96 m, and are reversed twice each hour to avoid any systematic errors. A ten minute period allows for reversal and equilibration at the new level. The remaining 20 minutes at each level were used for two 10 minute averages. The measurement of the 76 wet- and dry-bulb differences allows for the computation of the Bowen ratio (6 = Q /Q ): G HB EB K (AT + r Az) 8 = — {1 + (€-2)(e/P)} (3.2) K [(s+r)/y]AT - AT E w d o where ATd = dry-bulb temperature difference ( C), AT = wet-bulb O O — 1 temperature difference ( C), T = dry adiabatic lapse rate ( C m ), s = slope of the saturation vapour pressure curve at T (Pa C ) with T as w w the wet bulb temperature, y = psychrometric constant (Pa C ), e = ratio of molecular masses of water vapour to dry air (0.62197), e = hourly mean vapour pressure (Pa) and P is the barometric pressure (Pa). It i s usually assumed that K = K under a l l st a b i l i t y conditions. H E s was obtained according to Lowe (1977) and z through y = c P/eA , p v where c = specific heat of air at constant pressure (J kg 1 K 1) and A p v = latent heat of vaporization (J kg 1) calculated according to Henderson-Sellers (1984): A = 1.91846 106 (T /(T -33.91))2 (3.3) v w w where T is the wet-bulb temperature in K. w The term in braces in (3.2) is a small correction factor which allows for the small vertical wind component attributable to the sensible heat flux density, affecting the measured value of the latent heat flux density, as discussed in Webb et al. (1980). Q can now be determined from 8 using the so called Bowen H G ratio-energy balance method: 77 MB G r b U where Q* = net all-wave radiation flux density, Q = the anthropogenic F heat flux density and AQ = the storage heat flux density. Similarly Q S E can be obtained by: Q = (Q* + Q„ - AQ )] / (1+3 ) (3.5) EB F S G The errors for 8 and the errors associated with the sensible and 1 G latent heat fluxes derived from the Bowen ratio-energy balance approach were computed following Kalanda (1979) . 3 . 4 Observation programme Observations were gathered on eight days at the beginning of July, 1989. Table 3.2 summarizes the dates and main average weather characteristics of the runs. Fourty-three 60-min turbulence runs were collected during the times indicated in Table 3.2. Every attempt was made to perform the measurements under stationary atmospheric conditions. Unfortunately the summer in 1989 was subject to frequent small weather disturbances resulting in occasional cloud cover and rain. This is reflected in Table 3.2 in the column headed 'cloud cover'. Previous to the observation period 9.4 mm of rain were measured at the Vancouver International Airport on July 1st and traces of rain were observed on the 2nd, 3rd and 4th. During the measurement period on July 10 there was 5.8 mm of rain. Starting on July 6 (YD 187), the turbulent energy balance components 78 Day in July 1989 (YD) Time (LAT) q (g m"3) T (°C) U (m s" 1) (degrees) Cloud cover 5 (186) 1300-2000 8.0-9.4 17-19 2-4.5 230-300 clear 6 (187) 1200-1700 8.0-9.0 18-21 3-4.0 240-290 some As 7 (188) 0800-1700 8.3-11.0 16-22 1.5-4 100-230 dense Ac/As 11 (192) 1000-1900 9.8-11.0 18-22 2-4.7 220-270 clear 12 (193) 1000-1800 10-11.7 19-28 1.5-8 240-300 Cu/Ac 13 (194) 1400-1800 10.6-11 19-21 3-3.6 160-190 clear 14 (195) 0900-1600 9.5-11.2 17-21 1.2-3 100-210 clear w/Cu 15 (196) 1100-1500 8.3-9.0 16-18 4-6.5 140-160 As Table 3.2: Dates, times and relevant characteristics of turbulence measurement runs. As = Altostratus, Ac = Altocumulus, Cu = Cumulus. LAT = Local Apparent Time, YD = Yulian Day, q = absolute humidity, T = temperature, U = wind speed and <p = wind direction. 79 were measured on a more or less continuous basis (weather permitting) using the same instrumentation as for the turbulence measurements plus the net pyrradiometer and the RTDMS system. Because of the Lyman-alpha hygrometer source tube depletion this sensor was used less frequently than the Krypton hygrometers which do not have the same drawback. A total of about 90 useful hours was obtained during the course of the 7 days. 3.5 Data acquisition and processing Data recording and processing of the turbulent components was carried out in 3 main phases: 1) Recording on a PC-based data acquisition system. 2) Transfer of data from hard-drive to magnetic tapes and the main-frame computer for further processing; quality control of data set. 3) Application of software to perform calibrations, corrections, Reynolds decomposition, spectral computations and plotting. The turbulence sensors used in this study provided 15 output signals (and an additional channel with a reference voltage) which were fed into a custom made single-ended multichannel input system. In a f i r s t step the signals were low-pass f i l t e r e d with a cut-off frequency of 10 Hz using 6-order Butterworth maximum f l a t f i l t e r s (one per channel). Afterwards, each signal was amplified depending on i t s signal strength and desired output level. In a second step the signals were led into a 16 channel expansion multiplexer (MetraByte, EXP-16) which was connected to a A/D board (MetraByte, DAS-8) installed on a PC-XT. The DAS-8 features a high 80 speed, 12-bit sucessive approximation A/D converter providing a fixed +/-5VDC input with a resolution of 2.44 mV. Custom made software sampled the d i g i t a l signals at a rate of 25 Hz with an associated record length of 60 min and provided error l i s t i n g and correction i f necessary. The low and -3 high frequency limits of the measurements were therefore 0.28x10 and f = 12.5 Hz, where f is the Nyquist frequency. Turbulence s t a t i s t i c s were calculated over the entire frequency range, although the low frequency end is known to be s t a t i s t i c a l l y very unreliable (associated with only very few degrees of freedom). The data were subsequently written to the PC's 30 Mbyte hard drive. Each 60 min run resulted in almost 3 Mbyte of data which, once the hard drive was f u l l , was transferred onto magnetic tape which could be carried back to The University of B r i t i s h Columbia where the data was played back to the IBM main frame computer. Data processing on the computer consisted of applying the calibration factors, correction of the Kaijo-Denki measurements (see Appendix A.l), linear detrending of the 60 min time series, Reynolds decomposition, test for stationarity (run test according Bendat and Piersol, 1986) and subsequent computation of variances, covariances, fluxes, correlation coefficients, (co)spectra, quadrature, coherence and phase angle spectra as well as the spectral correlation coefficients (for theoretical background see 1.3). For plotting purposes the (co)spectral densities were averaged, resulting in equally spaced energy densities in the log frequency domain with about 10 points per decade. To obtain good representation of the low frequency end the f i r s t few points were not averaged (or only over a few data points) with the result that the low frequency side is s t a t i s t i c a l l y unreliable. 81 A l l slow response signals were recorded on three Campbell Sc i e n t i f i c (Model CR21X) data loggers. The sampling frequency was 1 Hz for a l l instruments and subsequently 10 min averages were computed and stored in the memory of the 21X. The resolution of the single- and double-ended (differential) inputs is 0.666 and 0.333 mV, respectively. The fast response sensors measuring the turbulent fluxes of heat and moisture (i.e. the sonic anemometer/thermometers and the hygrometers) were, in addition to the PC, also recorded on the 21X data loggers providing 20 min averages of the fluxes (sampling rate 5 Hz) for use in the energy budget analysis. The simultaneous recording of the same instruments on two different data acquisition systems was achieved by connecting jumper cables between the input terminals of the multichannel input system on the PC side and the input terminals of the 21X data loggers. Note that in the fin a l analysis three 20 min periods were averaged to give an hourly value. Transfer of the 21X data (on cassette tape) to the Univerity*s main frame computer was accomplished by using a C20 interface (Campbell Scientific). 82 P A R T II : T U R B U L E N T T R A N S F E R C H A R A C T E R I S T I C S 83 CHAPTER 4: TIME SERIES REPRESENTATION OF TURBULENT FLUCTUATIONS 4.1 I n t r o d u c t i o n Visual inspection of time series is helpful in characterizing and interpreting the turbulent transfer of atmospheric variables and fluxes and furthermore provides a check for the performance of the turbulence sensors. Since i t i s impossible to show a l l time traces the turbulence runs were examined in respect to any unusual but recurring features. The u, v, w, and T signals were found to behave rather conservatively between individual runs and no distinctive features on which to base a clas s i f i c a t i o n were observed. The humidity signal, however, was characterized by features which were present in some runs only. According to these differences the humidity transport tends to take place in two modes and as a consequence the time traces were cla s s i f i e d into two categories which w i l l be represented by a case study each. Of the turbulence runs analysed about 25% of the data clearly f a l l into the category represented by Run 18 below and another 25% are closely related to Run 17 below. A further 15% are very similar to Run 18 and 25% exhibit more of the features found in Run 17 than Run 18. The remaining 10% of the observations had characteristics observed in both categories. The two runs presented in the following are therefore representative of at least 50% of the data and bear typical features found in another 40% of the observations. On the basis of the present data i t was not possible to create a third category which would represent other distinctive features not observed in the two runs below. To simplify the 84 time series for plotting purposes averages over 1 sec were computed. The f i r s t run, Run 18 (Figures 4.1 - 4.5) was recorded on YD 192 between 0950 and 1050 LAT under clear skies, one day after a r a i n f a l l of 5.8 mm. Net radiation, temperature, absolute humidity, wind speed and direction were 594 W m~2, 19.5 °C, 11.0 g m~3, 2.73 m s - 1 and 252 degrees, respectively. The turbulent fluxes of sensible and latent heat -2 were about 230 and 110 W m , respectively. The f r i c t i o n velocity was 0.37 m s - 1 and s t a b i l i t y z'/L was -0.92. Figures 4.6 and 4.7 represent the second run, Run 17, recorded on YD 188 between 1550 and 1650 LAT. Atmospheric conditions were variable and a mixed Altostratus/Altocumulus cloud cover was present. Net radiation, temperature, absolute humidity, -2 ° -3 -1 wind speed and direction were 349 W m , 21.4 C, 8.3 g m , 3.66 m s -2 -2 and 165 degrees, respectively. Q was about 260 W m , Q « 200 W m , um H E = 0.49 m s 1 and z'/L v = -0.45. For the purpose of inter-sensor comparison Figures 4.1 - 4.5 for Run 18 include a l l variables measured from a l l fast-response sensors used. For Run 17 the entire set of variables w i l l be presented but only from selected sensors, namely the SAT/Lyman-alpha hygrometer combination and the Kaijo Denki three-dimensional anemometer. 4.2 R e s u l t s 4.2.1 Run 18 ( c l e a r s k i e s ) Figure 4.1 presents the velocity components measured by the SAT and Kaijo Denki sensors. The w' signals from a l l sensors (Figures 4.1a-d) 85 show the expected random like behaviour of up- and downdrafts without any preferential direction. The intercomparison between the sensors at the upper level (1130, 1127, KD; Figures 4.1a, b and d) is excellent raising confidence in the use of these instruments. The signal from 1126 (Figure 4.1c), mounted on the lower level, also compares well with the other sensors and differences between the upper and lower level traces are very small. The same is true for the other variables measured with different sensors and presented in the following sections. The v' and u' time traces (Figures 4.1e and f) show that the horizontal velocity components carry more of their energy at lower frequencies compared to w' . In addition the horizontal velocity fluctuations are larger than those in the vertical. The temperature traces in Figure 4.2 exhibit some high fequency v a r i a b i l i t y which, however, is superimposed on lower frequency 'signatures'. A large part of the variability is contained in these particular 'structures' which are characterized by a slow, irregular increase which becomes amplified until a sharp drop in temperature (e.g. at t = 1180, 1450, 1900, 2410, 2830 and 3330 s). The length of these features are 3 - 5 min (~ 500 - 800 m). Note that the behaviour observed in these temperature traces is similar, but not the same, as often observed over 'ideal' surfaces (e.g. Wilczak, 1984). In the 'ideal' case the temperature 'ramps' only last for about 100 sec or less and exhibit a clear saw-tooth appearance. In another suburban turbulence study from the same site Roth (1988) observed the same features in the temperature traces lasting from 3 to 9 0 500 1000 1500 2000 2100 3000 31O0 Time In s Figure 4.1: Time series traces (60 min) for Run 18 of w' (a-rl) , V (e) and u' (f ) , c) is measured at the lower level. The number in brackets refers Lo the sensor used (e.g. Table 3.1). KD = Kaijo Denki, Figure 4.2: Time series traces (60 min) for Run 18 of T' from SAT (a-c) and Kaijo Denki (d). c) i s measured at the lower level. 88 min. This time scale is in the order of typical time scales for convective boundary layers at this site; e.g. Steyn and McKendry (1988) find a typical z^ of 500 m which, combined with a convective mixed layer 1/3 —1 velocity ( = (g/T z (w'T ')) ) of 1.5 m s , yields a convective time v i v scale of 5 to 6 min. The physical processes leading to these 'structures' could be large thermals which are immediately followed by cold downdrafts. Indeed the temperature 'structures' at t = 1180, 2410, 2830 and 3330 s are a l l initiated by downdrafts associated with large negative w' deviations (Figure 4.1). No dependence of the temperature features on wind direction or other atmospheric conditions could be detected. The general behaviour of the humidity signals (Figure 4.3a-c) is similar to but not as marked as that of temperature. For example, the correspondence can be observed at t = 1900, 2410 and 2830 s where, like in the temperature signal, a slow rise is followed by a drop in humidity. The corresponding humidity spectrum is presented in Figure 4.8a. Although no r o l l - o f f can be observed at the low frequency end the normalized spectral densities level off towards the large scales. The humidity spectra in general are further discussed in 5.1.1. The w'T' covariances are presented in Figure 4.4. The heat transport is dominated by periods of active transfer (lasting for about 30 s to 1 min) separated by longer quiet periods. The active periods e.g. at t = 120, 300, 610, 1140, 2050, 2120 and 3310 s are a l l associated with positive peaks in the w' signal and generally occur when the temperature in a temperature 'structure' is close to i t s maximum value (i.e. warm updrafts). The smaller and slightly longer lasting peaks during the quiet a) I o.« e 0.3 t> 0.3 " 0.1 ? -o.i 5 -0-2 — -O.J b) c) d) o.« 0.4 0 3 0.0 -0.2 0.6 0.4 0.2 0.0 -0.2 e) f) 5 i )ILI,.JJL i i i—•—>—i—•—i—i—i—i—•—•— t • • • • 1 ' I J 1 1 , t t i- 1 • .1 1 1 1——» • • 1 1 i«nn irwi « n n J0Q0 3500 F i g u r e 4 . 3 : T ime s e r i e s t r a c e s (60 min) f o r Run 18 o f q ' (a-c) and the a s s o c i a t e d c o v a r i a n c e s w ' q ' f rom SAT/hygromete r c o m b i n a t i o n s ( d - f ) . c) and f) a r e measured a t the lower l e v e l . LYERC = Lyman-a lpha h y -g r o m e t e r . (The u n i t s o f the c o v a r i a n c e s a re a c o m p o s i t i o n o f the u n i t s o f the c o r r e s p o n d i n g S . D . ) . F i g u r e 4 .4 : Time s e r i e s traces (60 min) for Run 18 of w'T' covariances from SAT (a-c) and K a i j o Denki. (d) . (The u n i t s of the covariances are a composition of the uni ts of the corresponding S . D . ) . 91 periods (e.g. at t = 210, 1920, 2420 and 2830 s), however, are caused by negative w' and T' values, the latter often being associated with the low temperature part of a temperature 'structure' (i.e. cool downdrafts). The w'q' transfer (Figures 4.3d-f) is comparable to the heat transfer and is characterized by a few very active periods with long quiet intervals in between. The transfer is mainly caused by a correlation of positive vertical wind with positive humidity deviation, i.e. moist updrafts (e.g. at t = 600-700, 1140, 2040 and 2710 s). An exception to this is the time period before t = 500 s where negative w' values are associated with negative humidity values, i.e. dry downdrafts result in a net upward humidity transport (e.g. at t = 60, 220, 370 and 3510 s). At these same times the w'T' time series also exhibits small peaks (caused by negative T' correlated with negative w' values). As expected, the u'w' covariance is mainly negative (Figure 4.5a) and again the stress transport occurs in discrete, burst-like active periods. During the quiet periods the momentum transfer does not have a preferred direction. The negative covariance at t = 290 s is caused by an updraft (i.e positive w' associated with negative u') whereas at t = 2280 s, for instance, the reverse process results in a negative covariance. The mainly negative correlations between u' and T' (Figure 4.5b) usually result from negative u' values associated with positive T' deviations (e.g. at t = 290, 560 and 2620 s). Such a combination often occurs in thermally induced updrafts which explains why the u'T' time trace in some places looks like the mirror image of the w'T' signal. a) b) 2500 3000 c) a o.s >. 0.4 2 0.2 2 o.i V 0.0 o 0.6 S 0.5 N 0.* N 0.3 " 0.2 «*" °-' V 0.0 H -0.1 -I I I 3500 d) 2000 2500 r-v>.i. -J I l_ e) ~ 1.0 2 o-8 a 0.6 fM ~ 0.4 w 0.2 "V 0.0 t- -0.2 JJUJ 2500 1 • • • •/•Vin, J • i i i i i 1500 2000 Time in s Figure 4.5: Time series traces (60 min) of u'w' (a), u'T' (b) (both from Kaijo Denki) and T'q' from SAT/hygrometer combinations (c-e). e) is measured at the lower level. (The units of the covariances are a composition of the units of the corresponding S.D.). 93 Figure 4.5c-e shows the T'q' covariance time series which is characterized by frequent very discrete positive peaks which a l l result from a correlation of positive temperature with positive humidity deviations (e.g. at t = 1130, 2060, 2570 and 3120 s). The Tq correlation coefficient (eq. 1.55) is 0.60 which is higher than any other correlation coefficient from this run which are 0.56, 0.45, -0.26 and -0.25 for wT, wq, uT and uw, respectively. 4.2.2 Run 17 (cloudy skies) The time series of the three velocity components shown in Figures 4.6a-c are very similar to their counterparts from Run 18 (Figure 4.1). The only difference is the slightly larger magnitudes of the w and u fluctuations resulting in larger variances for these variables. The temperature signal (Figure 4.6d) is also similar to the one in Run 18 (Figure 4.2) and is again dominated by the previously described 'structures', which in this case last from 2 to 5 min (e.g. at t = 740, 1290, 1880, 2160, 2740, 2850 and 3080 s). On the other hand the humidity signal shown in Figure 4.6e is different from the one in Run 18 (Figures 4.3a-c) which was similar to i t s corresponding temperature signal. In Run 17 the structure of the fluctuations is dominated by a few very strong negative deviations of up _3 to 1.7 g m lasting between 15 s and about 1 minute. Apart from these 'pockets' of dry air (e.g. at t = 980, 1170, 1280, 1380, 1680-1780, 2110, 2290 and 3300 s) the remaining fluctuations are relatively weak. A more detailed discussion of the humidity and the associated moisture flux is Figure 4.6: Time series traces (60 min) for Run 17 of w' from SAT (a), v' (from Kaijo Denki) (b), u' from Kaijo Denki (c), T' from SAT (d) and q' from Lyman-alpha hygrometer (e) . (The units of the co-variances are a composition of the units of the corresponding S.D.). 95 given below. The humidity spectrum for this run (Figure 4.8b) i s , unlike in Run 18, characterized by increasing spectral densities towards the low frequency end, which indicates the considerable amount of variance contained at large scales. The large peaks visible in the w'T' trace at t = 220, 2030, 2620 and 3200 s (Figure 4.7a) are, like in Run 18, caused by positive w' and T' values, the latter generally associated with the 'peaks' in the temperature 'structures'. The quiet periods between the active ones are characterized by a large number of small, predominately positive, fluxes which often result from a combination of negative w' and T' values (e.g. at t = 1090, 1300 and 1900 s) which a l l correspond to times when the temperature i s lowest in the temperature 'structures'. The w'q' covariance signal (Figure 4.7b) is characterized by a few regions with increased activity (e.g. at t = 40 - 250, 900 - 1200, 1300, 1700, 1750 and 2500 - 2730 s). The positive peaks at t = 220, 1100, 1170, 1300, 1700, 1750, 2110 and 2290 s are a l l usually very well defined and last for about 30 s to 1 min. The flux at these times results from a correlation of negative w' values with the sharp negative humidity deviations observed earlier (dry downdrafts). The dry downdrafts are often associated with cooler air which also results in a positive w'T' covariance (as noted above). Some of the flux during the quiet periods i s transported by humid updrafts (e.g at t = 100 - 260 s or between 2500 -3000 s). The u'w' trace in Figure 4.7c is dominated by frequent, strong and a) b) c) d) e) 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 3 " ° vo £ 0.5 0.0 - -0.5 * -1.0 2 0 — -i > -2 3 -3 -4 -2 S i » -I -2 - 3 500 1000 1500 2000 2500 3000 3500 J I i i i i i I i i i i i _ -I I I L. 25O0 •i«/j( ii_Ji t-WI Vi til t •i.^Jf^i I I . . . L J J 1 . J T 1500 2000 Time in s 2500 3500 Figure 4.7: Time series traces (60 min) for Run 17 of w'T' from SAT (a), w'q' from SAT/Lyman-alpha hygrometer combination (b), u'V from Kaijo Denki (c) , u' T' from Kaijo Denki (d) and T'q' from SAT/ Lyman-alpha hygrometer combination (e). (The units of the covariances are a composition of the units of the corresponding S.D.). 97 F i g u r e 4.8: Normalized humidity spectrum f o r Run 18 (a) and Run 17 vs. f on a l o g - l o g p l o t . 98 well defined negative covariances. Again, both positive w' associated with negative u' and vice versa contribute to the negative u'w' covariances. As in Run 18 the u'T' signal (Figure 4.7d) mirrors the w'T' one (e.g. at t = 870, 2610, 2710 and 3190 s) but to a lesser extent. The T'q' time series (Figure 4.7e) is not as spikey as the one observed in Run 18 and a lot of the covariance is contained in bursts of 30 s to 1 min length. The positive peaks at t = 850, 1180, 1300, 1710, 1750 and 2300 s are caused by a correlation of negative q' with negative T' values whereas the opposite is true for the peaks observed at t = 210, 2010, 2610 and 3190 s. The correlation coefficients for Tq, wT, wq, uT and uw are 0.38, 0.56, 0.32, -0.39 and -0.40, respectively. The most notable changes compared to Run 18 are in the correlation coefficients for Tq and wq which are lower, and uT and uw which are higher, in this run. 4 . 3 D i s c u s s i o n The foregoing presentation of the two case studies draws attention to two interesting features. Fir s t l y , the analysis of the temperature traces reveals that the temperature signal near the surface is characterized by very particular ramp-like structures which last from 2 to 5 min. This is a time scale which is only slightly less than typical convective boundary layer time scales found at the present study site. This suggests that the temperature behaviour may be influenced by PBL scale processes and points to the poss i b i l i t y of a strong coupling of the surface and mixed layers (layer between surface layer and z ). 99 Secondly, differences occur in the behaviour of the humidity signal and the associated moisture flux from Run 18 (clear) to Run 17 (cloudy). (Note that exactly the same behaviour was measured by both the Lyman-alpha and the Krypton hygrometers at both the upper and lower level). In Run 18 most of the moisture flux results from a correlation of positive humidity fluctuations with positive w' and therefore corresponds to the textbook case where the evaporative flux i s driven from the surface as the source of moisture and the temperature and humidity signals are similar. In such cases the turbulence s t a t i s t i c s w i l l indicate large correlation coefficients for Tq and wq. A large part of the humidity flux in Run 17, however, is due to the negative humidity fluctuations in association with negative vertical winds. Furthermore, a l l of the dry air pockets in Figure 4.6e are also regions of lower temperatures as can be seen in Figure 4.6d (at t = 710, 850, 980, 1090, 1160, 1280, 1710, 1760, 2110, 2290, and 3300 s). It follows that a large portion of the positive ('upward') humidity flux in Run 17 is caused by dry, cool downdrafts. The dry humidity pockets in association with the negative w values indicate an import of dry air from the mixed layer above. The need to consider the role of the entire PBL on the humidity exchange at the surface (and for that matter of energy and momentum as well) was stressed by e.g. deBruin (1983) and McNaughton and Spriggs (1986) in the context of regional evapotranspiration modelling. This is particularly true in the urban case where the high roughness of the urban environment results in larger turbulence intensities and increased vertical mixing which are 100 both conducive to a strong coupling of the surface layer with the mixed layer. The PBL i t s e l f is modified by regional advective effects and the air above the PBL is affected by synoptic influences. To quantify possible advective effects and the degree of coupling between the surface and mixed layers, McNaughton and Jarvis (1983) develop a parameter (fi) which gives the appropriate weighting to the radiation and advective component of the Penman-Monteith evapotranspiration model: Q = 1 + s + K (4.1) where r and r are the canopy and aerodynamic (in the present study c a taken from ( Z q + d) to the instrument height) resistances, respectively. McNaughton and Jarvis suggest values of 0.2 for forests (aerodynamically rough) and 0.8 for grassland. Using the logarithmic wind profile yields r = 20 s m for Run 18 (15 s m for Run 17). Alternatively, the a semi-empirical aerodynamic expression of Thorn and Oliver (1977) gives r = 25 s m"1 (21 s m *). Both of these approaches to derive r are only valid in the homogeneous surface layer, a requirement which may not be met at the present measurement levels. Nevertheless i t is f e l t that these values are a good f i r s t approximation. Following deBruin and Holtslag (1982), r = 208 s m"1 (166 s m"1) which yields Q = 0.25 (0.26). This c result, together with Cleugh and Oke (1986) and Cleugh (1990) who compute fi = 0.44 and 0.3, respectively at the same site support the idea of a strong copuling between the surface and mixed layers over the 101 aerodynamically rough suburban surface. No boundary layer measurements were performed for the present thesis, however, a number of other studies demonstrated the coupling between the surface and the mixed layer in the urban case. Hildebrand and Ackermann (1984) measured moisture flux profiles over St. Louis, MO in summer. They observed the fluxes to increase strongly with height. Further, they point out that the enhanced urban vertical turbulence intensities extend through the urban boundary layer, resulting in stronger entrainment at the urban inversion. This in turn causes enhanced vertical fluxes at the inversion which can again affect the processes near the surface. Cleugh (1990) reported on measurements performed at the same site used in the present study. She concludes that the latent heat flux at the surface i s not just a factor of the available energy but also depends on the moisture status of the suburban canopy and the atmospheric humidity above the surface layer. Her analysis shows that the vapour pressure d e f i c i t (vpd) of the PBL contributes to the day-to-day variation observed in the flux partitioning (Bowen ratio). In particular meso-scale processes such as the sea-breeze and synoptic-scale situations are referred to as having an influence on the vpd of the PBL. In light of her results Cleugh suggests a classification scheme for Bowen ratios based on wind direction and vpd. The Bowen ratios for Run 18 and 17 are 2.1 and 1.3 and the vpds are 0.79 and 1.43 kPa, respectively. Run 18 f i t s Class I of Cleugh's classification scheme which is characterized by anticyclonic, westerly flow-dominated situations with a Bowen ratio between 1 and 2.5 and moderately high vpds. None of Cleugh's other three classes can 102 accomodate Run 17. The two classes which in terms of the wind direction and synoptic conditions would qualify for run 17 are both associated with relatively large Bowen ratios and suppressed vpds, unlike those observed in Run 17. It should be noted that Cleugh*s (1990) classification i s for mean daylight-hours Bowen ratios and i t is therefore possible that two individual runs as presented above may not f a l l into any or the wrong category. The two examples presented, however, were usually representative for the atmospheric conditions of the entire day. The dry air pockets were dominant in the runs observed on YD 186, 187, 193, and 196 whereas YD 188, 192 and 194 could be characterized by Run 18. Both types were observed on YD 195. Reference to Table 3.2 suggests a dependence of the nature of the humidity transport on cloud conditions. The dry air pockets occur mainly under partially cloudy conditions whereas the Run 18-types are associated with clear days. The exception is YD 186 which, although clear, has a high occurrence of cases characterized by Run 17. Also note that during YD 188, which has an unbroken stratus-type cloud cover, no humidity pockets could be observed. A dependence of the moisture structure on cloud cover was observed by Hildebrand and Ackermann (1984) in their St. Louis aircraft study. They measured stronger moisture flux divergence under partly cloudy skies compared to the clear case. A possible physical explanation for the high occurrence of dry downdrafts under partly cloudy conditions is given by Nicholls (1985) who finds that the release of latent heat in clouds leads to large vertical velocities within the clouds which result in large water vapour fluxes which are compensated by increased downward transport 103 of dry air. Boundary layer moisture structure and vertical humidity divergences have been studied by Mahrt (1976, 1991). Based on Mahrt (1991) the boundary layer can be classified according to two prototypical moisture regimes (with probably numerous exceptions as Mahrt points out): Type 1) The moistening boundary layer corresponding to vertical convergence of the moisture flux which is associated with positive moisture skewness and large positive correlations between moisture and temperature and moisture and vertical velocity. This type tends to be characterized by relatively low Bowen ratios. Type 2) The entrainment drying boundary layer which i s associated with vertical divergence of the moisture flux and negative moisture skewness in association with significant entrainment of dry air at the boundary layer top and relatively high Bowen ratios at the surface. In the Type 2 entrainment boundary layer, dry air from the upper part of the boundary layer occasionally reaches the surface (this would particularly be the case over the rough suburban surface because of the strong coupling between the surface and mixed layers) resulting in negative moisture skewness and associated lower Tq and wq correlations. Mahrt also points out that the dry downdrafts reaching the warm moist lower part of the boundary layer w i l l be significantly drier but not warmer (as observed in this study) than the surrounding warm and relatively moist updrafts. 104 Some of the characteristics observed in the two case studies presented above suggest that Run 18 corresponds to a Type 1 and Run 17 to a Type 2 boundary layer. The behaviour of the observed humidity fluctuations for Run 17 in conjunction with the low Tq and wq correlation coefficients f i t s the suggested model of a Type 2 boundary layer quite well. Visual inspection of Figure 4.6e also suggests a negatively skewed absolute humidity (the skewness was not computed in the present study) which results when the strongest moisture fluctuations correspond to dry events. In the present study the humidity signal is dominated by occasional pockets of especially dry air. According to the Bowen ratio Run 17 should be associated with Type 1 and Run 18 with Type 2. However, the Type 2 boundary layer in Mahrt's classification typically occurs under calm, sunny and dry conditions with weak surface evapotranspiration which therefore results in an energy partitioning at the surface which favours the sensible over the latent heat flux. In conclusion i t appears that the moisture transport during the present observation period in particular under cloudy skies was, apart from the surface boundary conditions, influenced by the entire boundary layer. It is shown that under these conditions the temperature and humidity signals do not behave similarly. The two runs presented above neither f i t the Cleugh (1990) nor the Mahrt (1991) clas s i f i c a t i o n schemes completely. Run 17 (cloudy skies) in particular exhibits features the two classifications do not account for. A suggested mechanism for the observations of Run 17 could be as follows: Because of the strong coupling of the surface and mixed layers over the rough suburban surface strong entrainment of dry air, which is enhanced by the cloud effect 105 described in Nicholls (1985), occurs at the top of the PBL. The dry downdrafts easily reach the surface and contribute to a positive latent heat flux at the surface (negative w' correlated with negative q'). The imported dry air also results in an increased vpd which tends to enhance the latent heat flux at the surface therefore keeping the Bowen ratio relatively low. This last mechanism may not always occur because, as Cleugh (1990) points out, an increase in the vpd is not necessarily associated with an increase in the latent heat flux (decrease in Bowen ratio) because the transpiring surfaces may respond with increased stomatal resistances. It should be noted that the dry humidity downdrafts do not necessarily have to be related to entrainment of dry air at the top of the PBL. Assuming lapse conditions near the surface, any air imported from above (e.g. by organized structures) would be dryer and cooler. The results in this chapter are mainly of qualitative nature. A more thorough analysis which would result in a more appropriate comparison of the present results with the two classification schemes mentioned above would, however, require appropriate PBL layer data. The humidity observations presented here should be looked at as an unexpected discovery and i n i t i a l l y this thesis did not set out to explore the relationships between fluxes at the surface and the structure of the PBL. 106 CHAPTER 5: SPECTRAL CHARACTERISTICS This chapter presents the s p e c t r a l r e s u l t s from the o b s e r v a t i o n a l programme. The f i r s t S e c t i o n contains the (co)spectra normalized by t h e i r r e s p e c t i v e (co)variances. The second presents the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s , coherence and phase angle spectra, S e c t i o n three looks at the s t a b i l i t y dependence of the ( c o ) s p e c t r a l r e s u l t s presented w i t h i n the MOS framework and S e c t i o n four contains a summary and d i s c u s s i o n . The t h e o r e t i c a l background f o r the n o r m a l i z a t i o n used i n t h i s chapter i s giv e n i n 1.3.2. 