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Anthropogenic heat and its relation to building and urban climate in Inuvik, N. W. T. Nicol, Keith Sherman 1976

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ANTHROPOGENIC HEAT AND ITS RELATION TO BUILDING AND URBAN- CLIMATE IN INUVIK, N.W.T. KEITH SHERMAN NIGOL B.A., University of British Columbia, 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE THE FACULTY OF GRADUATE STUDIES (Geography Department, U.B.C.) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA by OF MASTER OF SCIENCE i n December, 1976 Keith Sherman Wicol, 1976. In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t ha t t he L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment of 6G06iCAf rrV The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e dArJ Z?} 149-3-ABSTRACT . . . Previous studies involving energy u t i l i z a t i o n and climate have stressed the importance of anthropogenic energy release ( i . e . that energy generated by human a c t i v i t i e s ) on urban climate. The reverse influence, climate's e f f e c t on energy use, i s less frequently discussed. This i n v e s t i g a t i o n examined the influence of various atmospheric parameters that act to create a space heating demand, and some of the c l i m a t o l o g i c a l e f f e c t s of the consequent anthropogenic heat release i n the extreme case of an A r c t i c settlement i n rtdd-winter. Inuvik, N.W.T. (68° 22', 133° 45') was chosen as the study s i t e , p r i m a r i l y because of the