5.1 Normalized with (co)variance Composite (co)spectra normalized w i t h t h e i r corresponding (co)variances and p l o t t e d against the non-dimensional frequency f on l o g s c a l e s are presented i n the f o l l o w i n g s e c t i o n . Composite ( c o ) s p e c t r a are the average of a l l i n d i v i d u a l (co)spectra of a p a r t i c u l a r v a r i a b l e (or combination of two v a r i a b l e s ) . Averaging has been performed over p r e v i o u s l y chosen non-dimensional frequency bands to gi v e e q u a l l y spaced ( i n the log-frequency domain) composite ( c o ) s p e c t r a l d e n s i t i e s and a s s o c i a t e d standard d e v i a t i o n s , cr. As pointed out by Large (1979) the s c a t t e r i n the averaged s p e c t r a l d e n s i t i e s i s not f u r t h e r reduced by averaging over F o u r i e r bands, because t h i s g r e a t l y increases the band-width, which should be kept as narrow as p o s s i b l e i n order to keep the averages r e p r e s e n t a t i v e of t h e i r frequencies. This i s e s p e c i a l l y true at lower frequencies where there are only a few p o i n t s i n each band. As a consequence cr can be extremely large and not i n d i c a t i v e of the 107 v a r i a b i l i t y of the mean (Large, 1979). Since the single runs used in the 1/2 construction of the composite spectra are independent, cr = cr/(M ) is m taken as an estimation of the standard deviation of the mean, where M is the number of runs. This assumes that the statistics behave in a Gaussian fashion. This condition should be approached with a large number of runs and i f NP, the number of points in a band, is much larger than M or even as NP approaches M. When NP becomes less than M, each point comes from a 1/2 different run and cr = cr/(NP ) is assumed (Large, 1979). In the m following figures the vertical bars indicate plus and minus one standard deviation. To maintain the readability of the figures and since the standard deviations did not vary from one sensor to the other, cr values m are only plotted for one of the signals. The s t a b i l i t i e s encountered during the measurements range from z'/L^ = -1.80 to -0.05 with a mean of -0.62 at the upper level and -0.40 at the lower level. There is some sta b i l i t y dependence in the (co)spectra but no attempt was made to classify them according to stability. The effect of atmospheric str a t i f i c a t i o n on the observed (co)spectral characteristics w i l l be investigated in Section 5.3. Where available the results from the present study w i l l be compared to observations taken at the same site in 1986 under unstable conditions (mean z'/L = -0.75) (Roth et al., 1989) and rural reference results obtained by Anderson and Verma (1985) at a height of z' = 1.74 m over a 0.75 m high soybean crop. Although not from completely 'ideal' surface conditions the Anderson and Verma data were chosen as a reference because i t is one of the few studies available which presents most of the variables normalized by the respective (co)variances measured in the present study. In the following figures the 108 symbols always denote measurements from the present study and in particular the asterisk symbol (*) refers to the results from the lower level. The solid lines of -2/3 (-4/3) slope indicate the proportionality —5/3 —7/3 of the (co)spectral densities to f (f ) according to the in e r t i a l subrange law (Ch. 1.3.2). It should be noted that in computing f at the lower level the mean wind speed measured with the three-dimensional Kaijo Denki anemometer at the upper level was used. Considering the decrease in wind speed as one approaches the surface the 'true' f value at the lower level would therefore be slightly higher than that computed. This should result in a minor shift of the (co)spectra towards lower frequencies compared to the 'true' position. However, analysis of cup anemometer data from both levels revealed that the lower level wind speeds were usually only sli g h t l y lower and sometimes there was no difference at a l l . (The cup anemometer data were not used in the normalizations because they were too unreliable. Comparison of cup anemometer observations with the three-dimensional Kaijo Denki anemometer at the upper level showed a consistent but also variable cup anemometer overspeeding). Since the f r i c t i o n velocity from the upper level was used in the derivation of z'/L at the lower level (u t was not measured at the lower level) and u f has been observed to increase with height in the urban roughness sub-layer (Rotach, 1990), (there is some evidence that the present sensor levels were below z*; see below) the use of the upper level f r i c t i o n velocity would result in z'/L values which are too small at the lower v level compared to their 'true' value. 109 5.1.1 Spectra Vertical wind The composite w spectra from a l l sensors are presented and compared against those from other studies in Figure 5.1. Intercomparison between the results from the 4 different sensors is excellent, the only differences occurring at the high frequency end. The high frequency r o l l - o f f for the Kaijo Denki (KD) signal is faster than the other sensors at the upper level. Mitsuta (1966) shows that the 90% cut-off frequency is defined by n = 0.26U/d . This results in a 10% down non-dimensional frequency f = 0.26z'/di. The reduction in the frequency response of the KD sensor can therefore be attributed to i t s larger sensor spacing (0.2 m compared to 0.1 m for the SAT). The faster r o l l - o f f at the high frequency end i s also observed in the SAT (1126) signal measured at the lower level, but obviously this cannot be explained through such instrumental effects. The lower height can in part account for the faster high frequency r o l l - o f f occurring at lower frequencies, however, close inspection of Figure 5.1 shows that lower spectral densities can already be observed at f as low as one. As w i l l be shown below this effect is found in a l l (co)spectra and is usually more pronounced than observed in the w component. Agreement between the present results and both those of the 1986 study and a spectral model developed by Hojstrup (1981) is very good. The spectral model has the form: n S (f)/u 2 = [32f/(l+17f ) 5 / 3] (-z'/L ) 2 / 3 + 2f/(l+5. 3 f 5 / 3 ) (5.1) W * V 110 F i g u r e 5 .1 : Normalized composite spectra of w vs f on l o g - l o g p l o t ; t h i s study (symbols) compared with 1986 r e s u l t s (dashed l i n e ) and a model developed by H a j s t r u p , 1981 ( s o l i d l i n e ) . V e r t i c a l l i n e s are +/- 1 cr . I l l 2 where can be replaced by the variance using an expression for the normalized vertical velocity variance (Panofsky et al. , 1977): (cr Au 2) = 1.5 + 2.9(-z'/L ) 2 / 3 (5.2) W V The model is based on the Minnesota results (Kaimal, 1978) which constitutes the rural reference for this variable. The only two differences observed between the present data and the rural results are: 1) sli g h t l y more low frequency energy in the present data with an associated shift of the peak towards lower frequencies (f = 0.2; the m associated wavelength A is derived from f = z'/A -» A = 5z') and 2) m m m m s l i g h t l y lower values at the high frequencies with a faster high frequency r o l l - o f f , reflecting the sensor response limitations. The agreement at the low frequency end between the two levels is good. The spectral densities at the low frequencies are associated with slightly larger standard deviations. This is partly due to variation in s t a b i l i t y between individual runs, but also to the reduced degree of freedom in the computation of the spectra. The same can be observed in a l l (co)spectra presented in the following. The -2/3 slope is followed in the region of the i n e r t i a l subrange, more so for the upper than the lower level sensor. Horizontal wind The spectra of the horizontal wind components are shown in Figure 5.2. Compared to the vertical velocity both horizontal components contain much more low frequency energy. Agreement between the u component composite spectrum from the present study and the results from 1986 is good (Figure 5.2a). Compared to Anderson and Verma (1985) (for neutral conditions) the present results r o l l - o f f faster at the low frequency end 112 a) 10° 10-N3 to 10" 10" - * I Anderson and Verma, 1985 (neutral) - - 1986 study O u-KD (z' = 18.9 m) • i t t i i 111 t i t i i i 111 i i i i 1111 • t i i i i 111 • i i i i i 111 10" io- 2 10"1 10° / = nz'/U 101 102 b) 10° £ io- 2 a to 10" 10" 5 5 5 l ? - r m as j 1 a •• Anderson and Verma, 1985 (neutral) O v-KD (z' = 18.9 m) _ i i I I I _ i 1 i i i 111 • 1 t I I H I I I I I tilt 10" 10" 10"' 10° / = nz'/U 10' 102 Figure 5.2: Normalized composite spectra of u (a) and v (b) vs f on a log-log plot; this study (symbols) compared with Anderson and Verma, 1985 (dotted line) and the 1986 results (dashed line). Vertical lines are +/-1 cr . m 113 and are higher at high frequencies, however, s t i l l follow the -2/3 slope across a large frequency range. The v component in Figure 5.2b shows more low frequency energy when compared to Anderson and Verma, however, i t is in agreement with the results of Steyn (1982) from the same site as the present study and McBean (1971), from a study performed over short grass. Kaimal (1978) points out that the high frequency end of the horizontal wind components obeys MOS whereas the low frequencies scale with mixed layer variables (e.g. z^). The transition region between the two regimes is marked by a point of inflexion as is evident in the present results for both components (more prominent for v) at f = 0.1. The -2/3 slope in the v component is not reached until a higher non-dimensional frequency compared to u. The peak frequencies for u and v are about 0.021 (A = m 48z') and 0.013 (A = 77z'), respectively. m Temperature The composite temperature spectra presented in Figure 5.3a follow each other closely but when compared to the 1986 and Anderson and Verma studies exhibit slightly lower values at the low frequency end and slig h t l y higher values at medium and high frequencies. The values from the two SAT systems (1130 and 1127) at the upper level are essentially identical whereas the spectral densities from the KD (output option 2) are lower than the SAT's at the low frequency end and higher at the high frequency end. It should be remembered that the KD temperature measurement is based on the temperature dependence of the velocity of sound. The temperature fluctuations are therefore derived using the same ultrasonic pulse propagation times used in the calculation of the 114 - ^ * s!» * 2 o * _ o ^ • ' ^ m o * O * * _ b • * • * * o o f * I - Anderson and Verma, funstabie,} * T - - - - 1986 study (z' = 19.0 m) * O T-SAT(1130) (z1 = 18.9 m) - x T-SAT(1127) (V = 18.9 m.) _ O T-KD (zl = 18.9 m) * T-SAT(1126) (z- = 11.0 m) • 1 t i i 111 i i " i i 1 i t i i • i | | i i t i 111 i i—i i i i 111 1 0 - J 10-2 1CT1 .10° 101 • 102 / = nz'/U Anderson and Verma, 1985 (neutral) I o q-SAT(1130)/Ly-alpha (z' = 18.9 m) x tj-SATfl 127)/KH1016 (z' = 18.9 m) * q-SAT(1126)/KH1011 (V = 11.0 m) i i ' • t i i i 111 t i t i t i 111 ' • ' i i i 111 i 1—i—i i i 111— 10"3 10-J 10"' 10° 101 10J / = nz'/U 5.3: Same as Figure 5.2 but for T (a) and q (b). 115 v e r t i c a l v e l o c i t y which agrees wel l with the other observat ions (Figure 5 .1 ) . The KD temperature measurements are a f f e c t e d by humidity and h o r i z o n t a l wind f l u c t u a t i o n s . Corresponding c o r r e c t i o n s (based on a procedure by Schotanus et al. , 1983) were a p p l i e d to the i n t e g r a l s t a t i s t i c s r e s u l t s presented l a t e r , but not to each s i n g l e temperature f l u c t u a t i o n va lue . However, i t seems u n l i k e l y that the humidity and h o r i z o n t a l wind e f f e c t s could r e s u l t i n the observed systematic d e v i a t i o n s of the KD high frequency end from the SAT r e s u l t s . The SAT thermocouples which are supposed to have a frequency response of about 30 Hz, d i s p l a y an unexpectedly f a s t r o l l - o f f . T h i s may have been caused by d i r t contamination which was observed on the thermocouples. The r e l a t i v e l y f l a t peak has i t s maximum value at f = 0.04 (A = 25z ' ) which m m i s s l i g h t l y higher than found i n the 1986 study but i n agreement with the value reported by Coppin (1979). When compared to the upper l e v e l the lower l e v e l s p e c t r a l d e n s i t i e s are s l i g h t l y higher at the low frequency end with an associa ted s h i f t i n the peak frequency (f = 0.03, A £ 33 m m z ' ) S i m i l a r to the w component, the T values are c o n s i s t e n t l y lower at the h i g h frequency end with d e v i a t i o n s s t a r t i n g at f = 0.4. As a r e s u l t , only a short segment with a -2/3 slope can be observed i n the i n e r t i a l subrange. Humidity F i g u r e 5.3b presents the composite humidity spec t ra . The observat ions from the two sensors at the upper l e v e l agree very w e l l with each other which i s reassuring since two d i f f e r e n t instruments were used 116 (Lyman-alpha and Krypton hygrometer). The only difference is at the high frequency end where the spectral densities of the Krypton hygrometer increase rapidly. With a Nyquist frequency of 12.5 Hz and a low-pass f i l t e r cut-off frequency of 10 Hz no aliasing back of potential energy contained above the Nyquist frequency is expected. Even after consultation with the manufacturer of the Krypton hygrometer the source of this high frequency energy could not be explained and they were unaware of any potential electronic problem in their sensor which could result in high frequency contamination (B. Tanner, Campbell Scientific, 1990; personal communication). The Lyman-alpha sensor also shows an increase in high frequency energy but to a lesser extent. Apart from one individual spectrum based on 45 min of data presented by Coppin (1979) these are the f i r s t humidity spectra measured in a suburban atmosphere. Unlike in the present results Coppin observed a -2/3 slope at the high frequency end. The results from the lower level Krypton hygrometer correspond very well with the upper level. The only minor differences are the slightly lower spectral densities at around f = 0.05 and the consistently lower values at high frequencies. The -2/3 slope is not reached until about f = 2 at the upper level and maintained only over a short range (especially for the Krypton measurements) because of the high frequency 'contamination'. No statement regarding the onset of a -2/3 slope can be made at the lower level because of the high frequency 'contamination'. The high frequency behaviour observed in the present study is different from other studies. For example Elagina (1969), Smedman-Hogstrom (1973) and Ohtaki (1985) observe the -2/3 slope from about f = 0.3, Phelps and 117 Pond (1971) measure a -2/3 slope in their BOMEX data over sea from f = 0.6 and Anderson and Verma (1985) over crops at f = 1.3 (see curve in Figure 5.3b). The behaviour of the low frequency end of the humidity spectrum is not well established in the literature. Obviously the results from this study deviate from those of Anderson and Verma (Figure 5.3b) which, however, are from neutral conditions. The observations by Hogstrom and Smedman-Hdgstrom (1974) show a point of inflexion at f = 0.1 and a broad peak at around f = 0.02 associated with a lot of scatter at the low frequency end, a feature evident in a l l observed humidity spectra. Ohtaki (1985) measures a peak at f = 0.08. McBean (1971) notes that his humidity spectra do not have well defined maxima, nevertheless there is an indication of a slight r o l l - o f f at the low frequency end. The results from the present study resemble most the humidity measurements by Phelps and Pond (1971) over sea and the Minnesota results from unstable conditions analysed by Schmitt et al. (1979). In agreement with the present study these workers do not observe a low frequency r o l l - o f f . The influence of the 'spikes' (dry air pockets) observed in the humidity time series in Figure 4.6e (and evident in other time series) on the power spectrum is d i f f i c u l t to assess. Let us assume that a spike can be approximated by a Delta function whose Fourier transform is a straight horizontal line. This would introduce the same amount of energy at a l l frequencies ('white noise'). The energy content of each spike would thererfore be distributed over the entire frequency range and the effect on the power spectrum would be minimal. If a series of such 'spikes' is 118 present the argument i s more complicated but with e s s e n t i a l l y the same r e s u l t . Inspect ion of Figure 4.6e shows that a l o t of energy i s contained at low harmonics (or long ' o s c i l l a t i o n ' ) . With the exceptions of very unstable cases s i m i l a r low frequency components were observed i n most humidity time s e r i e s regardless of time of day, c loud c o n d i t i o n s , wind speed, wind d i r e c t i o n or wind d i r e c t i o n f l u c t u a t i o n s . These long ' o s c i l l a t i o n s ' are probably the main cause of the large energy content observed at the low frequency end. This i s exempl i f ied i n F i g u r e 4.8 which shows the normalized humidity spectra f o r the two case s t u d i e s presented i n Chapter 4. Compared to Run 18, Run 17 e x h i b i t s more energy at large s c a l e s . 5.1.2 Cospectra Momentum and h o r i z o n t a l s e n s i b l e heat The momentum f l u x cospectrum shown i n Figure 5.4a g e n e r a l l y f o l l o w s the o v e r a l l shape of the Anderson and Verma observat ions from n e u t r a l c o n d i t i o n s . The increased energy observed i n the present study at the low frequencies may be due to the d i f f e r e n t s t a b i l i t y c o n d i t i o n s encountered i n the present study. The peak frequency of the r e l a t i v e l y f l a t peak r e g i o n can be found at f = 0.03 (A = 33z') which compares w e l l wi th the m m observat ions of Coppin (1979) but i s s l i g h t l y lower than observed i n the reference curve and also as reported by Pond et al. (1971) (from BOMEX; s l i g h t l y unstable) and McBean and Miyake (1972) (over short grass ; u n s t a b l e ) . The slope of the r o l l - o f f at the high frequency end i s not s t r a i g h t which makes i t d i f f i c u l t to determine whether i t conforms to a 119 10" I o I I O " 2 I O " 3 10" .1' * ' ' ••I / X ' 10- 10"2 Anderson and Verma, 1985 (neutral) - - 1986 study (V = 22 0 m) O uw-KD (zl = 18.9 m) • • i i i i 1 1 1 i I I i • 1 1 1 1 i i i i i i 1 1 1 i i i i i i 1 1 1 1 — i — i t i > & i 10"' 10° / = nz'/U 10' 10° b) 10" ^ i o - 2 3 10" 10" I I I x uT-KD (z' = 18.9 m) I I I I I I I I I I t I I I I I I I I I I I I I I I I i I I I I I I I t 10"3 I O " 2 10"' 10° / = nz/U 10' 102 Figure 5.4: Same as Figure 5.2 but for uw (a) and uT (b). 120 -4/3 slope. At around f = 0.5 (X = 2z') lower energy densities are observed. This is similar to the 1986 results which, however, are from a limited data set only. The uT cospectrum in Figure 5.4b looks very similar to that of uw with a peak at around f = 0.03 {X = 33z'). A -4/3 slope is reached at m m about f = 2 but similar to the uw cospectrum the slope at the high frequency end is marked by a lot of variability, the last points being negative. The uT cospectra compares well with that of Kaimal et a l . (1972) who, however, observe a -3/2 slope at the high frequency end which, as they point out, cannot be justified with dimensional arguments. The -4/3 line in Figure 5.4b is intended to provide a reference slope only (but f i t s the present data well) because the theoretical prediction of Wyngaard and Cote (1972) would be -2. Sensible heat The heat flux cospectra presented in Figure 5.5a agree very well with the 1986 results and the observations by Coppin (1979). The results from the two SAT systems (1130 and 1127) at the upper level are identical whereas the KD observations from the same level experience a faster r o l l - o f f at the high frequency end which is probably due to the response deficiencies of the KD observed in the w measurements (Figure 5.1). The heat flux cospectrum measured at the lower level (1126) agrees very well with the upper level results at the lower frequencies, however, i t again exhibits consistently lower spectral densities at the middle and high frequencies (from f = 0.4). Comparison with the findings of Anderson and 121 a ) io° 10-' I 3 10-3 io - I I I I 111 Anderson and Verma, 1985 (unstable) - - 1986 study (z' = 19.0 m) O wT-SAT(1130) (z' = 18.9 m) x wT-SAT(1127) (z' = 18.9 m) O wT-KD (z' = 18.9 m) * wT-SAT(1126) (V = 11.0 m) 1 i i i i 111 i i i ' i i i 11 i i i i i i 111 • * O * $ d o'o 10" b) 10° 10" 10" 10° 10' nz'/U 10* 10" 'I i o - J * I » J 10"3 : O x * Anderson and Verma, 1985 (neutral) u>q-SAT(1130)/Ly-alpha (z' = 18.9 m) wq-SAT(1127)/KH1016 (z' = 18.9 m) wq-SAT(1126)/KH1011 (z' = 11.0 m) 10" ' n ' 1 • • • • • • • 10- 10" 10"' 10° / = nz'/U 10' 10* Figure 5.5: Same as Figure 5.2 but for wT (a) and wq (b). 122 Verma (Figure 5.5a) and McBean and Miyake (1972) is good apart from slightly more energy observed at lower frequencies in the present study and an associated shift of the peak (f = 0 . 0 4 ; A = 25z') towards the m m low end. A -4/3 slope is evident for both the lower and upper level measurements. At the high frequency end i t s e l f the spectral densities r o l l off faster due to mainly sensor response limitations. This is a feature observed in a l l cospectra. The estimates at the highest frequencies are very close to zero or negative. Moisture The moisture flux cospectra in Figure 5.5b closely resemble the heat flux results. Similar to wT, the observations from the upper level (Lyman-alpha and Krypton hygrometers) are almost identical. The lower level measurements are again similar to the upper results at the low frequency end and exhibit lower values (from f = 0.3) at the higher frequencies. The relatively organized low frequency r o l l - o f f observed in the humidity cospectrum is striking, bearing in mind that the humidity spectrum i t s e l f did not show a r o l l - o f f at a l l (Figure 5.3b). This reflects the fact that the cospectra is a combination of two variables, w and q, and as shown in Figure 5.1 a pronounced low frequency r o l l - o f f can be observed in the w spectrum. In addition, the wq spectral correlation coefficients are low at large scales (Figure 5.8b). Compared to the wT cospectrum the moisture flux exhibits more va r i a b i l i t y at lower frequencies. The agreement with the results of Anderson and Verma is f a i r (Figure 5.5b) but the increased cospectral densities observed at low frequencies in the present study may be caused by a difference in 123 s t a b i l i t y conditions between the two studies (theirs being for neutral conditions). Correspondence with the unstable rural results of McBean and Miyake (1972) is good. Schmitt et al. (1979) observe a broad peak region at 0.02 < f < 0.1 in the unstable Minnesota data. The peak frequency in the present observations can be found at around f = 0.03 (A = 33z') and m m a -4/3 slope is followed for a short range in the i n e r t i a l subrange (f = 4), but the cospectral densities show some high frequency varia b i l i t y . The f i r s t point at the low frequency end of the upper level results was negative (but plotted as a very small positive value), indicating the high occurrence of negative cospectral estimates at the low frequencies in the individual moisture flux cospectra. This i s the f i r s t wq cospectrum measured in a suburban atmosphere. The good agreement with observations from the homogeneous surface layer in respect to the overall shape and the location of the peak indicates a promising degree of similarity (of energy distribution with respect to frequency) between the two different environments and raises confidence in the use of the eddy correlation method to measure the latent heat flux. Temperature - moisture The Tq composite cospectra (Figure 5.6) exhibit a small r o l l - o f f at the low frequency end and a progressively steeper r o l l - o f f towards the high end. Intercomparison between the sensors mounted at the upper level is again excellent and the observations at the lower level display the now familiar lower densities and faster r o l l - o f f at the higher 124 10° 10" o 10-2 • I -2/3 10" O Tq-SAT(1130)/Ly-alpha (V •= 18.9 m) x Tq-SAT(1127)/KH1016 (V = 18.9 m) * Tq-SAT(1126)/KH1011 fz' = 11.0 m) 10" • t i i 111 i i i i i i 111 i i t i i i 111 I I i i i i 111 i V. 4 '«U ' M i o - 10" 10"1 10° / = nz'/U 10' 102 F i g u r e 5 .6 : Normalized composite spectra of Tq vs f on l o g - l o g p l o t from the present study (symbols) . V e r t i c a l l i n e s are +/- 1 cr . 125 frequencies (from f = 0.4). The f l a t peak region is marked by a maximum at f = 0.04 (A = 25z'). The peak at the lower level is at f = 0.03 (A m m m m = 33z') Wyngaard et al. (1978) predict a -2/3 slope for locally isotropic turbulence and the assumption of a constant spectral correlation coefficient in the locally isotropic region. The measurements reported in McBean and E l l i o t t , 1981 (5.8 m above almost ideal terrain) trend towards a -2/3 slope for f = 0.3 but decrease much more rapidly afterwards. A -2/3 slope can be observed in the present study at 0.7 < f < 2 followed by a much steeper slope at higher frequencies. Tq values at the low and high frequency end are observed to have occasional negative values. Medeiros Filho et al. (1988) report observations performed at the top of a 50 m high building in central London. They find a negative Tq correlation at scales characteristic of the inertial subrange (with a -2/3 slope for 0.1 < n < 9) which they attribute to local effects. 5.2 Spectral correlation coefficients, coherence and phase angle spectra The mathematical definitions of the spectral s t a t i s t i c s presented in this section are given in 1.3.3. The normalized cospectra indicate which scales are important in contributing to the transfers but the correlation coefficients as a function of frequency are more useful in investigating how these transfers take place. With l i t t l e net transfer R (f) w i l l be i j small but w i l l reach unity when there is optimally efficient turbulent transfer. For these reasons the term 'transfer efficiency' has been associated with the spectral correlation coefficient (e.g. McBean, 1973). The s t a b i l i t y dependence of the spectral correlation coefficient w i l l be discussed in Section 5.3. The coherence indicates i f two time series have 126 a similar structure at a certain frequency without regard for the presence of a phase shift. The coherence is closely related to the spectral correlation coefficient. The phase angle spectrum indicates the phase shift between two variables at each frequency. In the following the results for the uw, uT, wT, wq and Tq transfers are presented in Figures 5.7 and 5.8. Figure 5.7 is constructed as follows: The f i r s t column contains the composite spectral correlation coefficients for uw (top), wT (middle) and uT (bottom) measured with the Kaijo Denki. The second column presents the composite coherence spectra in an identical order and the third column shows the composite phase angle spectra. Construction of Figure 5.8 is identical but for wT, wq and Tq, respectively, measured with the the SAT/hygrometer combinations. The spectral correlation coefficient for uw (R (f)) (note that uw -R (f) is plotted) are small at high frequencies (Figure 5.7a). This is uw a result of instrumental effects and randomization due to the turbulent energy cascade (Phelps and Pond, 1971) and can be observed in a l l transfers. A peak of about 0.65 is reached at f s 0.01 (A = 100z') and m m high values are maintained throughout the low frequency end. Although the correlation coefficients are high at large scales (and have large variability) these do not contribute much to the total transfer because the spectral densities of w, and therefore uw, are relatively small at these frequencies. R (f ) from the present study is larger than observed uw m in reference data; e.g. McBean and Miyake, 1972 measure a peak value of about 0.4 at f = 0.06. The coherence for uw shows the same behaviour as the spectral correlation coefficient and the phase angle is out of phase 1Q- ' I 0 " ! 1 0 " ' 10 ° O KB i 0 - l 1 0 " ' ' 0 C / = TI 2 yu O KB .1 150 100 50 0 - 5 0 - I C O - 1 5 0 2 0 0 1 ' i ' " " " 1 ' ' " *-* , " i e i , " r . « . ; » » » » « » " « * * ' . • ' I T 1 0 _ ] 1 0 " ' I O " 1 10 ° Figure 5.7: Composite composite phase angle spectral correlation coefficients ( l e f t ) , composite coherence spectra (middle) and spectra (right) vs. log f for uw (a), wT (b) and uT (c), a l l using the KD system. 128 by 180 degrees for the entire frequency range up to f = 2. This is reasonable because a negative w is associated with positive u or vice versa. At the very high frequencies the phase angle becomes meaningless because the coherence is very small. Note that at f = 0.06 a 'dip' is observed in the spectral correlation coefficient and coherence spectra. These same frequencies correspond to slightly smaller values in the corresponding cospectra (Figure 5.4a) (the same is observed for uT). The wT correlations (Figure 5.7b) reach a peak of almost 0.8 between f s 0.01 - 0.02 (A = 100 - 50z'), similar to the location of the R (f) m m uw peak, but drop off to either side. As was the case for R (f) the peak is uw reached at a lower frequency compared to the peak in the corresponding cospectrum (Figure 5.5a). These results compare well with the rural results of McBean and Miyake (1972) in regard to the magnitude of the peak and i t s location which they found at f = 0.01. The phase angles are close to zero which is to be expected i f the surface is a source of the sensible heat (positive w associated with positive T). The uT spectral correlation values in Figure 5.7c (plotted as -R (f)) reach a maximum uT value of about 0.7 at very large scales but do not display a well defined peak. The overall shape is very similar to the uw curve as is the uT phase spectrum. The u and T components are out of phase by about 170 to 180 degrees for most of the frequency range. This result i s expected since positive u values are associated with negative T values and vice versa. Figure 5.8a presents the composite spectral correlation coefficients, coherence and phase angle spectra of wT for the three SAT systems. The 129 correspondence with the KD statistics presented in Figure 5.7b is very good, in particular a peak value of about 0.75 is reached at f = 0.02. The phase angles are slightly negative for f < 0.02 and positive for f > 10 (where the coherence drops to 0.1). The coherence values from the present study are higher than the ones observed by Othaki (1985) which show a broad peak of about 0.6 in the frequency range from f = 0.01 - 0.1 and reach about 0.2 at f = 2. The correlation and coherence for wq (Figure 5.8b) is less than for wT at a l l scales indicating a less efficient transfer of moisture. The maximum spectral correlation coefficient is about 0.5 observed at f = m 0.03 (A = 33z') which is also the peak location in the wq cospectra m (Figure 5.5b). McBean and Miyake (1972) observe a peak value of almost 0.6 at a slightly higher frequency of f = 0.07. The coherence observed in the present study is slightly less than measured by Othaki (1985) whose wq results are similar to his wT observations (see above). At the larger scales (f < 0.02) the signals are slightly out of phase by 30 to 40 degrees (similar to wT) which can be expected since T and q are in-phase (Figure 5.8c) and w and T are out of phase by about the same. A constant negative phase of about 10 to 20 degrees is observed between 0.07 < f < 0.3, and at f > 0.2 the phase angles for each sensor combination start to deviate from each other. The Tq spectral correlation coefficients (Figure 5.8c) are relatively high (0.65) for an extended frequency range (0.04 < f < 5) and drop off rapidly and almost symmetrically to either side. The overall shape looks similar to measurements presented by Phelps and Pond (1971). The Tq a) s o . . i r O "so X f 127 # " 2 6 b) o - 3 1, i o - 3 1 0 ° 10 ' 1 0 J O "30 X 1-27 * "16 10 ° c) l i 0.4 O "so X 1127 * UK <o- ! 1 0 " ' 10 ° ' 0 J O S <e3 o.4 O "So X lilt * " 2 « 'f. o.e O " 3 0 X ,,17 * "ie it i 0 ~ ? i 0 " 3 ' O - ' 10 C ' C 1 . ' 0 3 •C 0.* O " 3 0 } f j * " 2 S . i « ! t 10--' ' 0 - ' 1 0 ° / = rxZ'/V 1 0 ' 200 ' 5 0 ' 0 0 50 0 - 5 0 - ' 0 0 - 1 5 0 O "so X " 2 ? * "*« .." i i m m i •e ft. ft. 1 0 200 *50 ' 0 0 5 0 A - 5 0 - 1 0 0 - 1 5 0 - 2 0 0 l 200 150 100 50 0 - 5 0 - ' 0 0 - ' 5 0 I O " 3 1 0 " ' 10 ° 10' ' 0 * O " 3 0 X f 127 * " 2 6 ' " 1 ' • I O " ' 1 0 " ' 1 0 " 10' O "30 X ' ' 2 ' * me ••-••••H^-l -1 0 " ' ' 0 ° / = nf/U Figure 5.8: Same as Figure 5.7 but for wT (a), wq (b) and Tq (c) using the three SAT systems. 131 correlations measured by Medeiros Filho et al. (1988) are around 0.9 for 0.006 < n < 1. An interesting feature is the tendency of the Tq correlation to reverse sign at the lowest frequencies. A positive correlation can be expected i f for instance warm and wet are correlated (convection from the surface) whereas a warm and dry combination would lead to a negative correlation. This latter behaviour was observed in the BOMEX results (McBean, 1973). The T and q signals are essentially in phase for most of the frequency range but behave differently (for each individual sensor combination) for f > 0.03. The phase and correlation coefficient behaviour seem reasonable. If either the surface i s the source for both moisture and heat fluctuations or i f dry air is entrained from above (e.g. Figure 4.6e) resulting in negative moisture fluctuations associated with cooler temperature, an in-phase relationship between temperature and humidity exists. In general, intercomparison between the three sensor combinations used i s good. As noted for the (co)spectral peak locations the maximum values of the spectral correlation coefficients and coherence spectra are found at slightly lower f values at the lower level compared to the upper level. In similarity with the (co)spectral results, where the sensor from the lower level constantly experienced less energy at high frequencies, decreased correlations and coherences can be observed at mid and high frequencies. This is most prominent for the Tq transfer. 5 .3 N o r m a l i z e d w i t h i n t h e Monin-Obukhov s i m i l a r i t y f r amework As outlined in 1.3 the behaviour of (co)spectra of turbulence in the 132 homogeneous surface layer can be described within the framework of similarity theory. With appropriate normalization, the (co)spectra are reduced to a family of curves which spread out according to z'/L at low frequencies but converge to a single universal curve in the ine r t i a l subrange. Observational evidence for this behaviour was obtained during the AFCRL Kansas measurements described in Kaimal et al. (1972). The empirical results from the AFCRL study are used as a standard against which the suburban results are compared. In the following the phrase 'reference (co)spectra' w i l l refer to the (co)spectral results from this study. They are also refered to hereinafter as the 'reference', 'Kaimal' or 'Kansas' data. In order to analyse the data from this study systematically the turbulence runs were, on a subjective basis, divided into s t a b i l i t y groups. These groups with their stability limits and the number of runs in each group (in parenthesis) are: A) -0. 01 > z'/L V > -0. 10 (3) B) -0. 10 > z'/L V > -0. .40 (15) C) -0. 40 > z'/L V > -1. . 10 (18) D) -1. 10 > z'/L > -1. ,80 (4) V For humidity and the moisture flux the number of runs in group B) and C) are 9 and 17, respectively. This reduction was necessary because some of the time series of humidity had to be rejected due to non-stationarity. For uw the corresponding number of runs for groups A), B) and C) are 2, 14 and 8, respectively. No uw results for the most unstable group are plotted because the scatter was very large with occasional negative 133 values at both low and high frequencies. In addition the uw correlations for this group were very low. In a manner similar to the composite (co)spectra normalized by the (co)variances, a composite (co)spectra was computed for each s t a b i l i t y class. Standard deviations were also calculated but are not indicated in the figures to maintain the readability of the plots. Obviously the standard deviations are higher than the normalized (co)spectra because some of the s t a b i l i t y classes contain only a few runs. In the presentation of the (co)spectra in the following Sections 5.3.2 and 5.3.3 the observations from the lower level w i l l be compared to the results from only one of the systems used at the upper level, namely the SAT(1130)/Lyman-alpha combination. The results from the other sensors installed at the upper level were virtually identical to the SAT(1130)/Lyman-alpha data. In order to demonstrate the generality of the results from the present study observations from a turbulence programme conducted in 1986, and analyzed within the MOS framework, are included in Appendix B. Although less extensive (only u, w, T and wT were analysed) the 1986 data set i s shown to be sufficiently similar that i t provides a viable extension of the present results. (Co)spectral representation within the similarity framework requires the computation of the dissipation rates for each variable so as to be able to derive the non-dimensional dissipation and normalization functions which are used in the normalization of the (co)spectra (eq. 134 1.31 - 1.33 and 1.49 - 1.51). 5.3.1 Non-dimensional dissipation and normalization rates The dissipation rates for turbulent energy, temperature and humidity were obtained using (1.25) - (1.27) which are based on Kolmogorov's hypothesis for the inertial subrange. In practice the spectral densities in (1.25) - (1.27) were determined as the average over a small number of spectral densities (which were already averaged over frequency bands) within the -2/3 region of the spectra (subjectively determined; usually around f =1 - 2). The non-dimensional dissipation rates plotted in the following are computed from (1.28) - (1.30). In a similar way the normalization functions for the cospectra of momentum, heat and moisture flux (eq. 1.46 - 1.48) are computed using the cospectral densities within the -4/3 region (usually at around f = 5). A plot of <f>^ (derived from the w component) versus z'/L^ is shown in Figure 5.9a. The solid line represents the dimensionless dissipation rate for the Kansas data (Wyngaard et al. , 1971) expressed as: <j> = [1 + 0.5(-z'/L ) 2 / 3 ] 3 / 2 (5.3) e v The dashed curve is obtained from the St. Louis study (Clarke et al. , 1982) for their suburban site. The results from this study diff e r markedly from the Kansas data but they agree well with the St. Louis study at small negative z'/L . With increasing i n s t a b i l i t y </>£ from the present study assume a value between the Kansas and St. Louis data and follow a trend similar to the Wyngaard curve. The values from the two SAT 135 a) b) c) 2.0 1.5 0.5 0.0 O X * O W-SAT(1I30) ~ ~ ~ vi-SAT(1127) w-SAT(1126) w-KD Wyngaard and CaiS (1371) Clark* tt al (1982) -2.0 2.5 3-0.5 2.5 9-0.0 -1.5 -1.0 O SAT(I130) X SAT(1I27) # SAT(me) O KD — Kaimal tt aL (1972) -0.5 0.0 O SATf1130) X SAT(1127) * SAT(II28) — Kaimal tt at (1972) T 7 9 x -1.5 0.0 Figure 5.9: Non-dimensional dissipation rates for turbulent kinetic energy (a), heat (b) and moisture (c) vs. z'/L . The solid line is the V rural reference (Kaimal et a l . , 1972). The dashed line in (a) is from the St. Louis study for the suburban site (Clarke et al. , 1982). 136 sensors at the upper level are a l i t t l e bit higher than the ones derived from the Kaijo Denki vertical wind. The lower level measurements are slightly lower towards neutral compared to the upper level. The <p£ values derived from the horizontal wind components (not shown) are slightly higher than those in Figure 5.9a (but s t i l l lower than the rural reference), and they also show more scatter. The present results agree well with measurements by Roth (1990) obtained for his 1986 study. The non-dimensional dissipation rates for temperature in comparison with the Kansas results (solid line) expressed as <t> = 0.74(1 - 9z'/L ) " 1 / 2 (5.4) N v are shown in Figure 5.9b. Agreement is good at middle to large i n s t a b i l i t i e s . Towards neutrality the present observations exhibit some va r i a b i l i t y and are generally slightly lower than the reference but s t i l l follow the trend of the Kaimal curve. The same was observed by Roth (1986) (unpublished results) at the present study site as part of the measurements presented in Appendix B. The values from the lower level are systematicaly lower than the upper level data reflecting the fact that the spectral densities in the inertial subrange were always lower (Figure 5.3a) and often did not exhibit a -2/3 slope. The non-dimensional dissipation rates for humidity (</> , Figure 5.9c) If are compared with the temperature prediction based on the Kansas results (no such data are available for humidity but e.g. Othaki (1985) shows that <b is similar to <j> over wheat fields). The observations from the present study are marked by a lot of scatter and are generally below the 137 reference curve. Again the d> values measured at the lower level are below the corresponding upper level data. The scatter in the normalization function for momentum (G(z'/L )) is considerable and the values are often larger than the reference value of unity (Figure 5.10a), especially at higher i n s t a b i l i t i e s . A similar increase of G(z'/L ) with increasing instability was observed by Roth V (1986) (unpublished results). The large scatter is probably due to the fact that no well defined spectral region with a -4/3 slope could be observed in the momentum flux cospectra (Figure 5.4a). The normalization functions for heat flux are shown in Figure 5.10b and compared against the Kaimal prediction of unity (solid line). Generally H(z'/L ) from the present study is smaller than unity and characterized by scatter. A similar result was obtained by Roth (1986) (unpublished results). The measurements from the lower level are again generally lower especially towards neutral. The Q(z'/L ) data presented in Figure 5.10c are V consistently lower than the Kaimal reference value of unity (solid line), by a factor of about 2 for the upper level data and a factor of about 4 for the lower level and show the same scatter as observed for H(z'/L ). V The decreased normalization function values observed at the lower level can be attributed to the faster r o l l - o f f observed in the corresponding cospectrum (Figure 5.5b). As seen in (1.28) - (1.30) and (1.46) - (1.48) the non-dimensional dissipation and normalization functions contain the f r i c t i o n velocity in the denominator. It was mentioned earlier that u ¥ measured at the upper level was also used for the lower level. This may not represent the low 138 a) -2.0 -1.5 -0.5 b) 2.5 2.0 -V-5 5; i.o 0.5 O SAT( 1130) X SAT(112?) * SAT(me) — Kaimal sf a l (197Z) c) 3 O 1.0 O SAT(1130)/Ly-atpna X SAT(1127)/KM0t6 # SAT(I126)/KH101I — Kaimal et al (1872) 0.0' -2.0 » *V « t * -1.5 -1.0 0.0 Figure 5.10: Normalization functions for the fluxes of momentum (a), heat (b) and moisture (c) vs. z'/L . The solid line at unity is the rural V reference (Kaimal et al., 1972). 139 level turbulent processes and may be expected to be larger than the 'true' value. Without the appropriate measurements, i t is d i f f i c u l t to assess this effect but i t would most likely increase the non-dimensional dissipation constants as measured. An additional possible explanation for the observed lower values is, as mentioned above, the relatively fast high frequency r o l l - o f f observed in the lower level (co)spectra which in general do not exhibit the predicted -2/3 (-4/3) slopes. These non-dimensional dissipation rates, which are not measured within an in e r t i a l sub-range, will obviousely affect the normalization of the (co)spectra within the MOS framework. However, since the 'true' values are not known and the upper level dissipation results show that even when the dissipation constants are evaluated within the -2/3 (-4/3) regions, differences from the rural reference can occur, using the observed non-dimensional dissipation values is the only reasonable choice. However, i t is realized that this limits the interpretation and comparison of the lower level results with the Kaimal reference data. Since each (co)spectral density is divided by the non-dimensional dissipation rate, using a value which is not the 'true' one w i l l affect the energy content of the (co)spectra, i.e. the observed (co)spectra cannot be compared with the Kaimal curves along the vertical (energy) axis (in general they w i l l be larger). However, conclusions can s t i l l be reached in regard to the location of the peaks along the frequency axis since the horizontal position of the (co)spectra is not affected by the normalization procedure (but this location is s t i l l affected by not using a local U value for f (see 5.1)). 140 5.3.2 Spectra V e r t i c a l wind The composite v e r t i c a l v e l o c i t y spectra f o r the four s t a b i l i t y groups are p l o t t e d i n Figure 5.11. The s o l i d l i n e represents a composite Kansas spectrum f o r n e u t r a l s t r a t i f i c a t i o n (Kaimal et al. , 1972) and the dashed l i n e above i s the Kaimal spectra f o r z / L = -2. A l l spectra c o i n c i d e i n the i n e r t i a l subrange because of the n o r m a l i z a t i o n procedure. The behaviour of the high frequency end f o r a l l v a r i a b l e s measured has been d i s c u s s e d i n reference to the (co)spectra normalized by t h e i r corresponding (co)variances (Ch. 5.1) and w i l l not be repeated here. Apart from the lowest frequencies an o r d e r l y progress ion of both the s p e c t r a l peak and the s p e c t r a l d e n s i t i e s can be observed i n the d i r e c t i o n of i n c r e a s i n g l y smaller f as - z ' / L increases . This behaviour i s most V pronounced between 0.03 < f < 0.3. The least unstable c l a s s i s d i s t i n c t l y d i f f e r e n t from the other curves. Kaimal et al. (1972) found that the spect ra are not arranged according to - z / L between -0 .3 > - z / L > -2 .0 but c l u s t e r i n a random f a s h i o n w i t h i n the area between dashed and s o l i d l i n e s i n d i c a t e d i n Figure 5.11. The r e s u l t s from the present study, however, do show a tendency towards separat ion depending on s t a b i l i t y which i s i n agreement with MOS. The peak frequencies i n the present data are s l i g h t l y s h i f t e d towards lower values compared to the reference . Agreement with the 1986 study (Figure B . l a ) , which used a G i l l p r o p e l l e r anemometer f o r the measurement of the v e l o c i t y components, i s good. The measurements from the lower l e v e l show the same separa t ion 141 a) 10' 10° w 3-• 1 i o - ' to ti IO"2 10" SAT(f130) 2/3 -0.00 > z'/Lv > -0.11 > z'/Lv > -0.41 > z/Lv > -1.11 > z'/Lv > 0.10 0.40 1.10 1.80 o* Hogstrom (slightly unstable) _i i i i i i 111 1 1 I—L-10" 10 i-2 10"' 10° / = nz'/U 10' 102 b) 10' 10° <L i o - ' IO"2 : 10" SAT(1I26) * « * <$ ° X x ' *>oo 2/3 x -0.00 > z/Lv > -0.07 O -0.08 > z'/Lv > -0.30 * -0.31 > z/Lv > -0.90 & -0.91 > z'/lv > -1.S0 Hogstrom (slightly unstable) i i i i i 11 o ' 10" 10-2 10" 10° 10' 102 / = nz'/U Figure 5.11: Composite spectra of w from upper (a), and lower (b) level for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively. The dotted line i s from Hogstrom et al. (1982). 142 behaviour as the upper level but exhibit slightly higher energies than the upper level values. This is associated with a shift of the peak towards lower frequencies and is most pronounced for the least unstable class. Figure 5.11b also reveals that the -2/3 slope is only followed for a relatively short period. The correspondence between the results from the present study and the data from both the Hogstrom et al. (1982) at their central city site in Uppsala (dotted line in Figure 5.11) and the suburban study by Clarke et al. (1982) (Figure 2.1a) is good. The latter study also found slightly more energy at the lower frequencies, especially for near neutral data, when compared with the Kansas data. Horizontal wind The horizontal velocity spectra are presented in Figure 5.12. The area between the solid and lower dashed lines is what Kaimal et al. (1972) describe as an excluded zone which separates the stable from the unstable regime (caused by a sudden shift in the dominant scales of motion as -z'/L changes sign). The unstable data should f i t between the V two dashed curves. No separation according to st a b i l i t y is present in the u component in the present study (Figure 5.12a) and the spectral densities are close to the lower end of the Kaimal unstable region and within the supposedly excluded zone. Similarly, Clarke et al. (1982) also find their suburban results to f a l l in the Kaimal excluded zone and the lower part of the unstable area (Figure 2.2a). The data from the present study show a f a i r l y rapid r o l l - o f f at the low frequency end which is also observed by the near neutral data from Hogstrom et al., (1982) (dotted line). The results from the present study compare very well with the 1986 143 a) 10' 10° - \ i o - ' to 10-2 10" 10" b) 10' 10° ^10"' to IO"2 10"3 10-3 x -0.00 > z/Lv > -0.10 O -0.11 > z'/Lv > -0.40 # -0.41 > z'/Lv > -1.10 a -1.11 > z/Lv > -1.80 Hogstrom (slightly -unstable) _i i I i i I i 11 i i i t i i i 11 • i i i i 11 I 1 1 1 1 1 1 10-2 IO"1 10° 10' 102 / = nz'/U x -0.00 > z/Lv > -0.10 O -0.11 > z/Lv > -0.40 * -0.41 > z/Lv > -1.10 & -1.11 > z/Lv > -1.80 Hogstrom (slightly unstable) o & x* ' I I I I 11 -J I I I I II 10" 10-' 10° 10' 102 nz/U Figure 5.12: Same as Figure 5.11 but for u (a) and v (b) from upper level. The lower dashed line marks an excluded zone (see text). 144 study (Figure B.2a). The v component (Figure 5.12b) shows some separation according to s t a b i l i t y between 0.01 < f < 0.08, otherwise the results from the present study agree well with the Kaimal reference and the urban studies by Hogstrom et al. (1982) (dotted line) and Clarke et al. (1982) (Figure 2.2b). As mentioned earlier in reference to Figure 5.2 a transition region can be observed (at f = 0.1) in both the u and v component. It connects the high frequency end obeying MOS with the low frequency end which is governed by mesoscale processes. According to Kaimal et al. (1972) the low frequencies of the horizontal wind components do not scale with z/L as observed here for the u component and to a lesser extent for v. The low frequency end of the two horizontal components has been observed to depend on the height of the PBL (Kaimal, 1978), however, the available measurements were largely useless (because of instrumental problems) and the z^  dependence could not be tested. Temperature The temperature spectra (Figure 5.13) are again compared against the Kansas composite spectra for z/L = 0 (solid line) and z/L = -2 (dashed line). Kaimal et al. (1972) observe a shift in the spectra up to the z/L = -2 curve as the s t a b i l i t y changes sign from positive to negative. With increasingly negative z/L the spectrum moves back towards the neutral curve. This behaviour cannot be observed in the present data and no separation according to stability classes is evident at low frequencies. Unlike the Kaimal data, the present observations crowd into a relatively 145 a) 10' 10° a. t4 i o - ' CO I O " 2 10"3 SAT(1130) x -0.00 > z'/Lv > -0.10 O -0.11 > z'/Lv > -0.40 * -0.41 > z/Lv > -1.10 A -/.// > z'/Lv > -1.80 -I I I I I I 111 I I ' _l I • I I t 111 ' ' 10" 10-2 10" 10° 10' 102 / = nz'/U b) 10' 10° 7 s. E4 I O - ' ? to 10-2 i o - 3 SAT(1126) ft-2/3 x -0.00 > z/Lv > -0.07 O -0.08 > z/Lu > -0.30 * -0.31 > z'/Lv > -0.90 a -0.91 > z/Lv > -1.50 _i i i i i II i 10" 10-_l I 10" _l I I • I I I I' 10° 10' 102 / = nz'/U Figure 5.13: Composite spectra of T from upper (a) and lower (b) level for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively. 146 narrow band at the low frequency end. The results from the present study show higher energy content in the middle frequency range, as already observed in Figure 5.3a, and an inertial subrange level which is also higher compared to the reference. The present results correspond well with the 1986 study (Figure B.lb) at mid and high fequencies, however, exhibit less energy at the low frequency end. Agreement with the Clarke et al. (1972) data is good (Figure 2.1b), apart from the mid frequency range which exhibits more energy in the present study compared to the Clarke et al data. Compared to the Kaimal reference the peaks are observed at higher frequencies. The scale of the f l a t peak region at f = m 0.04 (A = 25z' £ 470 m) compares well with the length scale of the temperature 'signatures' identified in Ch. 4. The results from the lower level (Figure 5.13b) are similar except they show slightly higher energy densities at low frequencies. These are caused by the normalization procedure used since the <p^ values observed at this level (Figure 5.9b) were lower than the upper level. These <f> N values cause an apparent increase at the lower frequencies compared to the reference (and a decrease above the frequency where the dissipation constants were evaluated). The peak locations along the frequency axis (which are not affected by the normalization) are observed at slightly lower frequency values at the lower level compared to the upper level. Humidity The humidity data (Figure 5.14a) are compared against the same Kaimal temperature curves indicated in Figure 5.13 (no similar reference data 147 a) 10' 10° i S-^ 10-' 10-2 10"3 Ly-alpha x -0.00 > z'/Lv > -0.10 O -0.11 > z'/Lv > -0.40 » -0.41 > z'/Lv > -1.10 A -1.11 > z'/Lv > -1.80 ' i i 1 i i i • 11 i i i i i i i i i i 1—i I I i i 11 10 - 3 10-2 10" 10° 10' 102 / = nz'/U b) 10' 10° ^ i o - ' to-to IO' 2 IO"3 KH1011 _i i i i i i 111 x -0.00 > z/Lv > -0.07 O -0.08 > z/Lv > -0.30 * -0.31 > z'/lv > -0.90 & -0.91 > z'/Lv > -1.50 _i i i i i i 11 i i i i i i t 11 10- 10" 10-' 10° / = nz'/U 10' 102 Figure 5.14: Same as Figure 5.13 but for q. 148 exist for humidity). Assuming that humidity behaves like temperature a z'/L dependence similar to that observed for T would be expected for V humidity, however, unlike the Kansas results there is no tendency towards separation according to z'/L . McBean (1971) concludes that the humidity V fluctuations are not governed by z'/L , but instead by z'/L where L is v q q a s t a b i l i t y parameter defined in terms of the moisture flux. Schmitt et al. (1979) based on an analysis of the rural Minnesota data observe their data to be within the unstable zone of the Kaimal temperature spectra. The only difference they mention is a departure for 0 . 1 < f < 1 .0 marked by sli g h t l y larger spectral density values than the temperature reference. As noted before the humidity spectra do not experience a low frequency r o l l - o f f . This is especially true for the slightly unstable cases whereas the most unstable class shows a tendency towards lower values at the low frequency end. The behaviour at the high frequency end reveals that the 'contamination' refered to earlier is most pronounced for the least unstable class. The lower humidity observations (Figure 5.14b) agree well with the results from the upper level. 5 . 3 . 3 Cospectra Momentum The uw cospectra in Figure 5.15 are compared against Kaimal et al. (1972) who observe that a l l unstable cospectra crowd into a narrow band (indicated in Figure 5.15 as the area between the two dashed lines). The Figure 5.15: Composite cospectra of uw from the upper level for three s t a b i l i t y classes. The solid line is the neutral limit on the stable side and the upper and lower dashed lines approximate the upper and lower unstable limits from Kaimal et al. (1972). 150 data from the present study are indeed relatively close together at the low frequency end with peak locations not unlike indicated by the Kaimal curves. Two 'dips' can be observed at f = 0.06 (A = 17z') and f = 0.5 (A = 2z') in the present observations. The 'dip' at f = 0.06 occurs in accord with lower R (f) values (Figure 5.7a). Again no direct comparison uw with the Kaimal curves i s possible along the vertical axis. The -4/3 slope i s only approached at relatively high frequencies. Sensible heat Figure 5.16 shows the wT results (the meaning of the curves is the same as in Figure 5.15). The observations from the upper level are in good agreement with the Kaimal reference with a slight tendency towards higher values at large scales. There is a tendency towards separation according to s t a b i l i t y with the least unstable group having the lowest energy densities and highest peak frequency and vice versa. In general the peak locations are within Kaimal's unstable region. The present results are in good agreement with the cospectra from the 1986 study (Figure B.2b). The way the value of the normalization function can affect the position of a composite spectrum is clearly demonstrated for the least unstable group. As observed in Figure 5.10b the H(z'/L ) values close to V neutral are much smaller at the lower level compared to the upper level ones. This results in a dramatic shift of the normalized composite cospectrum for the st a b i l i t y group closest to neutral from i t s relatively low energy position at the upper level to a high energy position at the a) 10' p-10° 10" o O I 3 IO"2 10"3 io-" 151 10" b) io1 x -0.00 > z/Lv > -0.10 O -0.11 > z/Lv > -0.40 * -0.41 > z'/Lv > -1.10 A -1.11 > z'/L > -1.80 J I I I W I 11 _1 I " i t i i i i 11 t i i i i i i SAT(1130) 0 10" 10"' . • • 10° / = nz/U 10' I O 2 SAT(1126) 10° 10-o I ? 10-2 10"3 ^> M a x x x x -0.00 > z/Lv > -0.07 O -0.08 > z/Lv > -0.30 * -0.31 > z'/Lv > -0.90 & -0.91 > z'/Lv > -1.50 10" 10-3 10" _i i i i I i 111 10" -I I I I I I I 11 -I J I ' I ' l l ' • 0' i i i 11 10° 10' I O 2 / = nz/U Figure 5.16: Composite cospectra of wT from upper (a) and lower (b) level for four s t a b i l i t y classes. Dashed and solid lines are as indicated on Figure 5.15. 152 lower level. At the lower level the cospectral peaks occur at slightly lower frequencies compared to the upper l e v e l observations, most pronounced for the stability class closest to neutral. Moisture Humidity data from the Minnesota experiment analysed by Schmitt et al. (1979) and presented within MOS (but using H(z'/L ) instead of V Q(z'/L ) in the normalization) agree well with the Kaimal heat flux V reference curves. This indicates that the heat flux curves from the Kansas programme can be used as the moisture flux reference. The present moisture flux cospectra are compared with these Kansas reference curves in Figure 5.17. The wq cospectra crowd into a narrow band at low frequencies with slightly larger energy content at large scales compared to the reference. Again no direct comparison with the Kaimal data is possible at the lower level in regard to the energy content, but the observations show that the peak frequency for the least unstable class i s shifted towards a lower frequency at the lower level compared to the upper level. As observed for the heat flux cospectra the s t a b i l i t y class closest to neutral shows a sudden shift between the upper and lower level observations (again as a result of the normalization procedure). 5 . 3 . 4 Spectral correlation coefficients Momentum The composite spectra of the uw spectral correlation coefficients 153 SAT(1130)/Ly-alpha o* - * A > ^ % *-* : • X -0.00 > Z/LV > -0.10 t: * 0 A X | O -0.11 > z'/K > -0.40 r : * -0.4/ > A -/.// > z'/Lv *'AV > -1.10 > -1.80 * A. A O 1 1 1 1 1 f 1 1 I 1 1 1 I 1 1 1 1 1 L _L .1 1 i i i i > i — I — I I I I I il 1—J A I ijS&AU IO"3 1CT2 IO"1 10° 10' io 2 J = nz/U SAT(1126)/KH1011 x x x X * X X o* X -0.00 > z'/Lv > -0.07 O -0.08 > z/K > -0.30 * -0.31 > > -0.90 oo A -0.91 > z/K > -1.50 o a o I I I I I I I I ) , ,i 1 1—1 I I I I 11 1 1—I I I I I 11 1 1—U < I ' M li il li II +t+*t M ' — 10-3 IO"2 IO"1 10° 10' io 2 / = nz/U 5.17: Same as F i g u r e 5.16 but f o r wq. 154 (Figure 5.18) show increas ing values with decreasing i n s t a b i l i t y at almost a l l f requencies , i n d i c a t i n g that the momentum t r a n s f e r i s most e f f i c i e n t f o r near -neutra l c o n d i t i o n s . No low frequency r o l l - o f f i s evident and the larges t magnitudes can be observed at f requencies s l i g h t l y smaller than the peak frequencies i n the corresponding uw cospectra (Figure 5.15). This i n d i c a t e s very e f f i c i e n t momentum t r a n s f e r at large sca les which are p o s s i b l y r e l a t e d to organized s t r u c t u r e s i n the urban environment. A l l composite spectra show a ' d i p ' at f s 0.06 (A = 17z' ) which corresponds to regions i n the corresponding uw cospectra which have s l i g h t l y lower- cospectra l d e n s i t i e s (Figure 5.15) . The observed s t a b i l i t y dependence of the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s i s i n agreement with measurements by McBean and Miyake (1972) from a f l a t r u r a l s i t e , however, they observe a s l i g h t r o l l - o f f below f = 0.01. The R (f) peak magnitudes i n the present study are higher than observed by uw McBean and Miyake (1972). S e n s i b l e heat The heat f l u x s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s (Figure 5.19) at the upper l e v e l show a tendency towards a separat ion according to s t a b i l i t y f o r f requencies larger than f = 0.02 with an increase i n R (f) with wT i n c r e a s i n g i n s t a b i l i t y . This e f f e c t i s most pronounced f o r the t r a n s i t i o n from the s t a b i l i t y c l a s s c loses t to neutra l to the next unstable one. At the low frequency end a r a p i d d r o p - o f f i s v i s i b l e towards very low values regardless of the s t a b i l i t y category i n v o l v e d . This end i s a l s o marked by a l o t of s c a t t e r , e s p e c i a l l y f o r the most unstable group. The l o c a t i o n of the peak t r a n s f e r e f f i c i e n c y does not vary by much and can be found at f 155 1.0 0.8 x X x -0.00 > X x O -0.11 > z'/Lv > -0.10 z'/Lv > -0.40 0.6 O * # -0.41 > o X * * X z'/lv > -1.10 S i f 0.4 X V x * °»0 °x * * ?** * * o * x x "xx 0.2 **£$* x* **** 0.0 i " I t I i i i i i i i i i I I I I I I I 1 1 1 1 1 1 1 L_—1 1 1 1 1 1 1 1 ' ' I I I I I 111 I I I I I 111 I I I I 1 I 1—I I 1 —I I I • 111— 10-3 10"2 10"' 10° 10' 102 / = nz'/U Figure 5.18: Composite spectral correlation coefficients of uw from the upper level for three s t a b i l i t y classes. a) 1.0 0.8 0.6 ftfo.4 0.2 0.0 156 A A * O . * x o & x * A A A SAT(1130) x -0.00 > z'/Lv > -0.10 O -0.11 > z'/Lv > -0.40 * -0.41 > z'/Lv > -1.10 a -1.11 > z'/lv > -1.80 "I**1 ft x x 0 0 $ * / 2< x O* '4> x O* X * * A x x$ A . _ * x Oj*^  _ - I I I M M I ' i i i i i i i | | I I I I I I I I I I I I I I I I I l_ 10"3 10-2 10- 10° 10' 102 / = nz'/U b) 1.0 0.8 0.6 ft; 0.4 0.2 r h xo " A X ^  o o% O X * * % SAT(1126) x -0.00 > z / £ v > -0.07 O -0.08 > z'/Lv > -0.30 * -0.31 > z'/Lv > -0.90 A -0.91 > z'/lv > -1.50 ° H A t> A X X x $ * " X X X X X x o' * A o.o h - - -I I I I I I I _l ' ' l i l t I I I I 111 - I I 1 1 _ l ' I I I I 11 10 -3 lO" 2 10" 10° 10' lO2 / = nz'/U Figure 5.19: Composite spectral correlation coefficients of wT from upper (a) and lower (b) level for four s t a b i l i t y classes. 157 = 0.02-0.03 (X = 50 - 35z') which is only slightly lower than the peak frequency found in the corresponding cospectra (Figure 5.16a). McBean and Miyake (1972) observe a peak at around f = 0.01 (with sli g h t l y lower R (f) of about 0.6) but also find the largest correlation coefficients wT associated with the most unstable groups. They also report very low values at the largest scales. Around f = 0.2 (A = 5z') a 'plateau' region can be observed. The measurements from the lower level (Figure 5.19b) are in general agreement with the upper level results. Moisture The composite spectral correlation coefficients for wq from the upper level (Figure 5.20a) are marked by a lot of scatter at the low frequency end but they s t i l l have a tendency to decrease towards the largest scales. In general the least unstable group has the lowest R (f) wq magnitudes over the entire frequency range. At frequencies above f = 0.04 R (f) increases with increasing instability, as observed in the sensible wq heat spectral correlation coefficients. Similar to R (f) a 'plateau' wT region is evident at f = 0.3 ( A s 3z'). At the lower level separation according to s t a b i l i t y categories is more pronounced and can be found at f > 0.03. Compared to the upper level the two least unstable groups have lower correlations at the lower level, whereas the magnitude of the two most unstable groups remain about the same at both levels. McBean and Miyake (1972) observe a similar s t a b i l i t y dependence but sli g h t l y higher magnitudes in their spectral correlation coefficients. 158 i ) 1 0 0.8 0.6 of 0.4 0.2 0.0 SAT(1130)/Ly-alpha X -0 00 > z'/K > -0. 10 O -0.11 > *AV > -0.40 * -0.41 > > -1.10 A -1.11 > z'/K > -1.80 o* A X © A A A A * X * 0 0 A * A $0 o** * * * * * o ° A ° - o * o * * A Ox ° 0 * * * xxx x x O o O * A , * * A OO* * x O * A X x x * $ 6* _i t i i 11111 i i—i i 1111 A O* 4 x xO* . _i I i i i i i 11 ' i • 10" 10-2 10"' 10° / = nz'/U 10' lO 2 b) 1.0 0.8 0.6 of 0.4 0.2 0.0 SAT(1126)/KH1011 X -0.00 > z'Av > -0.07 O -0.08 > z'Av > -0.30 A * -0.31 > z/K > -0.90 A A -0.91 > > -1.50 * o Oo o ° *! X* x * oo . £ A A . * A * A ^ 0 0 x O ^ x x O ° 0 * * A X x x x x O * A Oo** $ o * t x x x O O* ^ x x 10" 1 I 1—L. 10-2 -I I I I I I I I ' ' i i i • i 11 10"' 10° / = nz'/U 10' 102 Figure 5.20: Same as Figure 5.19 but for wq. 159 Moisture - humidity The Tq spectral correlation coefficients presented in Figure 5.21 show a very strong dependence on stability, in particular for f > 0.09, with increasing correlation as the instability increases. At the low frequency end a sharp r o l l - o f f is observed with the f i r s t point at the low frequency end of the least unstable group having a negative value. Agreement between the upper and lower level data is good. 5 .4 Summary and discussion of (co)spectral results 5.4.1 Summary 5.4.1.1 Normalized with (co)variance Based on the results presented in 5.1 the following are the general findings for the (co)spectra normalized by their respective (co)variances. The overall shapes of the (co)spectra observed in the present study are similar to the ones from the homogeneous surface layer. At the upper level the peak frequencies occur at slightly lower values compared to reference data for w. The shift of the peak frequency is small but results in slightly higher energy content at larger scales. On the other hand the peaks in the u and T spectra are shifted towards higher frequencies. No conclusions can be drawn in regard to the peaks of v, uw and wq because the reference was from neutral st r a t i f i c a t i o n , but i f any differences were to occur they would likely be very small. The f m values measured in the present study are also included in Table 2.1 which 160 a) 1.0 0.8 0.6 a; 0.4 0.2 0.0 SA T( 1130)/Ly - alpha A A A A A A A A A a- # • m s\ o o 0 * A A * o * A o * x x X x x x x O* x O* X x -0.00 > z/Lv > -0.10 0 -0.11 > z'/Lv > -0.40 * -0.41 > z/Lv > -1.10 A -/.// > z/Lv > -1.80 x O A x o _ o _ _ _ _ _ »Qb _ i ' • • ' ' 1 ' ' ' ' ' i i i 1111 10" •10-2 10"1 10° / = nz'/U 101 102 b) 1.0 0.8 0.6 eto.4 0.2 SAT(1126)/KH1011 ° A * A A A A 'A A OO * O X x O 0 " « 0 ° O o * 0 * V O * A o * A A X O x x O O A A x * x * ** x X x x -0.00 > z / l v > -0.07 O -0.08 > z/L,, > -0.30 # -0.3/ > z/_ v > -0.90 A -0.9/ > z'/Lv > -1.50 • » O A .* A * A * * 0.0 - _ _ _ _ _ _ _ _ _ * _ - > , A A i i i i i i i t t i i i i i i x Ol X X ' I ' l l ' 1 " 10" 10-2 10"' 10° / = nz'/U 10' 102 Figure 5.21: same as Figure 5.19 but for Tq. 161 summarizes the r e s u l t s from other urban s tudies and compares them with the Kaimal data . Note that the peak frequencies of the Kaimal reference i n Table 2.1 represent the unstable range w i t h i n -2 < z / L < 0. The u spectrum shows a r e l a t i v e l y f a s t r o l l - o f f at the low frequency end ( s i m i l a r to the 1986 study) and the v spectrum compares w e l l with the Kansas data . Both h o r i z o n t a l wind components e x h i b i t the point of i n f l e x i o n mentioned by Kaimal (1978) connecting the high frequency wi th the low frequency end. The T spectrum i s s l i g h t l y s h i f t e d to higher f requencies compared to both the Kansas reference and the 1986 study but agrees w e l l with that of Coppin (1979). The q spectrum i s c h a r a c t e r i z e d by no r o l l - o f f at low frequencies . The s tudies a v a i l a b l e from r u r a l s i t e s report no c o n c l u s i v e r e s u l t s i n regard to the low frequency behaviour f o r t h i s v a r i a b l e and the observed low frequency trend i n the present study may be extreme but not too unusual . D i f f e r e n t , however, are the energy d e n s i t i e s i n the t r a n s i t i o n region from low to high f requencies which are ra ther low and no 'hump* as i s u s u a l l y evident i n spect ra , i s observed. At the h i g h frequency end i n the i n e r t i a l subrange a c l e a r -2/3 slope can be observed f o r w, u, v (at s l i g h t l y higher f requencies) and T ( for a short range o n l y ) . The q spectrum e x h i b i t s only a very short -2 /3 slope (longer f o r the Lyman-alpha mesurements) which i s due to the noise contamination at the high frequency end. The -4/3 p r e d i c t i o n i s fo l lowed i n the cospectra of wT and wq. The uw and uT cospectra seem to f o l l o w a -4 /3 s lope , however, the i n e r t i a l subrange values are marked by some v a r i a b i l i t y . The Tq slope at the high frequency end becomes p r o g r e s s i v e l y steeper wi th i n c r e a s i n g f . 162 The analysis of the lower level results is affected because no local U values were available for f. Therefore i t cannot be concluded i f the observed shift of most of the (co)spectral peaks towards lower frequencies at the lower level is real. The most obvious differences to the upper level measurements, however, are the faster high frequency r o l l - o f f s observed for a l l spectra and cospectra starting at f = 0.3 (A = 3.3z'). As a consequence the -2/3 (-4/3) slope predictions are not followed or then only for a short range (w and wT). 5.4.1.2 Non-dimensional dissipation and normalization rates Analysis of the upper level non-dimensional dissipation rates in 5.3.1 reveals smaller <j>^ values compared to the Kansas results, in particular at small negative z'/L , a result which compares well with V other urban observations by Clarke et al. (1982) and Roth (1990). At large -z'/L values, <p from the present study is between the Kansas and v e St. Louis results. The values of d> and <t> correspond with the trend of the Kansas prediction, however, they have slightly smaller values at small i n s t a b i l i t i e s which are associated with some scatter. The normalization function for the momentum flux G(z'/L ) exhibits a lot of V scatter but i s generally larger than the Kaimal prediction of unity. H(z'/L ) for the heat flux and Q(z'/L ) for the moisture flux are lower V V than the rural value of unity more so for Q(z'/L ). At the lower level a l l of above functions with the exception of <j>^, are lower. This can in part be attributed to the lower spectral densities observed in each of the i n e r t i a l subranges which often did not exhibit the -2/3 (-4/3) 163 s l o p e s . I d e a l l y l o c a l values (values measured at the l e v e l of observat ion) should be used i n the computation of the non-dimensional d i s s i p a t i o n and n o r m a l i z a t i o n f u n c t i o n s . This was not the case f o r U and u 0 at the lower l e v e l which could be another reason f o r the observed lower v a l u e s . 5.4.1.3 Normalized w i t h i n the Monin-Obukhov s i m i l a r i t y framework The r e s u l t s presented i n 5.3.2 and 5.3 .3 combined with the observat ions from the 1986 study (Appendix B) show that at the upper l e v e l the w r e s u l t s from the present study are s l i g h t l y s h i f t e d towards lower f requencies with an associated increase i n energy at large sca les compared to the Kaimal reference . The f values f o r u and e s p e c i a l l y T m (not i n the 1986 study) are found at s l i g h t l y higher values compared to the reference , whereas the peaks f o r v, uw, wT and wq remain roughly the same. The (co )spec t ra l shapes do i n general agree with the Kaimal curves . The u and v components agree wel l with the reference apart from the f a c t that the s p e c t r a l d e n s i t i e s f a l l w i t h i n the supposedly ' exc luded zone' as d e f i n e d by Kaimal et al. (1972). S i m i l a r to Kaimal et al. the low frequency end of the h o r i z o n t a l wind components i n the present study do not d i s p l a y MOS behaviour. Agreement with the urban s t u d i e s of Hogstrom et al. (1982) and Clarke et al. (1982) i s good, i n p a r t i c u l a r they a l l show a r e l a t i v e l y f a s t r o l l - o f f f o r u at the low frequency end. According to Kaimal et al. the low frequency end of the T spectrum s c a l e s with z ' / L , a feature which cannot be observed i n the present 164 study and only partly in the results from 1986. The T spectra observed in the present study are slightly shifted to higher frequencies, whereas the ones from 1986 agree better with the Kaimal curves. Assuming similarity of T and q fields, the q spectrum should separate according to z'/L^, but this is not observed in the present study. Observational support for such a z'/L dependency has also yet to be shown for rural surfaces. V The uw cospectra from different s t a b i l i t y groups a l l crowd into a narrow band at the low frequency end and show two minor 'dips' at f = 0.06 (A = 17z') and f = 0.5 (A = 2.5z'), respectively. The wT and wq cospectra both exhibit a slight dependency on z'/L^ at medium and low frequencies (increasing energy densities with increasing i n s t a b i l i t y ) . The lower non-dimensional dissipation and normalization functions observed at the lower level compared to the upper level obviously affect the (co)spectral densities normalized using these values, such that the (co)spectra are shifted in the vertical which makes comparison with the reference curves d i f f i c u l t (not with regard to the peak location on the frequency axis but the energy content). For cases when the normalization functions were almost the same at the two levels, comparison of the present w results at the lower level with the reference curves is good with the already noted slight shift of peaks towards lower frequencies (compared to the reference and the upper level results). The low frequency end of w at the lower level shows a z'/L dependence, whereas T and q do not (in agreement with the upper level). The peaks in T, wT and wq are a l l slightly shifted towards lower values. This is most pronounced for the s t a b i l i t y group closest to neutral. Again, the shift towards 165 lower frequencies at the lower l e v e l may be a t t r i b u t a b l e to f values which are not evaluated using the l o c a l U values. 5.4.1.4 Spectral correlation coefficients A n a l y s i s of the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t s (Ch. 5.3.4) r e v e a l s a strong s t a b i l i t y dependence, p a r t i c u l a r l y of the medium and high fequencies (the low frequencies are u s u a l l y a s s o c i a t e d w i t h a l o t of s c a t t e r ) , r e s u l t i n g i n decreasing c o r r e l a t i o n s w i t h i n c r e a s i n g i n s t a b i l i t y f o r uw and the opposite f o r wT and wq at a l l f values. The r e s u l t s show that i n general f o r unstable c o n d i t i o n s the t r a n s f e r i s more e f f i c i e n t f o r heat than momentum and l e a s t e f f i c i e n t f o r moisture. C l o s e r to n e u t r a l the t r a n s f e r e f f i c i e n c y of momentum i s higher than f o r heat whose t r a n s f e r e f f i c i e n c y i s i n turn higher than f o r moisture. The peaks i n the s p e c t r a l c o r r e l a t i o n c o e f f i c i e n t spectra occur at around the same ( f o r wq) or at s l i g h t l y lower ( f o r uw, wT) frequencies compared to t h e i r peaks i n the corresponding cospectra. R ( f ) e x h i b i t s a s l i g h t 'dip' at f uw = 0.06 (A = 17z'). This frequency a l s o corresponds to a re g i o n w i t h lower uw c o s p e c t r a l d e n s i t i e s . An i n d i c a t i o n of a 'plateau' region at f = 0.2 -0.3 (A = 5 - 3z' ) can be observed i n R ( f ) and R ( f ) . wT wq Transfer e f f i c i e n c i e s at the lower l e v e l are i n general s l i g h t l y reduced f o r the s t a b i l i t y category c l o s e s t to n e u t r a l compared to the upper l e v e l . The s t a b i l i t y dependence observed i n the present study i s i n agreement w i t h r u r a l observations (e.g. McBean and Miyake, 1972). There are, however, d i f f e r e n c e s i n the magnitudes: the uw ( e s p e c i a l l y f o r near n e u t r a l c o n d i t i o n s ) and wT s p e c t r a l c o r r e l a t i o n s from the present study 166 having r a t h e r high values, whereas those f o r wq are s l i g h t l y lower than observed by McBean and Miyake (1972). 5.4.2 Discussion The r e s u l t s from the previous s e c t i o n s demonstrate that the ( c o ) s p e c t r a l r e s u l t s from the present study measured over suburban t e r r a i n are remarkably s i m i l a r to ' i d e a l ' surface l a y e r data and the few a v a i l a b l e observations from other urban s t u d i e s . The only c o n s i s t e n t d i f f e r e n c e s occur i n 1) the peak frequencies of w which are s l i g h t l y lower compared to the reference, 2) the peak frequencies of u and T which are s l i g h t l y higher compared to the reference and 3) the o v e r a l l shape of the uw cospectra. In terms of MOS s c a l i n g ( i . e . z ' / L dependence of the V low f r e q u e n c i e s ) the only d i f f e r e n c e from the reference data occur i n the T spectrum which does not show the p r e d i c t e d behaviour whereas wT and wq have a tendency towards an organized behaviour at mid f r e q u e n c i e s . The measurements at the lower l e v e l i n general show s l i g h t l y lower peak frequencies compared to the upper l e v e l . P art of t h i s may be a t t r i b u t a b l e to the f a c t that the upper l e v e l wind speed was used i n the computation of the non-dimensional frequency. A n a l y s i s of the lower l e v e l data w i t h i n the MOS framework was complicated because the non-dimensional d i s s i p a t i o n r a t e s were g e n e r a l l y lower and based on ( c o ) s p e c t r a l estimates which d i d not d i s p l a y a -2/3 (-4/3) behaviour because of the f a s t e r h i g h fequency r o l l - o f f observed. This e f f e c t was l e s s f o r w and wT and both show good agreement w i t h the upper l e v e l and the reference data and experience a low frequency behaviour which i s dependent on z ' / L . 167 Although the (co)spectral shapes (i.e. the variance associated with each frequency) and the peak locations are in general agreement with the homogeneous surface layer data the observed 'anomalies' may be attributed to particular surface (e.g. roughness) features. A more detailed discussion of this follows in Ch. 8 The transfer of fluxes can only be regarded as similar i f the spectral correlation coefficients are similar over the entire frequency range measured. The present result show that the shapes of the correlation coefficient spectra are similar for wT and wq but the coefficients are systematically higher for sensible heat indicating a more efficient heat transfer at most scales compared to the moisture transfer. This result w i l l be further explored in 6.2. Compared to momentum wT and wq are generally more efficient at middle and high frequencies under unstable conditions, however, uw is more efficient at low and mid frequencies under near neutral conditions. The most pronounced differences between the upper and lower level results are observed at the high frequency ends which generally exhibit a faster than -2/3 (-4/3) ro l l - o f f at the lower level. Spectral slopes steeper than -2/3 at frequencies associated with the i n e r t i a l subrange have been reported for turbulence measurements of w in an almond orchard (Baldocchi and Hutchison, 1988) and in a deciduous forest (Baldocchi and Meyers, 1988). The measurements by the latter authors indicate steeper slopes for the three velocity components up to about 1.3 times the height of the trees (their Figure 2). Baldocchi and Meyers (1988) attribute 168 these steep slopes to the conversion of large-scale, shear-produced TKE into smaller-scale motions which are quickly dissipated via work against form drag. As discussed later, additional shear production due to form drag is li k e l y in the present environment which is characterized by many three-dimensional bluff bodies. The inertial cascade of energy from large to small scales is therefore augmented by the additional work against the form drag. This 'short-circuiting* of the energy cascade is also discussed by Shaw and Seigner (1985) and is usually found at wavenumbers larger than 1/z' (f > 1). Another possible reason for the steeper slopes could be that Taylor's Hypothesis used in the derivation of (1.21) is not valid at low heights in the suburban atmosphere. This is because this Hypothesis breaks down when turbulence intensities are large and when wind shear is great (Jensen and Busch, 1982). According to spectral theory turbulence is locally isotropic i f the ratio between the lateral or vertical and the longitudinal spectral densities equals 4/3 at frequencies in the in e r t i a l subrange. In the present study these ratios were evaluated at the upper level and were generally between 1.2 and 1.4 at f s 1 - 3 (even at higher f values the ratios would not converge to 4/3). Measurements by Hogstrom et al. (1982) at a central city site indicate an even lower ratio of about 1.1 (yet they do not observe a faster high fequency r o l l - o f f in their velocity spectra). Anisotropic behaviour has also been measured in the laboratory by Browne et al. (1987) for turbulence in the dissipation subrange of turbulent wakes. Above mentioned reasons can a l l result in steeper slopes at the high fequency end, however, i t cannot be concluded at this point what causes the observed behaviour. 169 MOS applied to the non-dimensional dissipation rates is successfull in the sense that the non-dimensional dissipation and normalization rates are, as prescribed, a function of z'/L , however, they are generally smaller than the reference data. The differences are relatively small for d> , <j> and H(z'/L ) but they are substantial for <j> and Q(z'/L). (Note N 7 v e that although the dissipation functions may be different from their respective reference values this does not affect the normalization as long as a -2/3 (-4/3) slope is observed in the iner t i a l subrange). The differences observed for <f>c are best explored using the framework of the TKE budget which contains the terms contributing to the production, transport and loss of the turbulent velocity fluctuations. The TKE budget non-dimensionalized by kz'/u^ can be written as (Clarke et al., 1982): <*=</>- z'/L + R (5.5) £ m v where the f i r s t and second terms on the right-hand-side represent the rate of production of energy by shear and buoyancy, respectively and R is a residual term which accounts for the vertical and pressure transport of energy and any advective effects. Clarke et al. (1982), who measure similar magnitudes for d> (z'/L ) as c v observed in the present study, evaluate the individual terms in (5.5). They conclude that differences in <j>^ compared to the rural reference can be attributed to any of the terms on the right-hand-side of (5.5). In particular under neutral and near neutral conditions, when the buoyant production and flux divergence terms can be neglected, lower dissipation values may be caused by lower <j> values. The latter is observed to occur 170 under neutral conditions over rough surfaces as a result of the reduced wind speed increase with height compared to the logarithmic prediction (e.g. Garratt, 1978a and b). Under unstable conditions Clarke et al. (1987) show that the ratio of buoyant production of turbulence relative to the shear production is the same at their suburban and rural sites. However, the dissipation was smaller and the residual term R was significantly larger at the suburban locations. They conclude that the larger residual component of the TKE budget at the suburban sites was due to vertical transport, flux divergence, pressure transport and possible horizontal advection. This is not very revealing, however, i t seems reasonable that large and organized vertical structures in the urban environment and transfer of energy through pressure-velocity intercations result in a transport of locally produced TKE away from the surface which would lead to a local production which is greater than the the local dissipation. Two main objectives of this thesis are to determine i f MOS can be applied to a suburban environment and to assess whether z' > z*. In respect to the f i r s t objective i t is concluded at this point that no general statements can be warranted because similarity theory seems to apply for some but not a l l turbulence statistics. In particular the results often display the required stability dependence, however, the magnitudes are often different from reference data and for instance indicate higher transfer efficiences for momentum and heat under some conditions in the suburban environment. This latter result and the slight anomalies observed in some of the (co)spectra and spectral correlation 171 coefficients also suggest that the present measurement levels were sometimes below z*. This does not mean that e.g. flux measurements performed within the roughness sub-layer are useless. The fact that the (co)spectral shapes of wT and wq (which represent the fluxes of heat and moisture) agree very well with homogeneous surface layer data indicates that the effects of the inhomogeneous surface on the energy distribution with respect to frequency are minimal. However, there is s t i l l the likelihood that these flux estimates are not entirely representative because they are taken in an atmospheric layer which is probably characterized by a spatially inhomomgeneous flux distribution. 172 CHAPTER 6: TURBULENCE STATISTICS 6 . 1 I n t e g r a l s t a t i s t i c s The standard deviation ir of a turbulent signal is one of i t s basic characteristics. Often the variance is computed with no consideration as to which scales contribute to that variance. Steyn (1982) argues that the most appropriate averaging band for the determination of the integrals should cover the f u l l range of micrometeorological fluctuations, i.e. from the low frequency end in the spectrum defined by the spectral gap ( i f present) up to the end of the inertial subrange. McBean (1971), however, points out that in the cases of u and v and to a lesser extent T and q, the computed variance depends on the length of record, which can be seen from the spectra of these signals which s t i l l contain some energy at low frequencies (especially for q in the present study). In the present study the integral statistics were evaluated over the entire frequency range available, realizing that this introduces some uncertainty and scatter into the results for u, v, T and q. Rough surfaces cause drag on the atmosphere which creates intense turbulence. The ratio u^/U represents the square root of the drag coefficient and is therefore a measure for the surface roughness. The literature suggests a wide range of u#/U ratios for 'ideal' (low roughness, homogeneous fetch) surfaces but they are generally less than 0.1 for z < 0.01 (Counihan, 1975 for z = 30 m). A plot of u, vs. U from o a l l s t a b i l i t y conditions encountered in the present study is given in Figure 6.1. The slope is larger than 0.1 and agrees well with the slope 173 F i g u r e 6.1 : P l o t of u , vs U. The dashed l i n e i s a l i n e a r f i t from C l a r k e et al., 1982 f o r t h e i r suburban s i t e (z ' = 25 m). 174 (0.13) of an estimated linear f i t obtained by Clarke et al. , 1982 (dashed line) for their measurements under near neutral conditions at the suburban site. Other urban studies report slopes of 0.1 (Steyn, 1987; personal communication) and 0.134 (Hogstrom et al. , 1982 for their central c i t y site). 6 . 1 . 1 S t a n d a r d d e v i a t i o n s o f v e l o c i t y The turbulence intensities of the velocity components depend on the height of observation and the surface roughness. Figure 6.2 presents the results from u, v and w plotted against z'/L . It appears that both horizontal components (Figure 6.2a) and the vertical component (Figure 6.2b) are functions of z'/L . The scatter is considerable for the V horizontal components but the general behaviour agrees well with observations from Clarke et al. (1982) for both v and w. The present and the Clarke et al. study observe higher turbulence intensities for the horizontal components which also increase faster with increasing i n s t a b i l i t y compared to the vertical one. Intercomparison between the different w sensors used is good (Figure 6.2b) with slightly higher values measured at the lower level. This is expected and the height effect would probably be more pronounced i f the local wind speed instead of that at the upper level had been available. Over rural areas the turbulence intensities are lower and for the u component cr /U = 0.1-0.15 u under near neutral conditions measured at z = 30 m (Counihan, 1975). MOS predicts the normalized velocity standard deviations to be a 1/3 function of s t a b i l i t y with a (-z'/L ) dependence in the limit of free 175 a) 0-« 0.5 0.4 X 0.3 0.2 0.1 0.0 o O u-KD (z' = 18.9 m) * v-KD (z' - 18.9 m) * O # o & o oo 9 >** C ^ 0 CP o o -2.0 •1.5 -1.0 *'/Lv -0.5 0.0 b) 0.5 0.4 0.3 0.2 0.1 0.0 o o 6 o ® O SAT(1130) (z- = 18.9 m) x SAT(1127) (z' = 18.9 m) O KD (z' = /S.9 m) * SAT(1126) (z l = /1.0 m) 8 8 X -2.0 -1.5 •1.0 -0.5 0.0 F i g u r e 6.2: Turbulence i n t e n s i t y vs . z ' / L f o r u and v (a) and w (b) 176 convection. The ratios cr A i * are plotted in Figure 6.3 and compared U, V w against the estimated f i t from Clarke et al. (1982) for their industrial 1/3 site expressed as cr/u, = 2.5(-z'/L ) in Figure 6.3a (dashed line). V V The cr /u # ratios from the present study are slightly higher than the Clarke et al. observations, however, i t should be noted that the latter authors found an inverse relationship with Z q in a l l three velocity components and their results varied slightly from site to site. In general cr A i # is slightly larger than cr /um and i t appears that cr^/u* increases faster with increasing instability than o^/u* in the present and the Clarke et al. study. This indicates that the wind direction i s relatively more variable in unstable than close to neutral conditions. Much attention has been paid to the neutral limits of the ratios. Extrapolation to neutral would be a dubious procedure, however, the data closest to z'/L =0 have values of 2.3 and 1.7 for u and v, respectively V which agree well with other observations from both rural and (sub)urban surfaces (Table 2.2). The normalized horizontal wind components are again shown in Figure 6.3b on a log-log plot which enables a better assessment of the slope. For -z'/L > 0.5 the data approximately increase with -z'/L to the 1/3 power. V Experimental data for the horizontal wind components are less supportive of the similarity prediction and i t is often argued and observed that u and v scale better with mixed layer variables (aside from z'/L ). However, Arya and Sundararajan (1976) show a definite increase of cr A u with increasing instability for the Kansas data, an increase u,v m which is also observed by McBean (1971) in another rural study. In particular McBean also measures a more rapid increase of cr /um with 177 a) b) 4.0 3.5 3.0 2.5 3 ^ 2.0 1.5 1.0 0.5 0.0 * o -2.0 10' . o o -* # o *# * * ° * * )&. O * o 6* o o O XL-KD (V = 18.9 m) * v-KD (z' = 18.9 m) — Clarke et al.. 1982 (for v) -1.5 •1.0 -0.5 0.0 3 \ 10° O u-KD (z- = 18.9 m) » v-KD (V = 18.9 m) O * * 10" 10° Figure 6.3: Normalized standard deviations of u and v vs. z ' / L compared V with an empirical f i t by Clarke et al. , 1982 (dashed line) for their industrial site (a) and on log-log plot (b). 178 increasing instability compared to cr a feature which is observed in the present study. Figure 6.4 presents the corresponding normalized standard deviations of the vertical velocity component. In the free convection limit MOS has 1/3 been shown to apply and the predicted proportionality to (-z/L) is usually observed over 'ideal' sites. The solid line in Figure 6.4a represents the empirical f i t by Panofsky et al. to tower and aircraft data over rural terrain given by: <r A u = 1.3(1 - 3z'/L ) 1 / 3 (6.1) W V Figure 6.4a shows that the data from the present study follow the trend of the reference curve but are generally lower. Agreement with the urban results of Clarke et al. , 1982 (dashed line and Figure 2.3) for their 1/3 suburban site represented by <r /u, = 1.2(1 - 2.5z'/L) is good at large i n s t a b i l i t i e s but at smaller z'/L the present observations are below V their curve. Intersite variability in the Clarke et al. study, however, was quite considerable and some of the observations from other suburban sites in St. Louis (not shown here) compare well with the lower values observed under slightly unstable conditions here. The measurements from the lower level are slightly higher compared to the upper level. Note that this difference cannot be accounted for by not having used the local u,, value. On the contrary, assuming the local value would be lower than that measured at the upper level would have further increased the ratios. On the other hand agreement between the two levels would be better after including the local u w in the computation of 179 — Panofsky et al.. 1977 — Clarke et al.. 1982 10' b) 10° 2.0 -1.5 -1.0 . -0.5 z'/K 0.0 o SAT(1130) (V = 18.9 m) X SAT(1127) f z ' = 18.9 m) O KD (z1 = 18.9 m) # SAT(1126) (V = 11.0 m) 1/3 _ *P o ** ® 6 ** 1 1 I t 1 l 6 * * * V & 8 ' ' i io - ' -10° Figure 6.4: Normalized standard deviations of w vs. zi'/L^ compared with empirical f i t s to rural data by Panofsky et al. , 1977 (solid line) and urban data by Clarke et al. , 1982 (dashed line) for their suburban site (a) and on log-log plot (b). 180 -z'/L . This would result in a shift of cr /u w ratios towards larger V w -z'/L values (this is true for a l l turbulence s t a t i s t i c s at the lower V level presented in the following). In the neutral limit, again taking the ratios from the least unstable cases, cr /u» is about 1.2 which is in agreement with other observations w (Table 2.2). Figure 6.4b shows that the predicted 1/3 slope is followed at both levels for -z'/L > 0.3. This compares well with the rural data V from Wyngaard et al. (1971). 3 Since z'/L contains u. in the denominator a pseudo-correlation may v * be introduced in the free convection similarity prediction because cr is w normalized by u„. Besides u, the free convection velocity scale (eq. 1.4) has been suggested to be important in conditions of strong upward heat flux and light winds. Based on a derivation from the turbulent kinetic energy budget Clarke et al. (1982) present the following functional 3 3 1/3 dependence of cr on both u_ and u : cr = cw where w = (u_ + 0.4u ) r w * f w m m * f and c is an empirical parameter, CT is plotted against w in Figure 6.5 w m and compared against the f i t to the Clarke et al. data (dashed line) obtained for their industrial and suburban sites (c = 1.18). The agreement between the results from the present study at both levels and the f i t of Clarke et al. is good. In a recent study Rotach (1990) evaluated the same functional dependence of cr on w . His data from an w m urban site in Zurich, Switzerland were well represented by a straight line with c = 1.12. 181 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 © SAT(1130) (z- = 18.9 m) x SAT(1127) (z' = 18.9 m) * SAT(1126) (z' = 11.0 m) -- Clarke et al., 1982 * 9 -* *© X * x> ^6 *x„ ' 0.2 0.4 0.6 w7n (fns-') 0.8 1.0 F i g u r e 6.5: Normalized standard d e v i a t i o n s of w vs . w^ compared w i t h a l i n e a r f i t by Clarke et a l . , 1982 (dashed l i n e ) f o r t h e i r i n d u s t r i a l and suburban s i t e s . 182 6 . 1 . 2 S t a n d a r d d e v i a t i o n s o f t empe ra tu r e In the free convection regime dimensional considerations show that the normalized standard deviations of temperature are a function of -(z'/L )" 1 / 3. The variation of o^/T* with s t a b i l i t y from the present study is shown in Figure 6.6. The solid line in Figure 6.6a represents the Wyngaard et al. (1971) f i t to the Kansas data given by cr /T~ = 0.95(-z'/L ) " 1 / 3 (6.2) T * v The suburban data from the present study agree very well with the rural reference. Very close to neutral the ratios become large. This has been observed in other studies and is due to the fact that although the heat flux (and hence T #) is close to zero, some temperature fluctuations caused by horizontal inhomogeneities (which in the ideal case are zero) w i l l be measured. The upper level Kaijo-Denki observations are sli g h t l y higher and experience more scatter than the SAT results. The values observed at the lower level are lower but s t i l l follow the shape of the rural reference curve. (Correspondence to the upper level observations would again be improved considering a slight shift towards larger -z'/L^ values). The observations from the present study also agree well with the suburban data of Clarke et al. (1982) (Figure 2.4). Figure 6.6b shows that the predicted slope of -1/3 is followed at both levels from z'/L = -0.2 which is the same as observed over rural surfaces (e.g. Wyngaard et al., 1971; Smedman-Hogstrom, 1973). 183 a) 4.0 3.5 3.0 2.5 X b 2.0 1.5 1.0 0.5 0.0 © SAT(1130) (z' = 18.9 m) x SAT(1127) (z1 = 18.9 m) O KD (z' = 18.9 m) * SAT(1126) (z- - 11.0 m) — Wyngaard et al.. 1971 -2.0 b) 101 \ b I 10° --1.5 •1.0 -0.5 * * * © SAT(1130) (z1 = 18.9 m) x SAT(1127) (z' =18.9 m) O KD (z' = 18.9 m) * SAT(1126) (z' = 11.0 m) O 0.0 - I I I L . 10- 10° Figure 6.6: Normalized standard deviations of T vs. z'/L compared with an empirical f i t by Wyngaard et al. , 1971 (solid line) (a) and on log-log plot (b). 184 6.1.3 Standard deviations of humidity In the limit of free convection humidity is predicted to exhibit a -1/3 dependence on -z'/L (e.g. H i l l , 1989). The variation of o*q/q# with s t a b i l i t y from the present study and compared against a curve based on rural data from Hogstrom and Smedman-Hogstrom (1974) (solid line) of the form <r /q. = 1.04(-z'/L ) " 1 / 3 (6.3) q V is given in Figure 6.7a. The scatter is large, especially for slig h t l y unstable conditions at around z'/L = -0.3 and the trend of the rural V reference curve is generally not followed. For sl i g h t l y unstable conditions cr /q* from the present study is larger than the reference. No q comparable data are available from other suburban sites. The ratios at the lower level are slightly smaller than measured at the upper level. As shown in Figure 6.7b on a log-log plot, the present data exhibit a slope which is larger than the free convection prediction. Rural observations presented by McBean (1971) exhibit a similar amount of v a r i a b i l i t y when plotted against z'/L , a variability which, however, i s decreased i f L V V i s replaced by L . McBean concludes that humidity scales better with a q s t a b i l i t y parameter based on the moisture flux instead of the heat flux. McBean further concludes that for every passive scalar (a passive scalar is a scalar whose variations do not significantly affect the buoyancy of an air parcel such as humidity in the present study) a new s t a b i l i t y parameter may be necessary, unless the scalar is highly correlated with temperature. In the present study the Tq correlation was generally higher for the more unstable cases (e.g. Figure 5.21), which may be one of the 185 a) 3 -\ b I 0 -2.0 O Ly-alpha (z' = 18.9 m) x KH1016 (z' - 18.9 m) * KH1011 (V = 11.0 m) — Hogstrom and Smedman-Hogstrom., 1974 x O S -1.5 •1.0 ''Ay -0.5 0.0 10' b) Cr \ b I 10° O Ly-alpha (z' = 18.9 m) x KH1016 (z1 = 18.9 m) * KH1011 (z' = 11.0 m) -i i i i i_ 10" 10° -*'AV F i g u r e 6.7 : Normalized standard d e v i a t i o n s of q v s . z ' / L ^ compared w i t h an e m p i r i c a l f i t by Hogstrom and Smedman-Hogstrbm, 1974 ( s o l i d l i n e ) (a) and on l o g - l o g p l o t (b) . 186 reasons why the magnitudes of the normalized humidity standard deviations are closer to the reference curve at large -z'/L values. V The large scatter observed in the humidity ratios is also a result of using a low integration limit. Spectral analysis showed (e.g. Figure 5.3b) that a considerable amount of energy is present at the large scales (which are also s t a t i s t i c a l l y very unreliable). This means that similarity theory might not be applicable anymore because similarity variables are based on local values and any experimental site i s also affected by the large-scale space and time inhomogeneities of the atmospheric motions (McBean, 1971). A similar argument holds for the scatter observed in the u and v components. 6.1.4 Covariances In the following is another test for the applicability of similarity theory to a suburban data set. Wyngaard et al. (1971) show that -u'T'/w'T' can be interpreted as the ratio of the buoyant production rates of stress and energy. Modifying the free convection scaling (to account for the fact that u'T' must vanish in free convection) they obtain an expression of the form -iFT'/vPT' = a <(> <t> (6.4) m h with 0 = 1 + 4.7z'/L (6.5) m v 0 = 0.74 + 4.7z'/L (6.6) h v Figure 6.8 compares this prediction (solid line) based on the Kansas data 187 4.0 0.0" 1 1 1 1--2.0 -1.5 -1.0 -0.5 0.0 Figure 6.8: Ratios of horizontal and vertical components of heat flux compared with an empirical f i t by Wyngaard et al. , 1971 (solid line). 188 (using a = 5) with the observations from the present study. The suburban results correspond very well with the rural reference. On the unstable side the ratio drops toward zero, which can intuitively be expected because in the free convection limit there should be no preferred horizontal direction, and therefore no correlation between u and T fluctuations. Considering the rough and inhomogeneous nature of the suburban surface the agreement between the two data sets i s surprising. One would expect that the horizontal temperature gradients introduced by the inhomogeneity of the surface would result in an anomalously high horizontal heat flux ( i f u' and T' are correlated). This could be due to small scale advection of sensible heat from warmer surface patches or large scale structures related to the urban heat island circulation. However, i t is also observed that the vertical heat flux over a suburban surface tends to be larger than that over adjacent rural areas (Clarke et al. , 1982; Cleugh and Oke, 1986) which may result in a possible cancellation of the two 'anomalies' when computing the ratio -u'T'/w'T'. Clarke et al. (1982) measure ratios of the two heat fluxes which are considerably higher than the Kansas curve and therefore the observations from the present study (e.g. the ratio is about 1 at z'/L = -2). They attribute their result to horizontal temperature gradients associated with the inhomogeneous nature of the urban surface. 6.2 Correlation coefficients 6.2.1 Momentum transfer correlation coefficients The correlation coefficients, r , presented in Figure 6.9a and uw 189 a) 10 0.8 0.6 0.4 0.2 0.0 -2.0 b) 1.0 0.8 -0.6 0.4 0.2 0.0 -2.0 O KD (z' = 18.9 m) — McBean. 1970 -1.5 O o 0 ° <5> i o o o o o •1.0 0.0 O SAT(1130) (z- = 18.9 m) x SAT(1127) (V = 18.9 m) O KD (z' = 18.9 m) * SAT(1126) (V = 11.0 m) — MOS prediction •1.5 •1.0 -0.5 0.0 Figure 6.9: Correlation c o e f f i c i e n t s vs. z'/L for momentum transfer (a) = V and heat transfer (b). The s o l i d l i n e i n (a) i n an empirical f i t by McBean (1970) to rural data and the s o l i d l i n e i n (b) represents the MOS prediction (see te x t ) . 190 plotted against z'/L are negative for a l l s t a b i l i t i e s . From relatively large values near neutral (0.4) the correlation decreases to a value of less than 0.2 at large instabilities. Thus the efficiency of the momentum transfer is decreasing with increasing instability. The solid line in Figure 6.9a represents an empirical f i t to rural data of the form r = -0.31(1 - 0.66 |z'/L I) (for -0.7 < z'/L < 0) from McBean (1970). Close I y I V to neutral and in slightly unstable conditions the present observations are considerably larger than the reference. 6.2.2 Heat transfer correlation coefficients The magnitude of the heat transfer correlation coeficients, r , as a wT function of z'/L is shown in Figure 6.9b. The solid line i s the MOS prediction derived by rewriting the correlation coefficient (defined in eq. 1.53): r _ = (u#/cr )(T*/tr ) (6.7) wT * w * T and substituting the normalized standard deviations with (6.1) and (6.2). In general the observations from the present study are higher than predicted by the similarity law and values observed by McBean (1970) (not shown here), however, the shape of the curve is followed. This result is consistent with Figures 6.4a and 6.6a, the former showing underprediction of the vertical velocity statistics by the suburban results and the latter agreement of the temperature statistics with the MOS prediction (note that the normalized standard deviations enter as the inverse in (6.7)). Intercomparison between the different sensors is good apart from the slightly higher values measured with the Kaijo-Denki compared to the 191 SAT observations, a feature already observed for cr /T- vs. -z'/L . The T * v differences between the upper and lower level data are small. 6.2.3 Moisture transfer correlation coefficients The moisture transfer correlation coefficients, r , and their wq variation with s t a b i l i t y is presented in Figure 6.10a. The solid curve is obtained through r = (u./cr )(q*/cr ) (6.8) wq w q and using eq. (6.1) and (6.3) to represent the normalized standard deviations. Although following the general trend the humidity correlation coefficients from the present study are lower than the similarity prediction over the entire s t a b i l i t y range observed. As noted for other humidity s t a t i s t i c s the variablity is large. Intercomparison between the different sensor combinations used reveals some scatter and slightly larger values for the SAT(1130)/Lyman-alpha combination, but in similarity with temperature there are only small differences between the upper and lower level measurements. As noted earlier r also depends on wq the temperature-humidity correlation and i t follows that a strong dependendence on z'/L cannot necessarily be expected. V 6.2.4 Temperature-humidity correlation coefficients The temperature-humidity correlation coefficients plotted against s t a b i l i t y (Figure 6.10b) exhibit considerable v a r i a b i l i t y with 192 © SAT(1130)/Ly-alpha (z' - 1 S.9 m) x SAT(1127)/KH1016 ( V = 18.9 m) * SAT(1126)/KH1011 ( V = 11.0 m) — MOS prediction x O © X © * X x o : * *# * * * I o * * © '*$**. © x x *©° i * * x v -2.0 •1.5 •1.0 -0.5 0.0 0.8 • © SAT(1130)/Ly-alpha ( V = 18.9 m) x SAT(1127)/KH1016 (z' = /fi.9 m) * SAT(1126)/KH1011 (z' = H.O m) © * © X * © © x * * X s * x © « * X * x -2.0 •1.5 •1.0 -0.5 0.0 Figure 6.10: Correlation coefficients vs. z'/L for moisture transfer (a • V and Tq (b). The solid line in (a) represents the M0 prediction (see text). 193 magnitudes ranging from 0.15 to 0.75. There is a slight tendency towards larger correlations with increasing instability. The lower level measurements exhibit the same amount of scatter and roughly the same magnitudes as those at the upper level. However, i t is important to note that the Tq correlation is less than the value of unity which is approached over 'ideal surfaces' (e.g. Swinbank and Dyer, 1967). A more instructive graph shows the dependence of the wq correlation on the Tq correlation (Figure 6.11). A clear relationship can be observed and larger r values are usually associated with larger r values. At wq Tq the low end both, r and r have roughly the same magnitude of 0.2 but Tq wq the one to one relationship breaks down for larger correlation coefficients. In the present study the largest r (and therefore r ) Tq wq values were associated with sunny days such as YD 192 and 194 and to a lesser extent on 188 and 195. The other days were marked by v a r i a b i l i t y but generally lower Tq magnitudes. 6.2.5 Comparison of correlation coefficients The relative values of correlation coefficients are of more interest than their actual values since the ratios are an indication of the relative transfer efficiencies of the fluxes. The variation of -r /r wT uw as a function of s t a b i l i t y and compared against an empirical f i t from rural data of the form |r /r I = 3|z'/L 1 1 / 4 (McBean and Miyake, 1972) 1 wT uw' 1 v 1 is plotted in Figure 6.12a. The ratios from the present study increase in an almost linear fashion with increasing instability. For the most unstable stratifications the effects of buoyancy make the transfer 194 195 a) 1 " \ o o b) -2.0 5,— -2.0 . O o O ft~"8"°~ ~ O SAT(1130)/KD (z1 = 18.9 m) — McBean and Miyake, 1972 — Kn/Ky from Businger et al., 1971 O o o •1.5 -1.0 -0.5 0.0 O Ly-alpha/KD (z' = 18.9 m) — McBean, 1970 O O -1.5 -1.0 Figure 6.12: Ratio of correlation coefficients vs. z'/L of heat transfer = V (a) and moisture transfer (b) to those of momentum transfer. The solid lines in (a) and (b) are empirical f i t s by McBean and Miyake (1972) and McBean (1970). The dashed line in (a) is K /K from Businger et al., 1971 H H 196 efficiency for heat about 4 times that for momentum. This large ratio is also caused by the low momentum correlations observed under unstable conditions (Figure 6.9a). The data points closest to neutral indicate a ratio of 1 which is in agreement with the idea that the mechanisms are similar for near neutral stratification. The observations from the present study are lower than the corresponding ratios observed by McBean and Miyake (1972) for near neutral and slightly unstable conditions. These lower ratios are mainly a result of the relatively high uw correlations measured in the present study compared to the rural reference (Figure 6.9a). The variation of -r /r with st a b i l i t y and compared against the wq uw McBean (1970) data of the form |r /r I =0.86(1 + 2.2|z'/L I) (solid 1 wq uw1 1 v 1 line) is given in Figure 6.12b. As was the case for -r /r the data s 6 wT uw suggest an almost linear increase of the ratios with increasing instability. At large -z'/L values the transfer efficency for moisture V is about 2.5 times that for momentum whereas near neutral the ratios drop to values of 0.4, indicating that momentum transfer is more efficient than moisture transfer. The present observations are again lower than the rural data. The st a b i l i t y dependence of -r /r should be interpreted wq uw with caution since i t was shown (Figure 6.11) that r also depends on wq r . Nevertheless these results indicate that near neutral the mechanisms Tq for the moisture and momentum transfers are different. Figure 6.13a presents r /r against stability. In general a l l wT wq values are larger than unity which shows that the transfer efficiency for heat i s larger than that for moisture at a l l s t a b i l i t i e s . This tendency 197 a) 5, v-3 O SAT(1130)/Ly-alpha (z1 = 18.9 m) x SAT(1127)/KH1016 (z' = 18.9 m) * SAT(1126)/KH1011 (z' = 11.0 m) x O x O o * x x* * * X X # O O * *x \ * * o o X O -2.0 -1.5 -1.0 -0.5 0.0 b) 5, O SAT(1130)/Ly-alpha (z' = 18.9 m) x SAT(1127J/KH10I6 (z1 = 18.9 ni) * SAT(1126)/KH1011 (z' = 11.0 m) X X \ O 9c xO x* * x* l^f* o o x O * o o 0.0 0.2 0.4 0.6 0.8 1.0 T9 Figure 6.13: Ratio of correlation coefficients vs. z'/L (a) and r (b) — V Tq for heat and moisture transfer. 198 is greatest for slightly unstable conditions, however, the scatter is large and again i t should be pointed out that r depends on the Tq wq correlation and not only on z'/L . Similar data presented by McBean V (1970) suggests a value of about 1.4 near neutral and 1.2 for z'/L^ = -0.6. The dependence of r /r on r is plotted in Figure 6.13b. The wT wq Tq transfer efficiency of heat compared to that of moisture i s considerably larger for small r T values. For increasing r T the temperature and humidity transfers become increasingly more similar and their ratio would probably reach unity for r T closer to one. It is only under these latter conditions that MOS applies ( H i l l , 1989). 6.3 Summary and discussion 6.3.1 Summary The turbulence intensities of the three velocity components show an almost linear increase with increasing instability, however, for u and v this behaviour is accompanied by scatter. The turbulence intensities are larger and increase faster with -z'/L for the horizontal components, cr /U is larger at the lower level than the upper level. For near neutral w conditions the ratios of cr/U, cr/U and cr/U are 0.27, 0.19 and 0.13, U V w respectively. These results agree well with suburban observations by Clarke et al. (1982) but are higher compared to rural observations for the u component by a factor of about 2 for near neutral conditions. MOS applied to the normalized standard deviations predicts a 1/3 proportionality to (-z'/L ) in the free convection limit. Rural 199 observations support the similarity prediction for w but less for u and v. The present suburban observations exhibit the required slope for a l l three velocity components from -z'/L > 0.3 for w (from z'/L^ > 0.5 at the lower level) and from -z'/L > 0.3 for u and v. The results from the horizontal components are marked by some scatter. Compared to the rural reference the cr /u # magnitudes from the present study are consistently lower. This is in agreement with the suburban results presented by Clarke et al. (1982). In the neutral limit the normalized velocity standard deviations suggest values of 2.3, 1.7 and 1.2 for u, v and w, respectively. These are in good agreement with other (sub)urban studies and the rural reference. The vertical velocity standard deviations are shown to be proportional to a velocity scale combining the the f r i c t i o n velocity and the free convection velocity. Comparison with other (sub)urban studies shows that this relationship seems to be general. The ratios measured at the lower level are slightly higher than the upper level ones, especially for larger i n s t a b i l i t i e s . It cannot be concluded i f this effect is real or due to the fact that u, values from the upper level were used in the computation of z'/L . This would result V in a slight shift towards larger instab i l i t i e s and better agreement with the upper level data. The normalized temperature standard deviations follow the free convection prediction very well and show the predicted proportionality to -1/3 (-z'/L ) from -z'/L > 0.2 at both levels. Agreement with the rural V V reference curve and the suburban observations from Clarke et al. (1982) is good. The normalized humidity standard deviations exhibit a lot of 200 scatter, are larger than the reference for slightly unstable conditions and do not follow the -1/3 slope predicted by similarity theory in the free convection limit. The -u'T'/w'T' ratios representing the buoyant production rates of stress and energy correspond well with a modified free convection prediction, showing large values close to neutral then decreasing rapidly towards ratios of less than 0.5 for -z'/L > 1.5. This disagrees with Clarke et al. (1982) who observe ratios larger than unity which they attribute to a large horizontal heat flux caused by the inhomogeneous terrain. The efficiency of the momentum transfer decreases with increasing i n s t a b i l i t y as shown by the correlation coefficients r which are about J 3 uw 0.40 near neutral and less than 0.2 for larger -z'/L . The magnitudes of V r measured in the present study are considerably higher than those of uw the reference data from a rural surface for near neutral and slighly unstable conditions. The heat transfer correlation coefficients measured in the present study follow the similarity prediction but are higher than the reference curve. Near neutral r is about 0.3 and asymptotically reaches a value of about 0.6 at higher i n s t a b i l i t i e s . No differences between the upper and lower level measurements can be observed. The scatter in the humidity correlation coefficients is large but they are generally lower than the similarity prediction, r is also influenced by wq the temperature-humidity correlation and i t was shown that high wq correlations are associated with high Tq correlations and vice versa. The ratios of the correlation coefficients are of prime importance in evaluating the relative transfer efficiencies of two fluxes. The suburban 201 results in the present study suggest an almost linear dependence of r /r on s t a b i l i t y with values of about 1 near neutral and increasing wT uw to 4 for z'/L = -1.8. These ratios are lower than the rural reference V for near neutral and slightly unstable conditions. This is mainly caused by the high momentum flux correlation coefficients observed in the present study under these conditions. A similar linear -z'/L dependence is observed for r /r , with again lower magnitudes in the suburban data wq uw compared to the reference. For slightly unstable and near neutral conditions ratios of less than unity are observed in the present study. The r /r ratio exhibits a lot of scatter but is generally larger than wT wq unity for a l l s t a b i l i t i e s , more so under slightly unstable conditions. This suggests that the transfer mechanisms for heat and water vapour are different, even close to neutrality, r ^ /r shows a strong dependence on r and the ratio decreases towards unity with increasing r . Tq Tq 6.3.2 Discussion In respect to the applicability of MOS to the suburban integral s t a t i s t i c s results no clear conclusions can be drawn. Similar to the (co)spectral results in Chapter 5 some of the s t a t i s t i c s agree well with the similarity predictions (e.g. oy/T*) whereas others do not obey MOS (e.g. cr /q»). However, i t should be noted that even in the homogeneous q surface layer humidity does not necessarily follow MOS (e.g. McBean, 1971). Those observations which show good agreement of humidity s t a t i s t i c s with similarity functions (e.g. Swinbank and Dyer, 1967; Hogstrom and Smedman-Hogstrom, 1974) are probably attributable to r Tq values which are close to unity. In general (with the noted exception of 202 q) the turbulence intensities, normalized standard deviations and correlation coefficients are a function of z'/L and follow the trends V given by the free convection similarity predictions. However, the magnitudes are often different from the ones observed in reference data over 'ideal' sites. Most notable are the relatively small cr /u # values which parallel the lower non-dimensional dissipation values for TKE observed in 5.3.1. The discussion of the TKE budget in 5.3.1 in respect to the Clarke et al. (1982) dissipation data indicates that the production of TKE was greater than the dissipation and thus transport processes are important. It is therefore not surprising that differences from rural reference data occur. The low cr /u~ values suggest that the momentum transfer is an w w efficient process at the present study site. The results in the previous section indeed show that the momentum transfer correlation coefficients are very high (larger than rural reference data) under near neutral and sligh t l y unstable conditions which w i l l result in smaller cr /u # ratios i f the standard deviations remain roughly the same. Enhanced transfer can qualitatively be explained through wake diffusion and horizontal inhomogeneity of the flow. The wake diffusion effect results in a flow with enhanced di f f u s i v i t y in the roughness sub-layer by the superposition of turbulent wakes generated by individual roughness elements upon the shear flow (Thorn et al., 1975). Dynamically, the enhanced vertical d i f f u s i v i t y for momentum may be associated with the 'horse-shoe vortex' which surrounds and extends downstream from buildings immersed in shear flow creating a region of interacting wakes (Raupach et 203 al. , 1980). These are characterized by small eddies which e f f i c i e n t l y transport momentum across the mean streamlines. Similar to momentum, the transfer efficiency of heat is observed to be larger than the reference. Although wake diffusion can be contributory to an enhancement of the diffusion of heat the possibility that buoyant convective effects are largely responsible for r enhancement is more appealing because i t can account for the observed s t a b i l i t y dependence. In the case of three-dimensional buildings free convection (e.g. off vertical walls) can be maintained by discrete heat sources or sinks (which are rather abundant in urban areas) to effectively enhance heat transfer (even in neutral conditions). It should be noted that for unstable st r a t i f i c a t i o n the vertical transfer of heat is in any case augmented by buoyancy which causes higher transfer coefficients for sensible heat than for momentum. The relatively large <r /q* ratios measured under sli g h t l y unstable conditions probably result from the generally low transfer efficiency of moisture and low o^/u* values (note that u w is in the definition of q*). The different magnitudes observed between the suburban and reference results in combination with the large transfer efficiencies of heat and momentum (low for humidity), which can be explained through wake diffusion effects attributable to the bluff-bodies in this environment, suggest that the present measurement levels were sometimes within the roughness sub-layer, i.e. below z*. This result has implications for measurement techniques which try to evaluate the turbulent momentum, 204 energy and mass fluxes on the basis of profile approaches which assume logarithmic profiles and knowledge of the eddy d i f f u s i v i t i e s . Similar to the transfer efficiencies the eddy d i f f u s i v i t i e s are most probably affected and modified by the underlying inhomogeneous surface. There is merit in exploring this topic in more detail because the turbulent fluxes presented in the following Part III are not only measured using the eddy correlation method but also using the gradient-flux approach. Central to the success of the flux-gradient approach, which relates the turbulent fluxes to the local mean gradients (for a review and c r i t i c a l evaluation see Dyer, 1974, Yaglom, 1977 and Hogstrom, 1988), is knowledge of the turbulent d i f f u s i v i t i e s . Different techniques require different degrees of specification. For example, the profile method requires complete determination of K , whereas the Bowen ratio-energy M, H, E balance method relies only on the assumption K = K (Thorn, 1975). H E It was pointed out in 1.3.3 that an estimation of the eddy d i f f u s i v i t i e s can be obtained by relating the ratio of the correlation coefficients to the ratio of eddy d i f f u s i v i t i e s using (1.59) - (1.61). McBean (1970) points out that experimental evidence indicates that the term in the square bracket in (1.59) is near unity for unstable stratifications. This can be expected i f the fluctuations are created locally by the vertical velocity fluctuations acting on the corresponding profiles. Of course (1.59) - (1.61) are only applicable to the homogeneous surface layer. In the roughness sub-layer with modified gradients the interpretation of the ratio of the correlation coefficients as the ratio of the corresponding eddy d i f f u s i v i t i e s becomes more 205 d i f f i c u l t . With these cautionary remarks in mind, the results in Figure 6.12a can therefore be interpreted as the ratio of K /K to within a factor of H M ( I T /cr ) [(3U/az)/(3T73z+r)] (see eq. 1.59) which is dependent on z'/L. T u v The suburban results are lower than McBean*s rural observations especially for near neutral and moderately unstable conditions. The dashed line in Figure 6.12a indicates an empirical f i t based on directly measured fluxes and gradients over a rural surface by Businger et al. (1971). The Businger et al. data suggest K /K = 1.35 for neutral H M conditions a ratio which increases slowly with increasing instability. There is some controversy with regard to the neutral value and for instance Dyer and Hicks (1970) and Hicks (1976) report a value of 1.12. (Note that some of the controversy is caused by the adaption of different von Karman constants used in different studies). The results in Figure 6.12a suggest that the ratio of the eddy d i f f u s i v i t i e s of heat to those of momentum are lower in the suburban environment compared to reference data under near neutral and moderately unstable conditions. This i s mainly due to the efficient momentum transfer observed under these conditions (Figure 6.9a). The fact that the correlation coefficients, which are a measure of transfer efficiency, are higher than the rural references, suggests that the eddy d i f f u s i v i t i e s are larger too. This is a commonly observed characteristic of a roughness sub-layer. Above forest or savannah in neutral or near neutral conditions, Garratt (1978a), Raupach (1979), Raupach and Thorn (1981), Raupach and Legg (1984) and Fazu and 206 Schwerdtfeger (1989) observe enhancement factors (defined as ratios of observed eddy d i f f u s i v i t i e s to expected values in the homogeneous surface layer) of 1.7, 1.1, 1.1, 1.0 and 1.65 for momentum and 1.9, 2.2, 3.0, 2.0, and 2.5 for heat, respectively. The ratio K/K is observed to be H N 2.0 (Raupach, 1979), 2.0 - 3.0 (Raupach and Thorn, 1981) and 1.6 (Fazu and Schwerdtfeger (1989). According to Raupach (1979) the enhanced d i f f u s i v i t y for momentum does not change appreciably with s t a b i l i t y whereas the di f f u s i v i t y for heat increases rapidly at small i n s t a b i l i t i e s (-z'/L < 0.1) before decreasing again and assuming an intermediate value V with increasing instability (up to -z'/L^ = 0.5). Fazu and Schwerdtfeger (1989) show that K is a function of the M surface roughness with the enhancement factor decreasing from 2 over a surface characterized by a low density distribution of roughness elements to about 1 for a surface with a high density of roughness elements. Using their relationship and the dimensions of the roughness elements for the Sunset site indicates an enhancement factor of about 1.5 (their Figure 7). Data available for the humidity transfer are less conclusive. Based on data above forests Raupach (1979) and Raupach and Thorn (1981) measure an enhancement factor for K of about 2 near neutral (similar to their E heat diffusivity) which increases to about 4 at z'/L = -0.25. The ratio V K /K i s of central importance in micrometeorology since the Bowen H E ratio-energy balance approach used for the determination of the fluxes of sensible heat and moisture on the basis of vertical temperature and humidity gradients (eq. 3.2) relies on the assumption of equality of 207 these two eddy d i f f u s i v i t i e s under a l l conditions. The interpretation of the results from the present study is again based on the assumed close relationship between r /r and K/K . Figure 6.13 shows that the wT wq H E r /r ratios are generally larger than unity, more so under slighly wT wq unstable conditions than at larger inst a b i l i t i e s , and are a function of r (Figure 6.13b). Tq H i l l (1989) shows that i f MOS is valid for humidity as well as temperature then r = r . Differences between the correlations are wT wq ascribed to the differential action of buoyancy on the humidity and temperature f i e l d . This can only occur i f temperature and humidity fluctuations are not perfectly correlated. This reasoning was originally put forward by Swinbank and Dyer (1967) who attributed the equality of the eddy d i f f u s i v i t i e s to the high Tq correlation coefficient of 0.9 measured in their study. Further observational support for this is given by Phelps and Pond (1971) and McBean and Miyake (1972) who suggest that when r_ is close to unity and moisture is a passive scalar the heat and moisture fluxes have similar characteristics to each other but when the r_ correlation is small the efficiency of the moisture transport is also decreased. The same is observed in the present study (Figure 6.11). Figures 6.10b and 6.13b show that r was less than unity and generally Tq lower than 0.6 resulting in relatively low r magnitudes and a r /r J wq ° wT wq ratio which is larger than unity. Less than perfect correlations can be caused by horizontal inhomogeneities, lack of stationarity or, for unstable conditions, the downward advection of air from the mixed layer (as observed in Section 208 4.2) where the Tq correlation may be smaller or have the opposite sign to that near the surface. Inhomogeneity in the surface structure can result in widely different locations in the sources of heat and water vapour. This i s especially true in the urban environment where the source locations not only vary in the horizontal but in the vertical as well. Such disparate source locations produce different average profiles of scalars within the canopy and imply differing transport out of the canopy which leads to a less than perfect scalar-scalar correlation. The foregoing results and discussion show that the equality of eddy d i f f u s i v i t i e s i s only applicable in a homogeneous surface layer with humidity acting as a passive scalar and a Tq correlation near unity. Despite these stringent requirements some authors have reported similar eddy d i f f u s i v i t i e s over inhomogeneous terrain. Denmead and Bradley (1985) for example observe K = K based on profile and eddy correlation H E measurements at heights of 22 and 27 m over 15 - 20 m t a l l trees. Raupach and Legg (1984) suggest the equality i f moisture acts as a passive scalar and is being released from the same source as heat, however, they do not provide observational support. Based on the present results and the qualitative assessement of the influence of disparate source and sink distributions for heat and moisture on the Tq correlation and therefore on the transfer efficiency of moisture, the larger transfer efficiencies of heat compared to those of moisture are explicable. This inequality is observed over the entire s t a b i l i t y range encountered (-1.8 < z'/L < -0.1). This result c a l l s for V a very careful application of the flux-gradient approach in the suburban 209 environment. In i t s favour works the fact that the largest inequalities in the transfer efficiencies of heat and moisture are observed under near neutral and slightly unstable conditions. These are usually associated with the evening and nighttime hours when the fluxes are relatively small. Towards larger instab i l i t i e s (daytime conditions with large fluxes) the ratio of the two efficiencies decreases towards unity and the influence on the gradient-flux measurements should be less. Another requirement for the applicability of the gradient approach i s constancy of fluxes with height. This topic is further explored in Chapter 7. As pointed out by Mulhearn and Finnigan (1978), the only way to be certain of flux estimates over a very rough terrain is to use eddy-correlation methods. In the following Part III of this thesis results from energy balance measurements w i l l be presented whereby the turbulent fluxes of sensible and latent heat were obtained using both the Bowen ratio-energy balance approach and eddy-correlation method. In light of the above, eddy-correlation measurements are expected to yield more reliable and representative flux estimates than those obtained from the flux-gradient approach. 210 PART III : ENERGY BALANCE MEASUREMENTS 211 CHAPTER 7: URBAN ENERGY BALANCE RESULTS 7.1 Introduction This chapter presents the energy balance results obtained during 7 days from YD 187 - 196 (for main weather characteristics during this period see Table 3.2). The observations were not continuous during these 7 days rather they represent individual periods, e.g. from the morning until the evening or from the afternoon until the morning of the next day. This was due to changing weather conditions and frequent maintenance of the turbulence sensors. The turbulent fluxes measured by eddy correlation were obtained from 20 min averages, three of which are combined to give the one hour averages. The 'hourly' averages of the Bowen ratio measurements are a composition of two twenty minute periods within the corresponding hour (see 3.3.3). The hourly values presented in the figures in this chapter are centered on the half hour. The anthropogenic heat flux density is too small to be plotted on the figures, however, when necessary was included in the computations. The notation used for the various terms in the energy balance is as follows. Directly measured fluxes using the eddy correlation approach are denoted without any additional subscripts (i.e. Q , Q and AQ , where the H E S latter is computed from eq. 2.2 as the residual of the energy balance and therefore contains a l l measurement errors and any advective effects since AQ was not measured). The parameterized heat storage is AQ (eq. 2.3) A SP and the turbulent fluxes obtained from the Bowen ratio-energy balance approach (eq. 3.4 and 3.5) are Q and Q , respectively. When directly 212 measured sensible heat fluxes and an estimation of the Bowen ratio using the gradient approach (3 ) are available the latent heat flux can be G obtained as: Q = Q /3 (7.1) EHB H G This leads to a further possibility of obtaining the storage heat flux through: AQ =Q* + Q - Q - Q (7.2) SHB F H EHB where AQ again contains measurement errors and the advection term. SHB The average diurnal energy balance (hourly ensemble averages) and two case studies representing parts of two days are presented in Section 7.3. In Section 7.4 the residual heat storage is compared to the one obtained using the parameterization. The Bowen ratios obtained from the directly measured fluxes and from the gradient method are compared to each other in Section 7.5. The chapter ends with a discussion of the implications of these findings for methods to obtain the storage heat flux. The Bowen ratio-energy balance approach only applies i f the fluxes are 'constant' with height, i.e. no vertical divergence or convergence. In the present study the turbulent fluxes were measured at two different levels which enables the analysis of the height dependence of the fluxes. Therefore i t should be possible to determine i f a 'constant' flux layer is present. These results are presented in the following section. 213 7.2 C o m p a r i s o n o f t u r b u l e n t f l u x e s f r om two l e v e l s The homogeneous surface layer is characterized by 'constant* (±10%) fluxes with height. Analysis of the height dependence of the turbulent fluxes between the two levels can therefore contribute to the evaluation whether z' > z* and help in the assessement i f the turbulent fluxes are representative of the underlying suburban surface or i f they are possibly affected by individual surface patches. The hourly sensible heat flux values from the upper (z' = 18.9 m) and the lower (z' = 11.0 m) level are presented in Figure 7.1. The observations (crosses) show a clear tendency towards higher values at the -2 lower level in particular for Q larger than about 150 W m . The dashed H _2 line in Figure 7.1 is a linear regression with an intercept of 0.4 W m and slope of 1.15. This trend is reduced for smaller fluxes. The mean -2 -2 sensible heat flux at the upper level was 120 W m compared to 138 W m at the lower level. The coefficient of determination (r ), index of agreement (d^) and root mean squared difference (RMSD) are 0.97, 0.98 and _2 32 W m , respectively (for a discussion of these s t a t i s t i c a l indices refer to Willmott, 1981). These values can be compared to the results from the intercomparison of the two SAT systems used at the upper level _2 (stars) which yields average fluxes of 183 W m for both sensors (note _2 that this value is different from the 120 W m above because the number of data points is different), r 2 = 0.99, d t = 0.99 and RMSD = 11 W m-2. -2 This latter value compares well with an inter-sensor RMSD of 13 W m observed by Cleugh (1990) at the present site and measurement level. It is assumed that the inter-sensor RMSD is due to instrument and data 214 0 SO 100 ISO 2 0 0 250 3 0 0 3 6 0 400 450 qM (SAT(II27) o i > ' - ia.a m) (r m-*) F i g u r e 7 .1 : Comparison of hour ly Q measured at the upper l e v e l ~~™~——-—————— . H • (SAK1127)) v s . that at the lower l e v e l (SAT(1126)) ( c r o s s e s ) . A l s o comparison with an a d d i t i o n a l sensor (SAT(1130)) at the upper l e v e l ( s t a r s ) . F i g u r e 7.2: Comparison of hour ly Q_ measured at the upper l e v e l (KH1016) v s . that at the lower l e v e l (KH1011) ( c rosses ) . A l s o comparison with an a d d i t i o n a l sensor (Ly-alpha) at the upper l e v e l ( s t a r s ) . 215 logging d i f f e r e n c e s alone. The re s u l t s i n Figure 7.1 suggest that the higher Q values at the lower l e v e l r e f l e c t a r e a l e f f e c t of the H d i f f e r e n c e s between the two leve l s . The increase i n sc a t t e r at the lower l e v e l may also be due to the decrease i n homogeneity of the sensible heat f l u x f i e l d closer to the surface. The latent heat fluxes measured by the Krypton hygrometers (Figure 7.2; crosses) are of s i m i l a r magnitude at both l e v e l s with a s l i g h t tendency towards higher values at the lower l e v e l f o r large Q . The _2 averages over a l l hours are 65 and 68 W m f o r the upper and lower l e v e l , respectively. The r 2 , and RMSD are 0.96, 0.99 and 12 W m"2, respe c t i v e l y . Intercomparison between the two sensors (Lyman-alpha and Krypton hygrometer) from the upper l e v e l (stars) i s s a t i s f a c t o r y , however, the latent heat fluxes measured by the Lyman-alpha sensor tend _2 to be s l i g h t l y lower (89 vs. 76 W m for the Krypton and Lyman-alpha hygrometer, r e s p e c t i v e l y ) . This i s also r e f l e c t e d i n the intercept and -2 slope of a l i n e a r f i t which are -9 W m and 0.96. The s t a t i s t i c a l -2 indices of the inter-sensor comparison are 0.94, 0.97 and 17 W m f o r 2 r , d^ and RMSD, respectively. Possible explanations f o r the observed d i f f e r e n c e s between the two types of sensors are: 1) Erro r s i n the evaluation of the c a l i b r a t i o n c o e f f i c i e n t s f o r the Lyman-alpha sensor (Appendix A.2). The Lyman-alpha c a l i b r a t i o n c o e f f i c i e n t s derived from Figure A.1 can vary by as much as ± 5% which would r e s u l t i n an error of the same s i z e i n the latent heat f l u x ; 2) The co r r e c t i o n f o r the Krypton hygrometer includes assumptions which can a f f e c t the magnitude of the oxygen term derived from (A.14). In p a r t i c u l a r the absorption c o e f f i c i e n t f o r oxygen, k , i s not well known (Tanner, 1990; personal communication). 216 Based on the available data i t is not possible to determine which system is closest to the 'true' latent heat flux, but the differences are generally less than about 15%. Figure 7.3 (for YD 195; 20 min averages) shows that both the oxygen and density corrections applied to the Krypton hygrometer measurements are substantial and can be as large as 20 W m~2 (~ 30% of the uncorrected flux). Both corrections depend on the magnitude of the sensible heat flux (eq. A. 14 and A. 17). (Note that the strong va r i a b i l i t y present in the latent heat flux was also associated with variable Q* values (not shown) due to clouds). Given the fact that the calibration coefficients and the correction procedures applied to the Krypton hygrometers were almost identical at both levels and therefore any errors contained in the correction would affect the results in the same way, i t can be concluded that the height variation in the latent heat flux was minimal and in any case smaller than that observed for the sensible heat flux. The diurnal variation (ensemble averages of hourly values) of the sensible heat fluxes from both levels is shown in Figure 7.4a. As observed in Figure 7.1 the largest differences between the two occur for large sensible heat fluxes, i.e. mainly during the daytime. Between 800 -- 1700 LAT the sensible heat flux is 12 to 21% (with a typical value of 15%) higher at the lower level. The sensible heat flux convergence observed in Figures 7.1 and 7.4a should result in a heating rate of about o -1 -2 17 C hr (assuming Q = 300 W m ) or in net radiative flux divergence. H Such a heating rate was obviously not observed and the net radiative flux convergence is usually insignificant under clear, daytime conditions 217 300 Figure 7.3: Diurnal variation of 20 min values of corrected and uncorrected latent heat fluxes with associated oxygen and density correction terms for YD 195. 218 2 2 2 2 2 2 2 2 3 1 3 5 5 6 6 6 6 6 6 6 6 6 3 2 Figure 7.4: Diurnal v a r i a t i o n of sensible (a) and l a t e n t (b) heat f l u x e s measured at the upper and lower l e v e l . The numbers i n (a) in d i c a t e the number of values used i n the averaging. 219 conditions (e.g. Arya, 1988, p. 34ff). A mechanism which could account for the observed divergence is based on the possibility of advection of heat plumes from surrounding dry areas which would especially affect the lower level. The midday hours are usually characterized by relatively unstable conditions. Schmid (1988) shows that the size of the source area of the sensible heat flux is dependent on the atmospheric s t r a t i f i c a t i o n and decreases with increasing instability. This means that the flux measured at a given level may be less representative of the underlying terrain under unstable conditions since the correspondingly smaller source area is less likely to include a representative sample of the surface conditions. With these small source areas the immediate surroundings of the observation site play a large role and i t is more li k e l y that the sensor at the lower level is preferentially influenced by a particular surface type. The tower site used in the present study is located in a transformer substation (e.g. Figure 3.4) and i t is possible that the measurements at the lower level under unstable conditions are affected by the gravel surface of this substation or other relatively warm surface patches nearby. The diurnal variation (ensemble averages of hourly values) of the latent heat fluxes measured at both levels is shown in Figure 7.4b. In general agreement between the two levels is good (as observed in Figure 7.2). Differences occur between 800 - 1400 LAT when Q at the lower level E is on average about 10% (4 - 13%) larger than Q at the upper level. In E the afternoon the observations from the two levels agree with each other. Unlike for the sensible heat flux the differences between the two levels seem to depend more on time than magnitude but are within the measurement 220 error. The sensible heat flux divergence observed during most of the daytime suggests that the measurement levels, in particular the lower one, were sometimes below z*. Based on the latent heat flux results alone one could get the impression that a homogeneous surface layer exists at the present site. This is somewhat deceptive considering that the turbulence moisture s t a t i s t i c s presented in Part II were often different from reference data, did not seem to follow MOS and were most probably influenced by the entire PBL. 7.3 A v e r a g e e n e r g y b a l a n c e and two c a se s t u d i e s The diurnal variation of the ensemble averages of the energy balance components based on 7 days of measurements between YD 187 - 196 is given in Figure 7.5a. The number of samples used in the computation of the ensemble averages are the same as in Figure 7.4a. (Note that the morning period is represented by a few samples only). This section also includes two examples of energy balances of individual days (Figures 7.6a and 7.7a). YD 192 and 195 were chosen because continuous measurements were available during a substantial part of these days. Observations from other days were of a similar nature in regard to the trends and magnitudes of the fluxes but marked with more va r i a b i l i t y caused by the presence of clouds. In the following, the main characteristics of the energy balance components wi l l be described in reference to the average diurnal energy balance in Figure 7.5a. The two case studies exhibit the same general features as observed in the average energy balance and w i l l 221 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 LAT Figure 7.5: Average energy balance at the Sunset site (a) and average Bowen ratio (£) (b) for YD 187 - 196. 222 223 a) 500 6 _ » 300 3 200 ! £ 100 * «• + °H _ q, x Ms O • • • *) S F 2000 LAT b) a 3 ~3 » - O B — © - O soo LAT Figure 7.7: Diurnal variation of energy balance components (a) and the ratios of fi and AQ /Q*. (b) for YD 195. s.sp 224 not be discussed separately. The peak in the net radiation occurs shortly after noon which is different than observed under cloudless skies (Figure 2.6b). This and the var i a b i l i t y observed in the daytime Q* values is probably a result of the variable cloud conditions encountered during the present study period. The net radiative input is mainly dissipated through Q which peaks at H around noon and maintains relatively large values into the late afternoon. Other studies (e.g. Yap and Oke, 1974, Kalanda et al., 1980, Ching et al. , 1983; Cleugh and Oke, 1986 (Figure 2.6b); Grimmond, 1988; Kerschgens and Kraus, 1990) observe maximum Q values which occur some H time after the peak in Q*. The relatively early peak and jagged appearance of the Q curve in the present study may be attributable to H the small sample size from a variety of cloud conditions. The high Q H values observed in the afternoon are a characteristic feature for relatively dry sites and can be related to the diurnal variation of convective instability which is usually highest in mid-afternoon associated with high surface temperatures. The evening decline of Q is H less rapid than i t s increase in the morning which appends a t a i l to the curve. The relatively high Q fluxes observed in the evening when Q* is H low or even negative are a result of the large energy release from heat storage which is augmented by a s t i l l unstable atmosphere. The latent heat flux peaks in the middle of the afternoon and similar to Q remains large and positive until close to midnight. Whereas the H t a i l in the curve of the sensible heat flux is often observed the Q t a i l E is a less characteristic feature of suburban sites and e.g. is not 225 present in the results from Cleugh and Oke (1986) (Figure 2.6b) or Grimmond (1988). Comparison between the Cleugh and Oke and the present study is also made d i f f i c u l t because Cleugh and Oke (1986) calculate Q as the residual of the energy balance (which includes a parameterized storage heat flux based on the linear regression model by Oke et al. (1981)) and because surface moisture conditions are different (the Cleugh and Oke (1986) observations followed a very wet early summer). Similar to Q , the Q t a i l may be caused by energy being released from storage which H E helps maintaining evaporation into the s t i l l convective atmosphere. The storage heat flux is characterized by a sharp increase in the early morning hours and more or less constant values until the afternoon. About two hours before the net radiation becomes negative the net heat storage changes sign. The largest losses occur just after the sign reversal in Q*. At night there is almost a balance of net radiation drain supplied from storage. The storage heat flux, AQs> in Figure 7.5a obtained as the residual of the energy balance is the f i r s t of i t s kind for an urban environment. It is different from the parameterized one, AQsp, in three ways: 1) in the morning AQg is larger and reaches an earlier peak than AQgp; 2) during midday and in the afternoon AQ is smaller than predicted by the model; 3) a marked dip in AQg (large heat release from storage) just after the evening transition period is not represented in AQgp. Figure 7.5b shows the average (computed as the ratio of the sums of the sensible to latent heat fluxes) diurnal variation of the Bowen ratio for three different studies. Absolute agreement of values is not to be 226 expected because different sites, years and sensors are involved, rather, the data il l u s t r a t e the range of conditions that can be observed at a suburban site. The 'Sunset (1978/80)' data, representing averages from two years, are from Oke and Cleugh (1987) who measured 6 using di f f e r e n t i a l psychrometry. The St. Louis data were obtained during a short term study (parts of three days) over an industrial site as part of the RAPS programme using directly measured Q and Q (Ching, 1985; H E personal communication). During daytime the (3 values from the Sunset (1978/80) study are f a i r l y constant and less than unity indicating water is available for evapotranspiration. The daytime values observed in the present study are almost twice as high. During the same daytime period the St. Louis values are highly variable and remain large in the evening indicating the importance of the sensible heat flux even after the transition period. Because of the small sizes of the turbulent fluxes the Bowen ratio i s generally unreliable during most of the nighttime and the morning transition periods. The Bowen ratios for the two case studies (Figures 7.6b and 7.7b) have slightly more daytime v a r i a b i l i t y but are otherwise in general agreement with the averaged observations. The above Bowen ratio results indicate that the present measurements represent rather dry summer conditions. Because of the temporal differences between the storage heat flux and the net radiation, i t is interesting to study the behaviour of the ratio A = AQs/Q* through the diurnal cycle. The observations from the three studies presented in Figure 7.8a are a l l based on AQg values derived as the energy budget residual, however, only the present and the St. Louis study have directly measured turbulent latent heat fluxes whereas the 227 Figure 7.8: Diurnal variation of the average ratios A = AQs/Q* (a) and x = Q /Q* (b) from this and other studies. 228 Sunset (1978/80) study derives Q from Q /B . The results from the E H G present study differ from the other observations and show a steady decrease during the daylight hours as the day progresses. A for the St. Louis data is more variable during the daytime (reflecting the small sample size and possible advective influences) whereas the results from the 'Sunset (1978/80)' study (Oke and Cleugh, 1987) exhibit an almost constant value of A = 0.25. A based on the parameterized heat storage is not able to follow the temporal trend set by the present observations, remaining too constant during the daytime. Just after the Q* sign reversal in the evening a l l studies exhibit a positive peak. This is more pronounced in the present study and caused by the large heat storage release observed at the same time (Figure 7.5a). Later in the night the net radiative loss is almost completely supplied from the ground heat reservior (A = 1). At the times of day-night transition a l l of the ratios tend to become unstable. The results from the two individual days (Figures 7.6b and 7.7b) are similar in respect to the trend and magnitudes observed in the ensemble averages. The nature of the asymmetry in Q is clearly displayed in Figure 7.8b H which shows the diurnal variation of x = Q /Q*- This is a useful ratio of H two important energy fluxes which is used in air pollution dispersion modelling. Q is a controlling parameter for the evolution of the PBL H height which determines the mixing volume available for the dispersion of pollutants. Note that both energy components used in this ratio are directly measured in a l l four studies indicated in Figure 7.8b. During daytime the results from the present observations are sli g h t l y higher than observed in the other two Sunset site studies, however, a l l studies 229 show an increase in x from the morning towards the evening. This can be attributed to the relatively high Q values observed in the late H afternoon which do not decrease in accord with Q*. The ratios during the transition periods are unstable and not worth considering. 7.4 Comparison of residual and parameterized storage heat fluxes The importance of the storage heat flux in urban climatology and the problems associated with i t s determination have been mentioned in 1.2. Possible methods to obtain the storage heat flux are outlined in 2.2.2, one of the most promising and best developed ones being the parameterization of the storage heat flux in terms of the net radiation and using a detailed surface description for the determination of the empirical coefficients (Grimmond et al. , 1991). The vali d i t y of these models has yet to be subjected to any form of test because of the absence of directly measured storage heat fluxes. Since the 'true' storage heat flux is usually not known and directly measured latent heat fluxes have until now not been readily available the model output has had to be validated against AQ derived from (7.2). The present study provides S8H the f i r s t longer term set of simultaneous directly measured sensible and latent heat fluxes. This enables the computation of the storage heat flux as the residual of the energy balance (AQ,.)- It is therefore valuable to compare the residual storage heat flux from the present study with the parameterization scheme from Grimmond et al. (1991) in more detail. Hourly AQs and &Qsp are compared with each other in Figure 7.9a. For positive storage heat fluxes the magnitudes derived from the model are -200 500 1000 1500 2000 2500 LAT Figure 7.9: Hourly residual (AQ_) vs. parameterized (AQ_p) storage heat fluxes (a) and comparison of storage heat fluxes obtained as the average residual, parameterized using (2.3) and the residual using (7.2) (AQ ) (b). SHB 231 often larger than L\Q^. The opposite i s true for negative fluxes which tend to be underpredicted by the model. As shown below this i s especially true for the early evening hours whereas the negative values measured during nighttime agree well. The diurnal variation of the average storage heat fluxes is shown in Figure 7.9b. Starting from midnight AQ_ and AQ s p agree well until the fluxes reverse sign. In the early morning hours AQ_ rises sharply and is larger than AQ_p- A maximum AQ_ value i s observed about two hours before noon. During most of the remaining daytime hours the residual storage heat flux tends to be lower than the model output. During the evening transition period the two curves converge but just before the sign reversal of Q* (1830 LAT), AQ_ drops more rapidly resulting in larger negative values compared to AQ_ p. Afterwards the residual heat storage slowly decreases to the level of AQsp. Also indicated on 7.9b is the storage heat flux obtained from (7.2). AQ and SP AQ are in very good agreement for most hours and only during the SHB evening is AQsp unable to predict the large observed heat storage release. This latter difference and the good agreement otherwise between the parameterized storage heat flux and AQ has been observed in SHB previous studies (e.g. Oke and Cleugh, 1987; Grimmond et al., 1991). (The unreal is t i c a l l y large AQ value in the early morning is due to a very SHB small negative Bowen ratio measured at this time). In previous studies (Oke and Cleugh, 1987; Grimmond, 1988; Grimmond et al. , 1991) a tendency for the storage heat flux to peak before noon has been observed. This hysteresis behaviour is one characteristic of the storage heat flux model used in the present study. Figure 7.10 shows the storage heat fluxes from the different methods plotted against the net 232 Figure 7.10: Hysteresis loop relation between residual (AQg)' parameterized (AQ ) and residual using (7.2) (AQ ) SP SHB storage heat fluxes and net radiation. Numbers on plot indicate time (LAT). 233 radiation. It is clear that the relationship using AQg describes a clockwise hysteresis loop during both the day- and nighttime. The hysteresis effect is very well established and larger than the one generated by the parameterization. Furthermore, the 'measured' storage heat flux exhibits a hysteresis departure during the nighttime hours before midnight which cannot be observed in AQgp. Compared to the model the hysteresis effect for AQ is also larger, however, i t is s t i l l not SHB as pronounced as that observed in the 'measured' storage heat fluxes from the present study. Although the 'measured' heat storage from the present study represents one of the most extensive data sets of i t s kind i t cannot be regarded as f u l l y representative of e.g. summertime conditions at the Sunset site. Apart from having data from various cloud conditions the crucial morning transition period in particular is only represented by a few samples. Nevertheless the present measurements indicate that some differences compared to the model may occur. These are further discussed below. 7.5 Comparison of Bowen ratios (and fluxes) measured using the eddy correlation systems and the gradient approach It was shown in this thesis that the two conditions for the gradient approach to apply (similarity of eddy d i f f u s i v i t i e s and 'constant' fluxes with height) may not always hold at the present site. A l l previous energy balance studies performed at the Sunset site employed the gradient method for measuring the Bowen ratio (6 ) from which Q was calculated using 234 (7.1) and AQ using (7.2) (e.g. Oke and Cleugh, 1987; Grimmond, 1988; SHB Grimmond et al. , 1991). Any errors in 3 w i l l therefore affect the Q G EHB and AQ estimates. It follows that there is considerable interest and SHB merit in comparing the Bowen ratio measured using the eddy correlation sensors, /3 , with B . F G 8 was obtained using the RTDMS sensors (e.g. Figure 3.5). The G temperature gradients AT and AT were often very small (and therefore d w resulted in a large error in 8 ), quite variable from one hour to the G other and negative gradients could be observed even during the daytime. Clearly anomalous 8 values (often associated with small vertical G temperature gradients) were rejected. This is accepted practice (e.g. Oke and Cleugh, 1987), however, i t does introduce some degree of subjectivity into the analysis. Almost 30% of the data could not be included in the fi n a l analysis. The last two days of the measurement period (YD 195 and 196) contributed most of the 'bad' data points and i t seems possible that the RTDMS sensors were not working properly. Following Kalanda (1979) who uses the s t a t i s t i c a l method of Cook and Rabinowicz (1963), the errors calculated for the daytime (3 values used in the f i n a l analysis were in G the range from 5 to 20% with a typical value of about 8%. At night the errors were slightly larger. The probable errors in Q and Q (eq. 3.4 HB EB and 3.5) were from 5 to 19% (typical value of about 10%) during daytime and 30 to 100% at night. Whilst some of these figures are large, they assume that a l l errors are systematic and operate in the same direction. This i s unlikely to occur. The results which follow should be considered with these limits in mind. 235 To be able to directly compare B with 6 , the eddy correlation F G measurements from the two levels were averaged to yield mean fluxes which would correspond to roughly the same height interval encompassed by the RTDMS sensors (Figure 3.5). In the following, the eddy correlation fluxes averaged over this height interval w i l l be denoted with an overbar (i.e. B = Q /Q ). F H E The average Bowen ratio obtained using the two different approaches are plotted in Figure 7.11. Although the B curve during the daytime is G not necessarily typical for the Sunset site (see Figure 7.5b for a more characteristic shape of a 6 curve, 'Sunset (1978/80)', obtained from a G large sample size), Figure 7.11 indicates that BG has a tendency to be larger than B at around noon and in the early afternoon and to be F s l i g h t l y lower in the evening. The differences in the early morning and the morning transition period are not worth considering since they are based on a small sample and are derived from ratios of small fluxes and gradients. The turbulent fluxes measured using the two different approaches are compared with each other in Figures 7.12 and 7.13. Q is obtained from EHB (7.1) whereas Q and Q are the solutions of (3.4) and (3.5), HB EB respectively. Note that AQg in (3.4) and (3.5) is the residual storage heat flux which therefore depends on the fluxes obtained using the eddy correlation systems. This introduces a circularity because the fluxes which are compared using the two different approaches are not completely independent of each other. However, using the same storage heat flux in both energy balances ensures that the available energy for the flux 236 Figure 7 .11: Average Bowen ratio determined using the fluxes measured by the eddy correlation, 6 (solid line), and RTDMS sensors, S F C (dashed line). The numbers in (a) indicate the number of values used in the averaging. 237 partitioning is the same in both approaches. Figure 7.12 presents the hourly values of the two turbulent fluxes determined with the eddy correlation method and Bowen ratio-energy balance approach. For the case of the sensible heat flux (Figure 7.12a) agreement between the two is good, especially when considering that these are turbulent fluxes measured in a suburban environment. For large fluxes Q sl i g h t l y overpredicts Q and the opposite is true for small sensible HB H _2 heat fluxes. The mean values for Q and Q are 115 and 127 W m , H HB respectively. The estimated linear f i t (dashed line) has an intercept of -11 W m"2 and slope of 1.19. The r 2 , and RMSD are 0.94, 0.97 and 41 W -2 m . Previous studies have reported Q values to be larger than Q (e.g. HB H Grimmond, 1988; Cleugh, 1990 for the same Sunset site ) . In these two studies the Bowen ratio results, measured over roughly the same height interval used in the present study, were compared to Q from a SAT sensor H mounted at the upper level only (no lower level data were available in previous studies). A true comparison between the two approaches can, however, only be performed i f measurements from both levels are available. As shown in Figure 7.4a the sensible heat flux at the upper level tends to be the smaller of the two (in particular during the daylight hours). Therefore i t seems likely that agreement should be better i f Q is available from both levels. However, i t w i l l be shown H below that several other processes have to be taken into account when comparing the fluxes from the two different approaches. 238 0 • 50 100 150 200 ?e>0 300 3bO 400 b) 0 50 100 150 200 ?S0 300 350 400 F i g u r e 7.12: Comparison of hourly s e n s i b l e (a) and l a t e n t (b) heat f l u x e s determined us ing the eddy c o r r e l a t i o n (Q ) and Bowen H, E r a t i o - e n e r g y balance (Q ) approaches. 239 Agreement between the two methods is less promising for the latent —2 — heat flux (Figure 7.12b). For values larger than about 50 W m , Q£ is generally larger than Q . For smaller fluxes the intercomparison is EB better. The relationship between Q and Q is not as strong as observed E EB for the sensible heat fluxes (dt = 0.84, RMSD = 38 W m~2) and the data suggest a non-linear relationship. Figure 7.13 shows the diurnal variation of the average turbulent fluxes determined using the two different approaches. Q i s generally HB larger than Q from 1000 - 1600 LAT by 5 to 317. with a typical value of H about 20%. (Figure 7.13a). In the early evening and towards midnight Q H is s l i g h t l y larger compared to Q . The results are similar for the HB latent heat flux (Figure 7.13b) but with reversed trends. Between 1100 -1700 LAT, Q is lower than Q by 5 to 58% with a typical value of about EB E 40%. Also indicated on Figure 8.13b is Q . A s expected agreement EHB between Q and Q is good and whenever Q is lower than Q , Q is EHB EB 6 H HB EHB lower than Q and vice versa which follows from (7.1). EB The magnitudes of the differences observed at around noon and in the early afternoon, compared to the probable errors in the Bowen ratio and flux estimates, suggest that these differences are real. There are several reasons why absolute agreement between the Bowen ratios measured using the eddy correlation and RTDMS sensors (and subsequently between the corresponding fluxes) is not to be expected. F i r s t l y , the gradient aproach assumes equality of eddy d i f f u s i v i t i e s . This requirement is probably not f u l l f i l l e d in a roughness sub-layer with distorted temperature and humidity gradients. Evidence in this respect is given in 240 a) 400 300 3 t-o> I*! 200 b) - 100 400 300 •» / \ ' /\ \ * QH + o H S (2 levels) ' / \ / \ * V \ / • V 11 \ / \ if y i • t. • f i N / / /  A /I i i i j V V \\ • N \ \ V\ vw +-_ j i -K '. L 500 1000 1500 2000 2500 # QE (2 levels) + QEB O QfHB _ 2001-3 ^ 100 P) ? - 100 500 1000 1500 2000 2500 LAT Figure 7.13: Comparison of average sensible (a) and latent (b) heat fluxes determined using the eddy correlation and Bowen ratio-energy balance (% B < Z B i Z m> approaches. 241 Figure 6.13 which shows that the ratios of the correlation coefficients for heat and moisture (which are related to the eddy d i f f u s i v i t i e s ) are generally larger than unity, in particular under near neutral and sligh t l y unstable conditions. In the present study the near neutral conditions were usually associated with evening and nighttime hours which are characterized by small fluxes. Therefore a large difference between transfer efficiencies at these times is not a serious problem. During the daytime conditions with large flux magnitudes the differences between the transfer efficiencies are smaller. It follows that the differences observed in 6 and B in the middle of the day may not necessarily be due F G to this effect. Secondly, the hourly average obtained by the eddy correlation system is a composite of three 20 min averages within the corresponding hour, whereas that for the Bowen ratio system only includes two 20 min averages within the hour because two 10 min periods are lost during the reversing of the RTDMS sensors (see 3.3.3). This leaves a potential to miss flux contributions during the 20 min gap. Inspection of temperature (Figures 4.2a and 4.6d) and humidity (Figures 4.3a and 4.6e) time series reveals that fluctuations which contribute to the gradients (and therefore fluxes) can easily be missed by the RTDMS sensors during a 10 min period because, for example, the l i f e time of a temperature 'burst* is generally in the order of 4 - 7 minutes. If the humidity and temperature transfers are similar (i.e. with a large Tq correlation) a missing 10 minute period does not have a big effect on the Bowen ratio since both, AT and AT are affected in a d w 242 similar way and 6 is proportional to the ratio of these two temperatures G gradients (eq. 3.2). However, i f the temperature and the humidity signals are not in accord with each other (e.g. a rise in temperature i s not paralleled by a rise in humidity) one of the gradients can be preferentially influenced. Considering the sporadic nature of some of the humidity time series observed (e.g. Figure 4.6e) a worst case scenario could see the 10 min reversing occurring between 900 and 1500 sec in Figure 4.6e. Although this would affect the dry bulb temperature gradient the influence on AT would be much stronger and in this case result in a w reduction compared to AT^. This would in turn cause an increase in fB^. No attempt i s made to quantify this influence and the above example should only be regarded as an illustration of possible effects on the Bowen ratio by not including the two 10 min reversing periods. Thirdly, i t was shown in Figure 7.4a that the sensible heat flux converges with height during most of the daytime hours. This implies that the dry-bulb temperature gradient is larger than in a 'constant' flux layer which would result in an increase of (3^ . It is also possible that the height dependence of K is stronger than usually observed. H Fourthly, the gradient approach requires the whole layer to be in equilibrium. This is not necessarily the case and individual plumes which, due to poor spatial sampling, affect only one of the RTDMS sensors therefore affect the entire result. The eddy correlation result, however, would remain unaffected since the sensor would s t i l l give the correct flux through that point and individual plumes only show up as flux v a r i a b i l i t y which to some extent is averaged out when the mean is 243 calculated from the two levels. 7 . 6 Summary and Discussion 7 . 6 . 1 Summary In this part of the thesis energy balance results from 7 days, representing relatively dry conditions, between YD 187 - 196 were presented. The turbulent fluxes were obtained using both the eddy correlation method and Bowen ratio-energy balance approach. This is the f i r s t data set with simultaneous directly measured sensible and latent heat fluxes (over an urban surface) for a sufficiently long period of time to enable the computation of the storage heat flux as the residual of the energy balance without having to rely on the Bowen ratio measurements based on the- gradient approach. The requirement of 'constant' fluxes with height could be tested using the observations from two levels. Comparison of hourly flux values based on the eddy correlation measurements from the two levels show that the sensible heat flux at the lower level i s typically 15% larger than that at the upper level. No similar height dependence can be observed in the hourly latent heat flux data. The average diurnal variation of the sensible heat flux from the two levels reveals that the higher Q h values at the lower level are observed during daytime especially at around noon. The Q convergence i s H suggested to be due to the particular location of the measurement site and the preferential sampling of heat plumes from especially dry surface 244 patches by the sensor at the lower level. This i s another piece of evidence which suggests that z' was sometimes below z*. The average diurnal energy balance reveals some interesting features. Whereas the diurnal behaviour of the sensible heat flux i s similar to results from previous studies the latent heat flux exhibits relatively large values until the late evening and parallels the t a i l observed for Q h - On the other hand the latent heat flux increase in the morning is slow. The storage heat flux is characterized by a sharp rise during the morning hours and reaches i t s daytime maximum about two hours before noon. Thereafter A Q G slowly decreases to become negative about two hours before Q * changes sign. The evening is marked by a large heat release from storage. Compared to the modelled storage heat flux, AQ_ is larger in the morning hours and reaches i t s peak earlier than A Q S _ . During most of the daytime the residual storage heat flux i s consistently lower than AQ__ but in the evening the model f a i l s to predict the large heat release from storage. During most of the nighttime agreement is good. The phase shift observed in the timing of AQ_ compared to Q * results in a hysteresis loop departure which is larger than that for A Q _ _ . Comparison of the Bowen ratios measured using the gradient (8 ) and G eddy correlation approaches (B ), respectively reveals that B tends to F G be larger than 8_ at around noon and in the early afternoon but slig h t l y smaller in the evening. It follows that during the same daytime period the sensible heat fluxes measured using the Bowen ratio-energy approach are larger than the directly measured fluxes by about 20%. The opposite is true for the latent heat flux and Q is about 40% lower than Q . EB E 245 7.6.2 Discussion The differences observed between the 'measured' and modelled storage heat fluxes is an important result of this thesis. Most recently Grimmond et al. (1991) compare AQsp with residuals obtained from (7.2) and reach the following conclusions which are relevant to the present study: 1) AQ underestimates values at the peak of the daily input cycle; 2) AQ SP *^ underestimates the storage release just after sunset; 3) the phase in AQsp may be delayed by about one hour. In light of the results from the present study i t seems appropriate to comment on these conclusions. Since AQ is a direct function of the net radiation the current SP results cannot directly explain the differences observed between AQg and AQsp. However, the 'measured' storage heat flux from the present study can be compared with the one obtained from (7.2) which is well represented by the model. Because of the nature of (7.2) AQ and AQ S SHB are similar whenever 8 and 8 are similar which is generally the case in F G the evening and at night. The higher storage heat flux from (7.2) compared to AQg observed during most of the daytime (Figure 7.9b) results from 8 being larger than 8 • The large 8 values w i l l result in lower G F G Q with a subsequent increase of the right-hand-side in eq. 7.2. Note EHB that a direct comparison of the differences in the Bowen ratio estimates from Figure 7.11 used to explain the differences in the storage heat fluxes in Figure 7.9b is complicated by the fact that the number of hours used in the ensemble averages is different in the two plots. Grimmond et al. (1991) reach their conclusion with regards to a 246 possible phase delay of about one hour by comparing AQsp with (a) the Heat Content Change Model (Peikorz, 1987; Kerschgens and Kraus, 1990) and (b) the Weighted Plate Model (Kerschgens and Hacker, 1985). The former calculates the storage heat flux from the sum of the heat content changes of a l l components of the urban system and the latter uses the storage heat flux from a combination of appropriately weighted heat storage fluxes through two typical surfaces, a paved parking lot and a lawn. The data necessary to evaluate those two models were gathered by their originators in Bonn, F.R.G. during parts of two days. The calculated heat storage from those two models was subsequently compared by Grimmond et al. (1991) to the objective hysteresis model using (2.3). They find the peak heat storage input is larger and observed about two hours earlier in (a) and (b) compared to AQsp. In the evening the negative peak in a l l three models occurs at around the same time but the magnitudes of (a) and (b) are again larger than observed in AQsp. The current results confirm the phase shift, however, the magnitude associated with the peak flux in the morning is lower than the peak in AQgp (Figure 7.9b). It should be noted that, because of the relatively small sample size, the data from the present study only warrant preliminary conclusions, especially in respect to the crucial early morning period A major advantage of the objective hysteresis model by Grimmond et al. (1991) is that i t provides an objective approach for modelling the heat storage of a very complex system in terms of the main energy flux driving the energy balance. Grimmond et al. (1991) combine independent data sets involving simultaneous measurements of storage heat flux and net radiation for a range of surface materials encountered in the urban 247 environment (see 2.2.2). However, they point out that their combined coefficients for the roof tops are based on only two studies which report quite different regression coefficients. In particular C_^, which accounts for the hysteresis effect, is not very well defined and could potentially be larger (but may be smaller?) than the value used in the current model. The former would result in a larger hysteresis departure in AQsp. The results from the present study also suggest that the geometry of the three-dimensional urban surface may play an important role in the timing of the heat storage uptake and release. Grimmond et al. (1991) allow for the three-dimensional nature of the suburban environment by computing a l l the areas which are in contact with the atmosphere (i.e. including the vertical walls which results in an active area which i s about 1.5 times the plan area for the present study site ) . Neglected, however, are the east-west aligned walls since the canyon parameterization in the model is only based on results from a north-south canyon. It is therefore possible that that the omission of the north and south walls, both of which are associated with a hysteresis effect, contribute to the observed differences of heat uptake and release in the model output compared to the 'measured' values. It is also possible that the parameterization neglects the fact that some of the surfaces are in a preferential position with respect to the incident radiation at different times of the day. The east walls (of buildings) for instance experience a high net radiation loading in the middle of the morning which is comparable in magnitude to the energy input at horizontal surfaces at around noon (Nunez, 1974). Yet the model output is based on the net radiation as received by a horizontal surface which is relatively 248 low at this time of the day. The following scenario could explain the storage heat flux pattern observed in the present study. The surface temperature reaches i t s lowest value in the early morning hours at which time the system has a large capacity for heat uptake. Just after sunrise the surface i s ready to restore i t s heat reservoir, but unlike a horizontal surface (which experiences a slow and smooth increase in the storage heat uptake because of i t s position with respect to the incident radiation during the course of the day) the average urban system responds with a sudden storage heat flux which is mainly caused by the east walls which are in a preferential position in respect to the incident radiation. The decline of the heat storage in the afternoon is a result of the unstable atmosphere which favours the dissipation of the net radiation gain as sensible heat rather than conduction into the substrate and the release of stored heat in response to the early shading experienced by some surfaces. In the late afternoon when the sun is at low angles the east walls (and subsequently, depending on the canyon geometry, the floors as well) become shaded, cool down and the urban system responds with a net release of stored heat. The large heat loss observed in the evening i s again augmented by the unstable atmosphere. 249 CHAPTER 8: OVERALL SUMMARY, DISCUSSION AND CONCLUSIONS The data presented in this thesis are among the f i r s t detailed results of (co)spectral and integral s t a t i s t i c s of a l l important atmospheric variables (u, v, w, T, q and appropriate covariances) measured in an unstable suburban atmosphere (-1.8 < z'/L^ < -0.05). In addition these f i r s t long-term, and simultaneous eddy correlation measurements of the sensible and latent heat fluxes enable the determination of the storage heat flux at a suburban location as the true residual of the energy balance. Section 8.1 summarizes the most important results and emphasizes any differences found in comparison with reference data. Section 8.2 attempts to combine and discuss these results in light of the structure of the surface layer in the suburban environment and further points out their implications for energy balance studies. Section 8.3 summarizes the conclusions in respect to the objectives outlined in 1.4. 8.1 O v e r a l l summary The (co)spectral results show only minor differences of energy distribution in respect to frequency and in the locations of the (co)spectral peaks in comparison with data from the homogeneous surface layer (see also Table 2.1 for a summary of peak frequencies from different studies). This is true for the (co)spectra normalized with the respective (co)variances as well as analysed within the MOS framework. The present observations are also in good agreement with the few studies available from other (sub)urban locations. Minor deviations in comparison 250 with reference data which may be particular to the present site (and may be suburban sites in general) include: 1) The peak of the w spectrum is slightly shifted towards lower f requencies. 2) The peak of the u spectrum i s slightly shifted towards higher frequencies and exhibits a relatively fast r o l l - o f f at the low frequency end with spectral energy densities f a l l i n g into Kaimal's supposedly excluded region. 3) The T spectrum is slightly shifted towards higher frequencies and the s t a b i l i t y dependence of the low frequency end is weak. 4) The q spectrum i s characterized by a low frequency end which does not show a r o l l - o f f for near neutral to moderately unstable conditions. 5) The uw cospectrum has two minor 'dips' at f = 0.06 (A = 17z') and f = 0.5 (A = 2z') and the -4/3 slope which is only slowly approached at high fequencies. The non-dimensional dissipation function for temperature i s in good agreement with the reference data and follows MOS. Although the other non-dimensional dissipation rates follow the trend predicted by similarity theory the following differences compared to reference data are observed: 1) <£_ is smaller, more so under slightly unstable conditions than at large i n s t a b i l i t i e s . 2) <p^ is slightly smaller, especially near -z'/L = 0.5. 3) H(z'/L ) is generally smaller. 251 4) Q(z'/L ) is much smaller. V 5) G(z'/L ) is generally larger. V A possible explanation for the generally smaller dissipation values observed is based on the variance budget: the local dissipation is smaller than the local production of energy because some of i t is exported with the help of organized vertical (and horizontal) motions therefore increasing the transport term in the variance budgets to values larger than usually observed. The observations at the lower level are only slightly different to those at the upper level (generally faster high frequency r o l l - o f f in the (co)spectra and smaller non-dimensional dissipation constants), however, i t cannot be decided i f these differences are caused by not having used the local U and u # values (in the computation of f, z'/L^ and in the normalizations) or i f they should be attributed to the low height of measurement over the rough surface (e.g. 'short circuiting' of the energy cascade; failure of Taylor's Hypothesis). However, the fact that no significant differences are present between the two levels in the f i r s t place is an indication that the turbulence structure is similar over the height interval available. The similarity of the transfer mechanism for a given z'/L is only V given i f the spectral correlation coefficients agree scale by scale for a l l scales involved in the transfer. The results from the present study show that under near neutral conditions the momentum transfer i s more efficient at low and mid frequencies than the transfers of heat and 252 moisture. Under unstable conditions heat transfer is most efficient at a l l scales followed by water vapour and momentum. Differences from reference data include: 1) Higher R (f) (especially at low frequencies). uw 2) A small 'dip' at f £ 0.06 (A = 17z') for slightly unstable R (f). uw 3) Smaller R (f) at most frequencies. wq 4) A small 'plateau region' at f = 0.2 - 0.3 (A = 5 - 3z') in R (f) and wT R (f). wq The spectral correlation coefficient results are confirmed by the analysis of the (linear) correlation coefficients. The general trend predicted by the similarity theory is conserved but the magnitudes are different: 1) -r is larger for near neutral and slightly unstable conditions. uw 2) r is sl i g h t l y larger for a l l s t a b i l i t y conditions. 3) r is smaller for most stability conditions. wq It i s shown that -r /r increases with increasing i n s t a b i l i t y from wT uw a value close to unity at near neutral to about 4 at z'/L = -1.8. V -r /r shows a similar increase with increasing i n s t a b i l i t y from about wq uw 0.3 to 2.5 (hence the transfers are different at near neutral). On the other hand, in the mean, r /r decreases from about 2.5 at near neutral wT wq to about 1.3 at z'/L = -1.8. This latter result implies that the V transfers of heat and water vapour are not similar at the present study 253 site. In agreement with rural reference data r and r /r are observed wq wT wq to be a function of r T . The temperature-humidity correlation coefficient is generally low (0.3 - 0.6) which could be due to dissimilarity in the source/sink distributions of sensible heat and moisture present in the suburban environment or large scale horizontal or vertical advection. This latter point is illustrated by a time series analysis of humidity traces which shows the occurrence of strong, dry downdrafts (especially under cloudy conditions) which are imported from the mixed layer. The turbulence intensities of a l l three velocity components show a dependence on z'/L and increase with increasing instability. The V applicability of MOS to the normalized velocity and temperature standard deviations is good in that they follow the predicted slopes. This i s somewhat unexpected for the horizontal wind components because observational support for their similarity is weak over rural surfaces (they are thought to depend more on mixed layer variables). Differences from reference data include: 1) cr is generally smaller. 2) cr /q # does not display a free convection behaviour (-1/3 slope). q The lower values observed for cr /u # can again be explained through the TKE budget and the possible export of locally produced energy. In addition transfer through pressure-velocity interaction may be important as well. These low normalized standard deviations also suggest a very efficient momentum transfer. This is confirmed by the large r values uw observed under near neutral and slightly unstable conditions. 254 The magnitudes of the normalized velocity standard deviations for near neutral conditions agree well with the neutral reference data and values from other (sub)urban studies. The interpretation of the lower level results i s again affected by the reasons mentioned above, but in general no obvious differences can be observed in comparison with the results from the upper level. Comparison of hourly flux values based on eddy correlation measurements show generally larger (by about 15%) sensible heat flux values at the lower level than the upper level. This effect is most pronounced during daytime with high Q values and may be due to the H preferential sampling of relatively warm surfaces in the immediate v i c i n i t y of the tower under these unstable conditions. No similar flux convergence i s observed for the latent heat flux. Comparison of the Bowen ratios measured by the eddy correlation method (B ) and gradient approach F (.B ) shows B > 3 around noon and in the early afternoon and vice versa G G F in the evening and early morning hours. This result may be attributed to sampling problems associated with the gradient method and the inequality of the transfer efficiencies of heat and water vapour mentioned above. The average diurnal energy balance is similar to that previously measured at the same site in summer conditions. In particular, Q is the H main energy loss at the surface during most of the daytime, however, Q E remains an important energy sink. Both turbulent fluxes exhibit the ' t a i l behaviour' into the late evening. The storage heat flux (measured as the residual of the energy balance) is characterized by a sharp increase in the early morning hours just after sunrise (based on a few hours of 255 measurements only) and reaches a peak about two hours before noon. Thereafter AQg remains high before dropping rapidly to reach a minimum (heat loss from storage) just after the sign reversal of Q*. This behaviour is slightly different from the prediction of the objective hysteresis model which peaks later and shows higher values from noon un t i l the late afternoon and f a i l s to predict the large heat storage release in the evening. The hysteresis effect observed in the 'measured' heat storage is larger than generated by the model. It is suggested that the model misses the large heat storage uptake (release) in the early morning (evening) because i t does not adequately take account of the role of the vertical walls with respect to absorption of incident radiation and shade patterns at these times of the day. 8.2 Genera1 disc u s s i o n A central goal of this thesis is to assess the degree to which the turbulence characteristics over suburban terrain conform to 'ideal' homogeneous surface layer conditions and follow MOS. The results summarized in the previous section exhibit some differences from the reference data, however, these do not seem to be systematic. For instance: 1) The w spectrum has a st a b i l i t y dependent low frequency end at both levels but the respective non-dimensional dissipation constants and the normalized standard deviations, although they follow the predicted trends, are smaller than the reference functions; 2) The low frequency part of the T spectrum generally does not behave according to MOS, however, the non-dimensional dissipation ' constants and the normalized standard deviations agree with the similarity predictions; 3) 256 The wT cospectrum is in good agreement with the reference but the normalization functions are smaller and the correlation coefficients are larger than similarity predicts. Nevertheless, with minor exceptions, the following general conclusions are warranted: 1) The (co)spectral shapes are remarkably similar to reference data and any differences occurring are small but may be attributable to surface influences. 2) The similarity functions are usually followed but the magnitudes are often smaller. 3) The humidity stati s t i c s generally do not follow MOS. This latter conclusion is also observed in the homogeneous surface layer for cases where the temperature-humidity correlation is less than one. Since the present data do not show a consistent departure from similarity theory i t is d i f f i c u l t to ascribe any physical basis for the observed differences but i t is likely that some of these anomalies can be attributed to organized vertical (and possibly horizontal) motions over the suburban surface (see below). There is some evidence that the humidity results, which often show a lot of scatter, are not only affected by the surface boundary conditions but also depend on large scale motions. As a result of the enhanced turbulence intensities and associated stronger mixing over the rough suburban surface the surface layer is strongly coupled with the mixed layer. Observational support for the linkage between these two layers is given by: 1) The analysis of humidity time series which show the occurrence of strong, dry downdrdafts (under mainly cloudy conditions) 257 which are most likely related to large scale structures; 2) The small McNaughton and Jarvis Q factors; 3) The relatively low r values which could result from disparate source distributions for temperature and humidity or large scale horizontal or vertical advection of air of different origin. These results suggest that universal relations pertaining to humidity (as a passive scalar) are unlikely. The particular 'signatures' observed in the temperature time series are also indicative of larger scale, mixed layer influences on the turbulent transfer near the suburban surface. The atmospheric layer immediately above a rough surface consists of a lower portion (roughness sub-layer) which is characterized by the influence of individual surface elements and an upper portion, above z*, ('constant' flux layer) where the flow is horizontally homogeneous and MOS applies. One objective of this thesis is to assess whether z' > z* at the present study site. Using the dimensions of the general Sunset area most of the z* values derived from the functions summarized in Table 1.1 suggest that the measurement levels were within or at the top of the roughness sub-layer. Based on the (co)spectral results from the present study which, in general, agree well with the reference data one could conclude that z' s z*. On the other hand the non-dimensional dissipation rates and some of the turbulence statistics indicate anomalies compared to reference data, suggesting that z' < z*. This is further supported by the convergence observed in the sensible heat flux (especially under daytime conditions) which does not conform to the requirements of a 'constant' flux layer. 258 It should be noted that the height of the roughness sub-layer is not necessarily the same for momentum, heat and water vapour. A roughness sub-layer (although this term s t r i c t l y only refers to the spatial v a r i a b i l i t y introduced by the bluff-bodies) develops in relation to the distribution of the momentum sinks, and heat and moisture sources, which do not necessarily coincide. The p o s s i b i l i t y that z' < z* at the Sunset site was also explored by Schmid (1988). He estimated the range of conditions when measurements at the present site are expected to be f u l l y representative and therefore observed in the homogeneous surface layer. His source area calculations in relation to s t a b i l i t y and normalized lateral velocity standard deviations define a criterion for the representativeness of a measurement which can be applied to the present observations. The and o^/u^ observations from the present study in combination with Schmid*s Figure 11.1 demonstrate that for most of the time the turbulence sensors were located below z*. Considering that z' is sometimes below z*, the good agreement of the spectral shapes with reference data is somewhat surprising since i t is often argued that close to the roughness-elements (within the roughness sub-layer) the dimensions of the surface structures w i l l affect the turbulence s t a t i s t i c s . However, observational support for roughness effects on (co)spectra are sparse, the exception being velocity measurements from within forest canopies (e.g. Baldocchi and Meyers, 1988). The spatial scales which would be most lik e l y to influence the turbulence measurements at the present site are for momentum the 259 house-row (50 m) and inter-house (20 m) spacing; and for temperature the spacing between house roofs and street surfaces (25 m) both of which have relatively warm temperatures during daytime. These scales were identified by Schmid, 1988 (using a roughness inventory and remotely-sensed surface temperatures of the general Sunset area) as the dominant contributions to a variance analysis of roughness and temperature features. Assuming that the individual wakes and plumes emerging from these sources are related to the corresponding scales one would expect that this would result in subsidiary spectral peaks at frequencies comparable to these scales, i.e. at f = 0.4, 0.8 or 0.9 ( for A = 50, 25 and 20m, respectively using z' = 18.9 m). Inspection of the spectral results, however, reveals no indications of such effects (not even at the lower level) with the possible exception of the high frequency dip in the uw cospectrum at X = 36 m which is of a similar wavelength compared to the important surface length scales identified above. It appears that surface features only introduce clearly identifiable anomalies into the (co)spectral shapes i f the sensors are located in the immediate v i c i n i t y of the particular surface features. A more likely scenario is that the wakes which are shed from buildings produce turbulent energy at a smaller scale than that produced by the mean wind shear. The wake and shear produced energy containing eddies w i l l result in an energy input at slighly higher frequencies compared to the homogeneous surface layer case. This might explain the relatively fast low frequency r o l l - o f f and the shift of the peak frequency observed in the u spectrum in the present study, as well as those of Jackson (1978), Clarke et al. (1982) and Roth (1990). It is 260 p o s s i b l e that a s i m i l a r e f f e c t i s resp o n s i b l e f o r the s h i f t i n the temperature spectrum. The w spectrum, on the other hand, i s not a f f e c t e d i n the same way because i t has most of i t s energy at r e l a t i v e l y high f r e q u e n c i e s which therefore adjust more r a p i d l y to changes i n roughness f e a t u r e s . The tu r b u l e n t wakes created by the b l u f f - b o d i e s are a l s o a zone of small eddies which develop i n response to v o r t i c e s shed from the edges of b u i l d i n g s . These eddies e f f i c i e n t l y transport momentum across the mean stream l i n e s . This may e x p l a i n the r e l a t i v e l y h i g h momentum (and to some extent heat) c o r r e l a t i o n c o e f f i c i e n t s observed under s l i g h t l y unstable and near n e u t r a l c o n d i t i o n s . Based on above r e s u l t s and d i s c u s s i o n there i s evidence that z' i s sometimes below z* at the Sunset s i t e . In respect to f l u x measurements from a p o i n t source (eddy c o r r e l a t i o n method) t h i s does not mean that the data obtained are use l e s s ; i t only means that the measurement i s not f u l l y r e p r e s e n t a t i v e of the underlying surface but i s more l i k e l y to be i n f l u e n c e d by unusually hot, c o l d , wet or dry surface elements. I t i s s t i l l p o s s i b l e to a r r i v e at a s p a t i a l l y r e p r e s e n t a t i v e t u r b u l e n t f l u x i n a s t a t i s t i c a l sense by averaging the f l u x estimates from many d i f f e r e n t source areas (Oke et al. , 1989). The i m p l i c a t i o n s f o r p r o f i l e methods are more s e r i o u s (see below). An important r e s u l t from t h i s t h e s i s i s that the r a t i o of the c o r r e l a t i o n c o e f f i c i e n t of s e n s i b l e heat to that of water vapour (which i s a measure of the r e l a t i v e t r a n s f e r e f f i c i e n c y ) i s g e n e r a l l y l a r g e r than u n i t y ( i n p a r t i c u l a r f o r s l i g h t l y unstable and near n e u t r a l c o n d i t i o n s ) . This means that the two t r a n s f e r s are not s i m i l a r . The 261 dissimilarity between the transfers of heat and moisture has implications for the use of profile methods (such as the Bowen ratio-energy balance approach) which are based on the assumption of equality of eddy d i f f u s i v i t i e s . Profile methods further assume that the fluxes are constant with height which is shown not to be true for the sensible heat flux at the present site. Depending on the relative magnitudes of the eddy d i f f u s i v i t i e s the Bowen ratio measured by the gradient method (6 ) may be under- or overestimated which results in an under- or overestimation of the turbulent fluxes determined using the Bowen ratio-energy balance approach. The increasingly larger ratio of the correlation coefficients of heat to water vapour observed towards near neutral conditions are usually associated with evening and nighttime conditions when the turbulent fluxes are relatively small. Therefore any differences in the transfer efficiencies would have a small absolute influence on the fluxes measured using the gradient approach at these times. During the daytime hours, which are characterized by unstable conditions, the transfers of heat and water vapour become increasingly similar and the effect on the relatively large fluxes w i l l be reduced. Nevertheless the observations in the present study show that around noon and in the early afternoon 8 is larger than 8 . Several reasons are G F suggested to account for these differences: 1) The missing 20 minute period in the supposedly 'one-hour' average of 8 ; 2) Preferential G sampling of individual plumes by one or the other of the RTDMS sensors which w i l l affect the entire result; 3) The sensible heat flux divergence 262 observed during daytime conditions. If the present observations (which are based on a relatively small data set) can be generalized the following are the implications for results from previous studies at the Sunset site using the Bowen ratio measured by the gradient method: 1) The Bowen ratio at around noon and in the afternoon may have been overestimated. 2) The latent heat flux which is often obtained from Q = Q /B (where EB H G Q is directly measured) is most likely underestimated during the same H hours when 6 is overestimated. 1 G 3) The storage heat flux obtained as the residual from the energy balance using Q and Q probably overestimated the peak values which occur H EB during daytime. This latter conclusion is in part supported by previous measurements (e.g. Grimmond, 1988; Grimmond et al., 1991) which found that for large fluxes the residual storage heat fluxes were generally larger than those from the objective hysteresis model. This of course assumes that the model i s able to represent the 'true' value which may not be the case. The present study (but based on a few hours of data only for the morning hours) indicates that the parameterized heat storage reaches i t s peak one or two hours later than is observed and is too low at the time of largest heat loss from storage in the evening. The results presented in this thesis suggest the pos s i b i l i t y that under certain conditions no 'ideal' surface layer may exist over suburban areas. Close to the roughness elements and the patchy surface (for 263 heights up to z' s 36Z q at the present study site) the observations seem sometimes to be affected by turbulent wakes shed from the buildings and the disparate distribution of sources and sinks of temperature and humidity which results in inhomogeneous turbulent flux f i e l d s . It is hypothesized that the irregular, high roughness surface leads to organized flow structures and modified (most likely enhanced) transfer efficiences of fluxes which could affect the turbulence s t a t i s t i c s . Ideally at larger heights turbulent mixing 'smears' these differences so that at some height the three-dimensional va r i a b i l i t y disappears. With increasing height of measurement larger-scale advection from upwind surfaces with different surface character (e.g. non-suburban) may become important, which, however, can be avoided with appropriate site selection. On the other hand the present study, in conjunction with other suburban observations, indicates the possibility of large-scale vertical advection due to the strong coupling of the surface and mixed layers. It follows that considerable attention and consideration has to be given to the application of a homogeneous surface layer concept in the suburban environment. 8 .3 Summary of conclusions In the following the specific conclusions drawn from the present study are summarized in respect to the objectives outlined in 1.4. * The (co)spectral characteristics of v, w, wT and wq measured at the present suburban location agree well with the homogeneous surface layer reference data in terms of the general shapes and peak locations. It is 264 concluded that the (co)spectra of these variables are i n accord with MOS (where a p p l i c a b l e ) . Comparison with reference data and a p p l i c a b i l i t y of MOS i s not as good f o r u, T, q and uw. This i s the f i r s t study to report humidity and moisture f l u x r e s u l t s from a suburban environment. The former do not exh i b i t s i m i l a r i t y behaviour (s i m i l a r to r e s u l t s from some studies over ' i d e a l ' s i t e s ) whereas the l a t t e r agree well with homogeneous surface layer observations. The coherence and phase angle spectra of a l l covariances analysed are i n general agreement with reference data. * The non-dimensional d i s s i p a t i o n rates derived from the spectra and the normalization functions from the cospectra generally follow the trend prescribed by empirical s i m i l a r i t y functions, however, the magnitudes d i f f e r and are usually lower. Exceptions are <f>^ which agrees well, and M(z'/L ), which i s generally larger than s i m i l a r i t y p r e d i c t s . V * The sp e c t r a l c o r r e l a t i o n c o e f f i c i e n t s f o r a l l covariances are a fun c t i o n of z'/L . Under near neutral conditions the transfe r of momentum V i s more e f f i c i e n t at large scales than both the reference data and the tra n s f e r s of heat and moisture from the present study. Under unstable conditions the transfer of heat i s more e f f i c i e n t than those of moisture and momentum at a l l scales. Compared to reference data the heat and momentum tran s f e r s are more e f f i c i e n t at low frequencies. The peaks occur at around the same frequency f o r wq and at s l i g h t l y lower values f o r uw and wT compared to the peaks i n the corresponding reference cospectra. * The turbulence i n t e n s i t i e s of a l l three v e l o c i t y components increase 265 with increasing instability. The normalized standard deviations of the velocity components and temperature can be described within the MOS framework but the values are smaller for the vertical velocity at a l l s t a b i l i t i e s . The normalized humidity standard deviations do not follow the similarity prediction. * The transfer f a c i l i t y was investigated through the analysis of the correlation coefficients of fluxes. Under near neutral and sl i g h t l y unstable conditions r is larger than reference data, indicating very uw efficient momentum transport under these conditions. It is shown that r^_ and r follow the free convection similarity predictions but the wq magnitudes are larger for the former and smaller for the latter, r and wq r /r are found to depend on r . The relative transfer efficiencies wT wq Tq -r /r and -r /r increase with increasing instability and are lower wt uw wq uw than the reference data under near neutral and moderately unstable conditions. Near neutral -r /r is about unity and -r /r is less wt uw wq uw than unity, r /r decreases from about 2.5 to smaller values with wT wq increasing instability. This is the f i r s t observational evidence that the transfers of heat and water vapour are not similar in the suburban environment. * It is concluded that the observation levels are sometimes below z*. This follows mainly from the analysis of the non-dimensional dissipation functions and the integral statistics since the (co)spectral shapes are found to be relatively insensitive to surface features. This thesis presents the f i r s t f u l l set of energy balance data 266 including longer term (7 days) directly-measured sensible and latent heat fluxes. Based on these observations the following tentative conclusions can be drawn in respect to the suburban energy balance and the u t i l i t y of the gradient approach in this environment. * The nature of the daily variation of the sensible and latent heat fluxes is similar to results from previous studies performed at the same site under similar summer conditions. Sensible heat i s the predominant energy sink but the latent heat flux remains an important term. Both fluxes show relatively large magnitudes late into the evening. * The storage heat flux determined as the residual of the energy balance using directly measured turbulent fluxes i s asymmetric about solar noon which results in a large hysteresis effect. The largest heat storage uptake is observed about two hours before noon and the maximum heat loss from storage occurs shortly after sunset and is in the same order of magnitude as the morning peak. This behaviour is slig h t l y different from the objective hysteresis model predictions which peak later, have larger magnitudes during the daytime and indicate a smaller loss in the evening. * At around noon and in the early afternoon the Bowen ratio measured by the gradient approach is generally larger compared to the Bowen ratio measured using the eddy correlation systems. The opposite is true in the evening but the differences are smaller. It is suggested that these differences are due to the inequality of the transfer coefficients for sensible heat and moisture, sampling problems associated with the RTDMS 267 sensors and the flux convergence of sensible heat. This thesis revealed some differences in the turbulence structure at the present site compared to the homogeneous surface layer. However, on the basis of the present observations i t is not possible to provide a physical basis for the observed anomalies. It is f e l t that further analysis of the variance budgets for TKE, temperature and humidity could contribute to a better understanding. Furthermore a coherent structure analysis could be instrumental in the identification of particular organized structures affecting the turbulent transfer processes. In addition i t would be worthwile to further investigate the processes affecting the humidity statistics. In respect to the energy balance there is a need for more observations of directly measured simultaneous turbulent fluxes (especially for the morning transition period) to strengthen the conclusion that the 'true' storage heat flux peaks earlier than predicted by the model. 268 REFERENCES Anderson, D.E., and Verma, S.B., 1985. Turbulence spectra of C02, water vapour, temperature and wind velocity fluctuations over a crop surface. Boundary Layer Meteorol. 33, 1-14. Arya, S.P.S., 1988. 'Introduction to Micrometeorology'. Academic Press, San Diego, 307pp. Arya, S.P.S., and Sundararajan, A., 1976. An assessment of proposed similarity theories for the atmospheric boundary layer. Boundary Layer Meteorol. 10, 149-166. Baldocchi, D.D., and Hutchison, B.A., 1988. Turbulence in an almond orchard: Spatial variation in spectra and coherence. Boundary Layer Meteorol. 42, 293-311. Baldocchi D.D., and Meyers, T.P., 1988. A spectral and lag-correlation analysis of turbulence in a deciduous forest canopy. Boundary Layer Meteorol. 45, 31-58. Bendat, J.S., and Piersol, A.G., 1986. 'Random Data; Analysis and  Measurement Procedures'. W'iley-Interscience, New York, 407pp. Bi l t o f t , C.A., and Gaynor, J.E., 1987. Comparison of two types of sonic anemometers and fast response thermometers. Proc. '6th Symposium on Meteorological Observations and Instrumentation', A.M.S., Jan. 12 -16, New Orleans, LA, 173-176. Bowne, N.E., and Ball, J.T., 1970. Observational comparison of rural and urban boundary layer turbulence. J. Appl. Meteorol. 9, 862-873. Browne, L.W.B., Antonia, R.A., and Shah, D.A., 1987. Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307-326. Brook, R.R., 1972. The measurements of turbulence in a city environment. J. Appl. Meteorol. 11, 443-450. Buck, A., 1985. The Lyman-a absorption hygrometer. In 'Moisture and Humidity, Measurement and Control in Science and Industry', Proc. 'International Symposium on Moisture and Humidity' , Washington, D.C, April 15 - 18, 775-777. Businger, J.A., Wyngaard, J.C, Izumi, Y. , and Bradley, E.F., 1971. Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181-189. Campbell, G.S., and Unsworth, M.H., 1979. An inexpensive sonic anemometer for eddy correlation. J. Appl. Meteorol. 18, 1072-1077. 269 Campbell, G.S., and Tanner, B.D., 1985. A Krypton hygrometer for measurement of atmospheric water vapor concentration. In 'Moisture and Humidity, Measurement and Control in Science and Industry', Proc. 'International Symposium on Moisture and Humidity' , Washington, D.C, April 15 - 18. Camuffo, D. , and Bernardi, A., 1982. An observational study of heat fluxes and their relationships with net radiation. Boundary Layer Meteorol. 23, 359-368. Champagne, F.H., Friehe, C.A., LaRue, J.C., and Wyngaard, J.C., 1977. Flux measurements, flux estimation techniques and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515-530. Ching, J.K.S., 1985. Urban-scale variations of turbulence parameters and fluxes. Boundary Layer Meteorol. 33, 335-361. Ching, J.K.S., Clarke, J.F., and Godowitch, J.M., 1983. Modulation of heat flux by different scales of advection in an urban environment. Boundary Layer Meteorol. 25, 171-191. Clarke, J.F., Ching, J.K.S., and Godowitch, J.M., 1982. An experimental study of turbulence in an urban environment. Tech. Report. U.S. E.P.A., Research Triangle Park, N.C., NMS PB 226085. Clarke, J.F., Ching, J.K.S., Godowitch, J.M., and Binkowski, F.S., 1987. Surface layer turbulence in an urban area. In 'Modelling the Urban Boundary Layer', A.M.S., 161-199. Cleugh, H.A., 1990. Development and evaluation of a suburban evaporation model: A study of surface and atmospheric controls on the suburban evaporation regime. Ph.D. Thesis, The University of British Columbia, Vancouver. Cleugh, H.A., and Oke, T.R., 1986. Suburban-rural energy balance comparisons in summer for Vancouver, B.C. Boundary Layer Meteorol. 36, 351-369. Cook, N.H., and Rabinowicz, E., 1963. 'Physical Measurement and  Analysis'. Addison-Vesley, Reading, Mass., 312pp. Coppin, P.A., 1979. Turbulent fluxes over an uniform urban surface. Ph.D. Thesis, The Flinders University of South Australia, Flinders. Counihan, J. , 1975. Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880 - 1972. Atmospheric Environment 9, 871-905. DeBruin, H.A.R., 1983. A model- for the Priestly-Taylor parameter a. J. Clim. Appl. Meteorol. 22, 572-578. DeBruin, H.A.R., and Holtslag, A.A.M., 1982. A simple parameterization of 270 the surface fluxes of sensible and latent heat during daytime compared with the Penman-Monteith concept. J. Appl. Meteorol. 21, 1610-1621. Denmead, O.T., and Bradley, E.F., 1985. Flux gradient relationships in a forest canopy. In 'The Forest-Atmosphere Interaction*. Eds. B.A. Hutchison and B.B. Hicks, 421-442. Doll, D. , Ching, J.K.S., and Kaneshiro, J. , 1985. Parameterization of subsurface heating for s o i l and concrete using net radiation data. Boundary Layer Meteorol. 32, 351-372. Dyer, A.J., 1974. A review of flux-profile relationships. Boundary Layer Meteorol. 7, 363-372. Dyer, A.J., and Hicks, B.B., 1970. Flux-gradient relationships in the constant flux layer. Q.J.R.Meteorol. Soc. 96, 715-721. Dyer, A.J., and Hicks, B.B., 1982. Kolmogoroff constants at the 1976 ITEC. Boundary Layer Meteorol. 22, 137-150. Elagina, L.G., 1969. The relation of frequency spectra of humidity fluctuations to moisture fluxes. Izv. Atmos. Oceanic Phys. 5, 621-622 Fazu, Ch. , and Schwerdtfeger, P. , 1989. Flux-gradient relationships for momentum and heat over a rough natural surface. Q.J.R.Meteorol. Soc. 115, 335-352. Gao, W. , Shaw, R.H., and Paw U, K.T., 1989. Observation of organized structure in turbulent flow within and above a forest canopy. Boundary Layer Meteorol. 47, 349-377. Garratt, J.R., 1978a. Flux profile relations above t a l l vegetation. Q.J.R.Meteorol. Soc. 104, 199-211. Garratt, J.R., 1978b. Transfer characteristics for a heterogeneous surface of large aerodynamic roughness. Q.J.R. Meteorol. Soc. 104, 491-502. Garratt, J.R., 1980. Surface influence upon vertical profiles in the atmospheric near-surface layer. Q.J.R.Meteorol. Soc. 106, 803-819. Grant, A.L.M., and Watkins, R.D., 1989. Errors in turbulence measurements with a sonic anemometer. Boundary Layer Meteorol. 46, 181-194. Grimmond, C.S.B., 1988. An evapotranspiration - interception model for urban areas. Ph.D. Thesis, The University of B r i t i s h Columbia, Vancouver. Grimmond, C.S.B., and Oke, T.R., 1986. Urban water balance 2: Results from a suburb of Vancouver, B.C. Water Resour. Res. 22, 1397-1403. Grimmond, C.S.B., Cleugh, H.A., and Oke, T.R., 1991. An objective urban heat storage model and i t s comparison with other schemes. Atmospheric 271 Environment, Part B. Urban Atmosphere (submitted). Hanafusa, T., Fujitani, T., Kobori, Y., and Mitsuta, Y., 1982. A new type sonic anemometer-thermometer for f i e l d operation. Pap. Metorol. Geophys. 33, 1-19. Hay, J.E., and Oke, T.R., 1976. 'The Climate of Vancouver'. B.C. Geographical Series, No. 23. Tantalus Research Ltd., Vancouver, B.C., 48pp. Henderson-Sellers, B. , 1984. A new formula for latent heat of vaporisation of water as a function of temperature. Q.J.R.Meteorol. Soc. 110, 1186-1190. Hicks, B.B., 1976. Wind profile relationships from the 'Wangara' Experiment. Q.J.R.Meteorol. Soc. 102, 535-552. Hildebrand, P.H., and Ackermann, B., 1984. Urban effects on the convective boundary layer. J. Atmos. Sci. 41, 76-91. H i l l , R. J. , 1989. Implications of Monin-Obukhov similarity theory for scalar quantities. J. Atmos. Sci. 46, 2236-2244. Hogstrom, U. , 1988. Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Boundary Layer Meteorol. 42, 55-78. Hogstrom, U. , and Smedman-Hbgstrdm, A-S., 1974. Turbulence mechanisms at an agricultural site. Boundary Layer Meteorol. 7, 373-389. Hogstrom, U. , Bergstrdm, H. , and Alexandersson, H. , 1982. Turbulence characteristics in a near neutrally s t r a t i f i e d urban atmosphere. Boundary Layer Meteorol. 23, 449-472. Hojstrup, J., 1981. A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux. Boundary Layer Meteorol. 21, 341-356. Jackson, P.S., 1978. Wind structure near a city centre. Boundary Layer Meteorol. 15, 323-340. Jensen, N.O., and Busch, N.E., 1982. Atmospheric turbulence. In 'Engineering Meteorology', Ed. E.J. Plate, Elsevier Sci. Pub., 179-231. Kaimal, J.C., 1978. Horizontal velocity spectra in an unstable surface layer. J. Atmos. Sci. 35, 18-24. Kaimal, J.C., 1980. Sonic anemometers. In 'Air-Sea Interaction, Instruments and Methods', Ed. F.Dobson, Plenum Press, 81-96. Kaimal, J.C., and Businger, J.A., 1963. A continuous wave sonic anemometer-thermometer. J. Appl.Meteorol. 2, 156-164. 272 Kaimal, J.C, Wyngaard, J.C, Izumi, Y. , and Cote, O.R., 1972. Spectral characteristics of surface-layer turbulence. Q.J.R.Meteorol. Soc. 98, 563-589. Kalanda, B.D., 1979. Suburban evaporation estimates in Vancouver. M.Sc. Thesis, The University of British Columbia, Vancouver. Kalanda, B.D., Oke, T.R., and Spittlehouse, D.L., 1980. Suburban energy balance estimates for Vancouver, B.C. using the Bowen ratio-energy balance approach. J. Appl. Meteorol. 19, 791-802. Kerschgens, M.J., and Hacker, J.M., 1985. On the energy budget of the convective boundary layer over an urban and rural environment. Beitr. Phys. Atmosph. 58, 171-185. Kerschgens, M.J., and Kraus, H. , 1990. On the energetics of the urban canopy layer. Atmospheric Environment 24B, 321-328. Large, W.G., 1979. The turbulent fluxes of momentum and sensible heat over the open sea during moderate to strong winds; Ph.D. Thesis, The University of British Columbia, Vancouver. Latimer, J.R., 1972. Radiation measurement. Int. Field Year for the Great Lakes Tech. Manual Ser. 2, NRC/USNAS/IHD, Ottawa, 53pp. Lettau, H.H., 1969. Note on aerodynamic roughness-parameter estimation on the basis of roughness-element description. J. Appl. Meteorol. 8, 828-832. Lowe, P.R., 1977. An approximating polynomial for the computation of saturation vapor pressure. J. Appl. Meteorol. 16, 100-103. Lowry, W.P., 1977. Empirical estimation of urban effects on climate: A problem analysis. J. Appl. Meteorol. 16, 129-135. Mahrt, L. , 1976. Mixed layer moisture structure. Mon. Wea. Rev. 104, 1403-1407. Mahrt, L. , 1991. Boundary layer moisture regimes. Q.J.R.Meteorol. Soc. (submitted). McBean, G.A., 1970. The turbulent transfer mechanisms in the atmospheric surface layer. Ph.D. Thesis, The University of B r i t i s h Columbia, Vancouver. McBean, G.A., 1971. The variations of the stat i s t i c s of wind, temperature and humidity fluctuations with stability. Boundary Layer Meteorol. 1, 438-457. McBean, G.A., 1972. Instrument requirements for eddy correlation measurements. J. Appl. Meteorol. 11, 1078-1084. McBean, G.A., 1973. Comparison of the turbulent transfer processes near 273 the surface. Boundary Layer Mateorol. 4, 265-274. McBean, G.A., 1986. The atmospheric boundary layer. In 'The Geophysics of Sea Ice', Ed. N. Untersteiner, Plenum Publishing Corporation, 283-337. McBean, G.A., and Miyake, M., 1972. Turbulent transfer mechanisms in the atmospheric surface layer. Q.J.R.Meteorol. Soc. 98, 383-398. McBean, G.A., and E l l i o t t , J.A., 1978. The energy budgets of the turbulent velocity components and the velocity-pressure gradient interactions. J. Atmos. Sci. 35, 1890-1899. McBean, G.A., and E l l i o t t , J.A., 1981. Pressure and humidity effects on optical refractive-index fluctuations. Boundary Layer Meteorol. 20, 101-109. McCaughey, J.H., Mullins, D.W., and Publicover, M. , 1987. Comparative performance of two reversing Bowen ratio measurement systems. J. Atmos. Oceanic Technology 4, 724-730. McNaughton, K.G., and Jarvis, P.G., 1983. Predicting effects of vegetation changes on transpiration and evapotranspiration. In 'Water Deficits and Plant Growth', Vol VII, Ed. T.T.Koslowski, Academic Press, New York, 1-47. McNaughton, K.G., and Spriggs, T.W., 1986. A mixed-layer model for evaporation. Boundary Layer Meteorol. 34, 243-262. Medeiros Filho, F.C., Jayasuriya, D.A.R., Cole, R.S., Helmis, C.G., and Asimakopoulos, D.N., 1988. Corrected humidity and temperature measurements in the urban atmospheric boundary layer. Meteorol. Atmos. Phys. 39, 197-202. Mitsuta, Y. , 1966. Sonic anemometer thermometer for general use. J. Meteorol. Soc. Japan 44, 12-23. Monin, A.S., and Obukhov, A.M., 1954. Dimensionless characteristics of turbulence in the surface layer. Trudy Geofiz. Inst., Akad. Nauk SSR 24, 163-187. Mulhearn, P.J., and Finnigan, J.J., 1978. Turbulent flow over a very rough, random surface. Boundary Layer Meteorol. 15, 109-132. Nicholls, S. , 1985. Aircraft observations of the Ekman layer during the Joint Air Sea Interaction Experiment. Q.J.R.Meteorol. Soc. I l l , 391-426. Nunez, M., 1974. The energy balance of an urban canyon. Ph.D. Thesis, The University of British Columbia, Vancouver. Ohtaki, E., 1985. On the similarity in atmospheric fluctuations of carbon dioxide, water vapour and temperature over vegetated fi e l d s . Boundary Layer Meteorol. 32, 25-37. 274 Oke, T.R., 1979. Advectively-assisted evapotranspiration from irrigated urban vegetation. Boundary Layer Meteorol. 17, 167-173. Oke, T.R., 1982. The energetic basis of the urban heat island. Q.J.R.Meteorol. Soc. 108, 1-24. Oke, T.R., 1984. Methods in urban climatology. In 'Applied Climatology', 25th International Geographical Congress, Symposium No.18, Zurich, 1984. Oke, T.R., 1987. 'Boundary Layer Climates', 2nd edition, Methuen, London, 435pp. Oke, T.R., 1988. The urban energy balance. Progress in Physical Geography 12, 471-508. Oke, T.R., and Cleugh, H.A., 1987. Urban heat storage derived as energy budget residuals. Boundary Layer Meteorol. 39, 233-245. Oke, T.R., and McCaughey, J.H., 1983. Suburban-rural energy balance comparisons for Vancouver, B.C.: An extreme case? Boundary Layer Meteorol. 26, 337-354. Oke, T.R., Kalanda, B.D., and Steyn, D.G., 1981. Parameterization of heat storage in urban areas. Urban Ecol. 5, 45-54. Oke, T.R., Cleugh, H.A., Grimmond, C.S.B., Schmid, H.P., and Roth, M. , 1989. Evaluation of spatially-averaged fluxes of heat, mass and momentum in the urban boundary layer. Weather and Climate 9, 14-21. Panofsky, H.A., and Dutton, J.A., 1984. 'Atmospheric Turbulence', John Wiley and Sons, New York, 397pp. Panofsky, H.A., Tennekes, H. , Lenschow, D.H., and Wyngaard, J.C, 1977. The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary Layer Meteorol. 11, 355-361. Panofsky, H.A., Lasko, D. , Lipschutz, R. , Stone, G. , Bradley, E.F., Bowen, A.J., and Hajstrup, J., 1982. Spectra of velocity components over complex terrain. Q.J.R.Meteorol. Soc. 108, 215-230. Paquin, J.E., and Pond, S. , 1971. The determination of the Kolmogoroff constants for velocity, temperature and humidity fluctuations from second- and third-order structure functions. J. Fluid Mech. 50, 257-269. Pasquill, F. , 1972. Some aspects of boundary layer description. Q.J.R.Meteorol. Soc. 98, 469-494. Pasquill, F. , 1974. 'Atmospheric Diffusion'. E l l i s Horwood, Chichester, 429pp. 275 Peikorz, G. , 1987. Die Energiebilanz einer stadtischen Struktur. Diploma Thesis, Rheinische Friedrich-Wilhelm-Universitat, Bonn. Phelps, G.T., and Pond, S. , 1971. Spectra of the temperature and humidity fluctuations and of the fluxes of moisture and sensible heat in the marine boundary layer. J. Atmos. Sci., 28, 918-928. Pond, S. , Phelps, G.T., Paquin, G.A., McBean, G.A., and Stewart, R.W. , 1971. Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. J. Atmos. Sci. 28, 901-917. Pond, S. , Large, W.G. , Miyake, M. , and Burling, R.W. , 1979. A G i l l twin propeller-vane anemometer for flux measurements during moderate and strong winds. Boundary Layer Meteorol. 16, 351-364. Ramsdell, J.V., 1975. Wind and turbulence information for vertical and short take-off and landing (V/STOL) operations in built-up urban areas - results of meteorological survey. Battelle, Pacific Northwest Laboratories, Richland, Washington, FAA-RD-75-94, Final Report. Raupach, M.R., 1979. Anomalies in flux-gradient relationships over forest. Boundary Layer Meteorol. 16, 467-486. Raupach, M.R., and Thorn, A.S., 1981. Turbulence in and above plant canopies. Ann. Rev. Fluid Mech. 13, 97-129. Raupach, M.R., and Legg, B.J., 1984. The uses and limitations of flux-gradient relationships in micrometeorology. Agric. Water Management, 8, 119-131. Raupach, M.R., Thorn, A.S., and Edwards, I., 1980. A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces. Boundary Layer Meteorol. 18, 373-397. Rotach, M. , 1990. Turbulence in an urban transition layer. Preprint 'Ninth Symposium on Turbulence and Diffusion', A.M.S., April 30 - May 3, Riso, Roskilde, Denmark, 289-292. Roth, M. , 1988. Spectral analysis of turbulence in an unstable suburban atmosphere. M.Sc. Thesis, The University of British Columbia, Vancouver. Roth, M. , 1990. Turbulent transfer characteristics over a rough urban surface. Preprint 'Ninth Symposium on Turbulence and Diffusion', A.M.S., April 30 - May 3, Risa, Roskilde, Denmark, 293-296. Roth, M., Oke, T.R., and Steyn, D.G., 1989. Velocity and temperature spectra and cospectra in an unstable suburban atmosphere. Boundary Layer Meteorol. 47, 309-320. Schmid, H.P., 1988. Spatial scales of sensible heat flux v a r i a b i l i t y : Representativeness of flux measurements and surface layer structure over suburban terrain. Ph.D. Thesis, The University of B r i t i s h 276 Columbia, Vancouver. Schmid, H.P., and Oke, T.R., 1990. A model to estimate the source area contributing to turbulent exchange in surface layer over patchy terrain. Q.J.R.Meteorol. Soc. 116, 965-988. Schmid, H.P., Cleugh, H.A., Grimmond, C.S.B., and Oke, T.R., 1991. Spatial v a r i a b i l i t y of energy fluxes in suburban terrain. Boundary Layer Meteorol. 54, 249-276. Schmitt, K.F., Friehe, CA. , and Gibson, C.H., 1979. Structure of marine surface layer turbulence. J. Atmos. Sci. 36, 602-618. Schotanus, P., Nieuwstadt, F.T.M., and deBruin, H.A.R., 1983. Temperature measurements with a sonic anemometer and i t s application to heat and moisture fluxes. Boundary Layer Meteorol. 26, 81-93. Shaw, R.H., and Seginer, I., 1985. The dissipation of turbulence in plant canopies. Proc. 'Seventh Symposium on Turbulence and Diffusion' , A.M.S., April 30 - May 3, Boston, 200-203. Smedman-Hogstrom, A-S., 1973. Temperature and humidity spectra in the atmospheric surface layer. Boundary Layer Meteorol. 3, 329-347. Steyn, D.G., 1980. Turbulence, diffusion and the daytime mixed layer depth over a coastal city. Ph.D. Thesis, The University of British Columbia, Vancouver. Steyn, D.G., 1982. Turbulence in an unstable surface layer over suburban terrain. Boundary Layer Meteorol. 22, 183-191. Steyn, D.G., 1985. An objective method to achieve closure of overdetermined surface energy budgets. Boundary Layer Meteorol. 33, 303-310. Steyn, D.G., and Oke, T.R., 1982. The depth of the daytime mixed layer at two coastal sites: a model and i t s validation. Boundary Layer Meteorol. 24, 161-180. Steyn, D.G., and Faulkner, D.A., 1986. The climatology of sea breezes in the lower Fraser valley, British Columbia. Climatological Bulletin, 20(3), 21-39. Steyn, D.G., and McKendry, I., 1988. Quantitative and qualitative evaluation of a three dimensional mesoscale numerical model simulation of a see breeze in complex terrain. Mon. Wea. Rev. 116, 1914-1926. Swinbank, W.C, and Dyer, A.J., 1967. An experimental study in micrometeorology. Q.J.R.Meteorol. Soc. 93, 494-500. Taesler, R., 1978. Observational studies on 3-dimensional temperature and wind fi e l d s in Uppsala. Proc. 'WM0 Symp. bound, layer physics applied to specific problems in air pollution', WM0 #510, Geneva, 23-30. 277 Tanner, B.D., and Green, J.P., 1989. Measurement of sensible heat and water vapor fluxes using eddy correlation methods. Final report, prepared for 'U.S. Army Dugway Proving Grounds'. Tanner, B.D., Tanner, M. , Dugas, W. , Campbell, E. , and Bland, B. , 1985. Evaluation of an operational eddy correlation system for evapotranspiration measurements. Proc. 'National Conference on Advances in Evapotranspiration' , American Society of Agricultural Engineers, Chicago, 111., Dec. 16 - 17. Tennekes, H. , 1973. The logarithmic wind profile. J. Atmos. Sci. 30, 234-238. Thorn, A.S., 1975. Momentum, mass and heat exchange of plant communities. In 'Vegetation and the atmosphere', Vol I. Ed. J.L. Monteith, 57-109. Thorn, A.S., Stewart, J.B., Oliver, H.R., and Gash, J.H.C., 1975. Comparison of aerodynamic and energy budget estimates of fluxes over a pine forest. Q.J.R.Meteorol. Soc. 101, 93-105. Thorn, A.S., and Oliver, H.R., 1977. On Penman's equation for estimating regional evaporation. Q.J.R.Meteorol. Soc. 103, 345-357. Tillman, J.E., 1965. Water vapor density measurements u t i l i z i n g the absorption of vacuum ultraviolet and infrared radiation. In 'Humidity and Moisture, Measurement and Control in Science and Industry', Vol. 1, Ed. A. Wexler, Reinhold, 428-443. Tillman, J.E., 1988. In situ water vapor measurements in the Lyman a and infrared spectrum: Theory and components. In 'Measurement and parameterization of land surface evaporation fluxes', Workshop, Oct. 10 - 21, Banyuls, France (unpublished). Townsend, A.A., 1976. ' The Structure of Turbulent Shear Flow', 2nd edition, Cambridge University Press. Wamser, C. , and Muller, H. , 1977. On the spectral scale of wind fluctuations within and above the surface layer. Q. J. R.Meteorol. Soc. 103, 721-730. Webb, E.K., Pearman, G.I., and Leuning, R. , 1980. Correction of flux measurements for density effects due to heat and water vapour transfer. Q.J.R.Meteorol. Soc. 106, 85-100. Wilczak, J.M., 1984. Large-scale eddies in the unstable s t r a t i f i e d atmospheric surface layer. Part I: Velocity and temperature structure. J. Atmos. Sci. 41, 3537-3550. Willmott, C.J., 1981. On the validation of models. Physical Geography, 2, 184-194. Wyngaard, J.C., 1973. On surface-layer turbulence. In 'Workshop on 278 Micrometeorology', Ed. D.A. Haugen, A.M.S. , 101-149. Wyngaard, J.C, 1981. The effects of probe-induced flow distortion on atmospheric turbulence measurements. J. Appl. Meteorol. 20, 784-794. Wyngaard, J.C, and Cote, O.R., 1972. Cospectral similarity in the atmospheric surface layer. Q.J.R.Meteorol. Soc. 98, 590-603. Wyngaard, J.C, and Zhang, S.F., 1985. Transducer-shadow effects on turbulence spectra measured by sonic anemometers. J. Atmos. Oceanic Technology 2, 548-558. Wyngaard, J.C, Cote, O.R. , and Izumi, Y. , 1971. Local free convection, similarity and the budgets of shear stress and heat flux. J. Atmos. Sci. 28, 1171-1182. Wyngaard, J.C, Pennell, W.T., Lenschow, D.H. , and Lemone, M.A. , 1978. The temperature-humidity covariance budget in the convective boundary layer. J. Atmos. Sci. 35, 47-58. Wyngaard, J.C, Rockwell, L. , and Friehe, C.A., 1985. Errors in measurement of turbulence upstream of an axisymmetric body. J. Atmos. Oceanic Technology 2, 605-614. Yaglom, A.M., 1977. Comments on wind and temperature flux-profile relationships. Boundary Layer Meteorol. 11, 89-102. Yap, D.H., 1973. Sensible heat fluxes in and near Vancouver, B.C. Ph.D. Thesis, The University of British Columbia, Vancouver. Yap, D.H., and Oke, T.R., 1974. Sensible heat fluxes over an urban area -Vancouver, B.C. J. Appl. Meteorol. 13, 880-890. Yersel, M. , and Goble, R. , 1986. Roughness effects on urban turbulence parameters. Boundary Layer Meteorol. 37, 271-284. Zhang, S.F. , Wyngaard, J.C, Businger, J.A. , and Oncley, S.P. , 1986. Response characteristics of the U.W. sonic anemometer. J. Atmos. Oceanic Technology. 3, 315-323. 279 APPENDIX A : CALIBRATION AND CORRECTION OF FAST RESPONSE SENSORS A . l K a i j o Denk i s o n i c anemometer c o r r e c t i o n s This section identifies three error sources together with their associated correction procedures. Firs t l y , the 'transducer shadow effect' causes a reduction of the wind speed in the wake of the transducers (e.g. Zhang et al. , 1986). The magnitude of the decrease depends on the angle between the sonic path and the wind direction. Secondly, the 'flow distortion effect' is caused by the bulk of the sonic array and alters the mean flow. Thirdly, misalignment of the transducers is the f i n a l source of error to be considered. Although the axes of the three sensors supposedly form an orthogonal array, deviations from this orthogonal frame of reference can be substantial. For the probe used in this study the angles were up to 1.4° in error (Rotach and Calanca, 1989; personal communication). The theoretical background to these three errors and the associated correction procedures closely follow those of Rotach and Calanca (1989; personal communication) who conducted a wind tunnel calibration on the same sensor used in the present study. The notation used is as follows: is the undisturbed instantaneous wind component at the point of measurement; 0^  is the flow with respect to an orthogonal frame of reference, distorted by the presence of the sonic array; stands for the same distorted flow, but using the sonic sensors' coordinate system, which is not necessarily orthogonal and U is the measured wind 280 component, including the additional influence of the transducer shadowing. The transducer shadow effect has been parameterized by Wyngaard and Zhang (1985) for a Kaijo Denki type transducer. The measured wind component along the i-th path can be expressed as: where a is the angle between the wind vector and the corresponding sensor axis, A and C are parameters depending on the path length (0.2 m) and diameter (15 mm) of the transducers respectively, and V is the absolute velocity. Correction for misalignment is equivalent to a transformation of the coordinate frame. Defining s t (a bold letter indicates a three-dimensional vector) as the i-th axis of the normalized coordinate frame spanned by the misaligned sensors, t as the j-th axis of the orthonormal coordinate system of the sonic anemometer and |3 as the angle between s and t , i t follows that: (A.l) with C(V) = C -C exp(-C V) 1 2 3 (A.2) j (A.3) c = cosS = s t ij i J (A.4) Wyngaard's approach to the problem of flow distortion (Wyngaard, 1981) is based on the assumption that the integral scale of the 281 turbulence in the undistorted flow is much larger than the characteristic length of the body which is responsible for the distortion. Under these conditions i t can be shown (neglecting second and higher order terms) that: 0 (x,t) = U (x,U ,U ,U ) + a (x)u '(t) (A.6) 1 i 1 2 3 i J j where x is the location of measurement, an overbar indicates a mean quantity, u^' are the turbulent deviations from the mean and au I a (x) = - ° (A.6) 1 J 3U J The matrix a contains the flow distortion coefficients, while the U subscript "0" indicates that the derivation has to be performed at the basic unidirectional state. The coefficients a can be estimated from wind tunnel measurements. Rotach and Calanca suggest the simple linear model: U = r U (A.7) i i j J where the coefficients r are fi t t e d by linear multiple regression. Using (A.7) to perform the derivatives according to (A.6) leads to the approximation of a^ by r . The use of temporal averages in (A.7) is necessary due to the inability to obtain instantaneous values of the undistorted flow in wind tunnel experiments. A detailed sequence of steps for the correction is summarized as follows: 1) Obtain a f i r s t guess for the angle of deviation from the nearest 282 sensor axis from measured and . Correct the component of the nearest sensor pair using (A.l) and (A.2). 2) Repeat step 1 with the improved deviation angle and absolute wind _x ~* speed until a prescribed accuracy (0.1 mm s ) for is reached. 3) Transform into a true orthogonal coordinate system using (A.3) 4) Correct for flow distortion using (A.7). The dimensionless coefficients derived for this probe and used in the correction are A = 11.8, C = 0.937, C = 0.218, C = 0.300 and 1 2 3 0.9990 0.0120 -0.0020 1.005 0.000 0.034 c = -0.0158 0.9997 0.0163 r = 0.063 0.974 0.135 U ij 0.0010-0.0173 0.9999 0.020 0.015 1.163 5) The two corrected horizontal wind components are aligned with the mean wind coordinates through: u = U cosa + U sina (A.8) 2 1 v = U cosa - U sina (A.9) 1 2 where a is the angle from the x-axis of the sonic anemometer. A . 2 L y m a n - a l p h a / K r y p t o n h y g r o m e t e r c a l i b r a t i o n s and c o r r e c t i o n s Figures A.l and A.2 show the calibration curves for the Lyman-alpha hygrometer and the Krypton hygrometer, respectively. The calibration for the former was performed in a climate chamber in the Atmospheric Science Department at the University of Washington in Seattle, whereas the 283 8.0 7.5 c c 7.0 D Q. _ O O 6.5 _a o I 6.0 5.5 O June 1, 1989 o - - - June 2. 1989 _ Sept. 12, 1989 8 10 12 Vapour density (g m - 3 ) 14 16 Figure A . l : Lyman-alpha hygrometer calibration curve. June 1 and 2, 1989 and Sept. 12, 1989 correspond to the calibrations performed before and after the measurement programme. 7.S 7.4 7.2 > £ 7 —H 6.8 c 6.6 3 6.4 SX +-> P 6.2 o —H 6 O 5.8 5.6 5.4 5.2 5 1 r \ X N j I — — N i i S i i N N 1 Xn 5 7 9 11 13 15 17 19 - 3 , Vapour density (g m ) Figure A.2: Krypton hygrometer calibration curve for S/N 1011 as obtained from Campbell Scientific. 284 Krypton hygrometer c a l i b r a t i o n s were obtained from Campbell S c i e n t i f i c (only a sample c a l i b r a t i o n f o r one of the sensors, S/N 1011, i s shown here). The absorption c o e f f i c i e n t s k are d e r i v e d from the slope of the w 2 -1 c a l i b r a t i o n curve d i v i d e d by the sensor spacing and have u n i t s of m g (when used as the c a l i b r a t i o n c o e f f i c i e n t s they correspond to a change of 1 mV i n the s i g n a l output). In general the water vapour a b s o r p t i o n c o e f f i c i e n t s are s i m i l a r f o r both systems used. The main d i f f e r e n c e , however, i s the stronger n o n - l i n e a r i t y of the l o g r e l a t i o n s h i p of the Lyman-alpha sensor compared to the Krypton hygrometers. As a r e s u l t d i f f e r e n t c a l i b r a t i o n c o e f f i c i e n t s were used f o r the two systems depending on the absolute humidity, but the range was much sm a l l e r f o r the Krypton hygrometers. The f o l l o w i n g k values correspond to a humidity w -3 range from 8 to 13 g m : Lyman-alpha: k = -19.2 -» -14.0 w KH20 (S/N 1016): k = -18.0 -» -16.9 w KH20 (S/N 1011): k = -17.8 -> -16.8 w The f o l l o w i n g d e r i v a t i o n of the oxygen c o r r e c t i o n f o r the Krypton hygrometer i s based on a report by Tanner and Green (1989). The f u l l equation d e s c r i b i n g the s i g n a l i n terms of abso r p t i o n of both Krypton l i n e s by water vapour and oxygen i s given by: V = V exp i - x ( k q + k p ) 1 + V exp -|-x(k q + k p ) i (A. 10) q °i I ° J °2 I ° I where V = water vapour s i g n a l from the hygrometer ( V o l t s ) , V q = water vapour s i g n a l without absorption ( V o l t s ) , k = water vapour a b s o r p t i o n w 2 —1 2 -1 c o e f f i c i e n t (m g ), k = oxygen absorption c o e f f i c i e n t (0.85 m g ), o 285 _3 p = oxygen density (g m ) and the subscripts 1 and 2 refer to the two o Krypton absorption lines. If V » V and i f k and k are of the same J 0 0 wl w2 1 2 magnitude, (A.10) can be simplified by approximating the individual absorptions of the two lines for either water vapour or oxygen with a single 'effective' coefficient for that entity: V « V q exp -j-xk qj- exp -j-xk p j- (A. 11) (A.11) i s used to compute water vapour fluxes and corrections for oxygen fluctuations from the hygrometer measurements. Assuming V q to be stable over the averaging period, taking the logarithm on both sides of (A.11), differentiating and approximating the partial derivatives with fluctuations yields for q' : V k p' q' = 3 - (A. 12) -xk V k w q w where the overbar denotes a time average. The second term on the right-hand-side represents the correction due to oxygen. It is not necessary for the Lyman-alpha hygrometer. It can be shown that the correction due to temperature-induced fluctuations in oxygen are more important than those induced by pressure fluctuations and (A.12) can be rewritten as: V ' (CMP) k q' = 3 _ + _ i _ r (A.13) -xk V (RT 2) k w q k w where C = atmospheric concentration of oxygen (0.21), M = molecular o o weight of oxygen (32 g mole 1 ) , P = mean pressure (Pa), R = universal gas 286 constant and is absolute temperature (K). After multiplication with w' the second term on the right hand side in (A. 13) can be expressed as a function, f , of the sensible heat flux: k k Q (CM) f = B — — with B = = 0.229 (A.14) k k T (c M ) w k p a where M is the molecular weight of dry air (29 g mole 1) and c is the a p specific heat of dry air (J g"1 K _ 1). To correct for the oxygen 'contamination', f (in units of W m ) can be simply added to the water k vapour flux directly measured by the Krypton hygrometer. For the water vapour variance the corresponding correction term f (in units of g 2 m 6) i s : (2 C M P) k f = °— - T'q' (A. 15) q (RT2) k k p c T'q' = 2B — - (A. 16) k T w k _3 where p is the density of air (g m ). Again, this correction function a can be added to the measured water vapour variance to obtain the oxygen correction. Tanner (1990; personal communication) points out that the weakness of above oxygen correction procedure lies in the fact that no reliable oxygen absorption coefficient, k , is available. This is because of the o non-linearity in the log relationship of the oxygen response of the 287 Krypton hygrometer as shown in Campbell and Tanner (1985). Eddy correlation measurements of a quantity whose density is measured directly in ambient conditions may require a correction for transport by a small mean vertical wind. The following correction is based on Tanner and Green (1989) who modify and simplify the original water vapour flux correction equation due to density effects derived by Webb et al. (1980): L q (L M ) q L = Q + - (w'q') (A. 17) (c T ) p M p p k a w a where L is the latent heat of vaporization (J g 1) and M is the w molecular weight of water (18 g mole - 1). L is an additional additive fd correction term (in W m ) to the water vapour flux and was applied to both the Lyman-alpha and Krypton hygrometer measurements. 288 APPENDIX B: (CO)SPECTRAL RESULTS FROM THE 1986 F IELD STUDY This Appendix presents (co)spectral results normalized within the similarity framework from a data set which was obtained during a turbulence measurement programme in 1986. Preliminary results from this study, namely an analysis of (co)spectra normalized with (co)variances, have been described elsewhere (Roth, 1988, Roth et al. , 1989). The following results are included here to provide a comparative data set to the one used in the main text of this thesis. These data were gathered under slightly different weather conditions and used a different sensor for the measurement of the u component. The 1986 results are not as comprehensive as those presented in the main text but they provide a useful extension to them. The 1986 study took place at the same (Sunset) site with instruments mounted at the top level of the same tower used in the present study. Sensors included a SAT system for the measurement of w, T, and wT and a modified G i l l propeller anemometer (Pond et al. , 1979) for the measurement of the u component. The effective measurement height for the SAT system was z' = 19 m and 22 m for the G i l l anemometer. The measurement period of 8 days was characterized by mainly anticyclonic weather resulting in very warm temperatures. Instabilities encountered were -2.366 < z'/L < 0.055 (note that L and not L was computed) leading to the s t a b i l i t y groups indicated on the plots. For the case of z'/L = 0.055 only one run was available (only plotted for w). Each of the other groups contained between 4 and 8 runs. The computation of the individual (co)spectra and the composite (co)spectra was identical to the procedure 289 used in the main study. The only difference is that the 1986 w and T results were not low-pass f i l t e r e d and the entire data acquisition was performed on one 21X microdata logger with a sampling frequency of 10 Hz. Averaging time was again 60 min. The results from the 1986 study are compared with the same Kaimal reference data (Kaimal et al. , 1972). Figure B.la shows the composite w spectra. At the high frequency end the spectra collaps onto one line, the same as the reference, and exhibit the required -2/3 slope. At the low frequency end the unstable spectra are within or slightly above the range observed by Kaimal with the most unstable group having the highest energy content and a sucessive ordering with decreasing instability. Associated with this decrease in energy is an orderly progression of both the spectral peak and low frequency r o l l - o f f in the direction of increasingly larger f as z'/L increases. This ordering is especially clear for 0.02 < f < 1. As 'required' the stable run from this study is within Kaimal's stable region (i.e. below the solid line) and shows the highest peak frequency. Comparison shows that these 1986 data are in good agreement with the results from the present study (Figure 5.11a). Figure B.lb shows that the temperature composite spectra follow the -2/3 slope for a short range at the high frequency end. At the highest frequencies the spectral estimates are contaminated by aliasing. For 0.1 < f < 2 the observed energy levels are higher than the reference resulting in a slight hump. Kaimal et al. (1972) note that for unstable conditions at the low frequency end the spectral peaks shift towards increasingly larger f values with increasing instability. This could not 290 i ) 10' 10° CO I O " 2 10"3 z'/L = 0.065 o -0.064 > z'/L > -0 218 * -0.329 > z/L > -0.570 A -0.611 > z'/L > -0.979 + -1.027 > z/L > -2.366 I ' -I ' ' I ' l l _1 I I ' _1 1 I I I I 111 _] I I t i l l b) 10 10' r IO"2 10"' 10° / = 712/(7 10' IO2 10° ^ i o - ' Co 10" 10"3 J 1 I I I I 111 10"-3 10-2 o # A + 10" -0.064 > z/L > -0.218 -0.329 > z/L > -0.570 -0.611 > z'/L > -0.979 -1.027 > z/L > -2.366 -j i i i i i 111 10° 10' 102 •nz/U Figure B.l: Composite spectra of w (a) and T (b) from the 1986 study for four s t a b i l i t y classes. The solid and dashed lines are the Kaimal et al. (1972) limits for neutral and z/L = -2, respectively. 291 be observed f o r a l l s t a b i l i t y c a t e g o r i e s i n the 1986 study, however, the most unstable category does indeed e x h i b i t the highest peak frequency. Compared to the present study (Figure 5.13a) the observations from 1986 show more s c a t t e r at the low frequency end but otherwise agree w e l l . The high frequency end of the u composite spectra (Figure B.2a) f o l l o w s the reference data (at high f r q u e n c i e s the G i l l data were c o r r e c t e d f o r l i m i t e d frequency response). The energy l e v e l s at the low frequency end are below those observed by Kaimal et al. and w i t h i n the exluded zone (also observed i n the present study). A small i n f l e c t i o n can be n o t i c e d at f = 0.2. As u s u a l l y observed f o r the h o r i z o n t a l wind components no o r d e r i n g according to z'/L can be n o t i c e d at the low frequency end. Again i t appears that the u data from the 1986 study compare w e l l w i t h the present observations (see Figure 5.12a). The heat f l u x composite cospectra (Figure B.2b) show e x c e l l e n t agreement w i t h the Kaimal reference at the high frequency end. In the mid range and at low frequencies s l i g h t l y higher c o s p e c t r a l estimates were observed i n the 1986 study and again comparison w i t h the r e s u l t s from the present study (Figure 5.16a) i s very good. 292 a) 10' 10° 9-\ i o - ' CO i o - ' 10" 3 © -0.064 > z'/L > -0.218 * -0.329 > z/L > -0.570 * -0.611 > z/L > -0.979 + -1.027 > z/L > -2.366 < i < 1 i i • 11 1 ' • i ' i i 1 1 1 - 1 I ' • i i n ' I I I I 11 I I I ' b) io-3 10' c — 10-2 10"' 10° / = nz'/U 10' 10* 10° N 10-' o3 IO"2 C I 10" 3 10" O -0.064 > z/L > -0.218 * -0.329 > z/L > -0.570 A -0.611 > z/L > -0.979 + -1.027 > z/L > -2.366 10" 10-2 10" 10° 10' 102 j = nz'/U Figure B.2: Same as Figure B. 1 but for u (a) and wT (b). The solid line is the neutral limit on the stable side and the upper and lower dashed lines approximate the upper and lower unstable limits from Kaimal et al. (1972). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0100669/manifest

Comment

Related Items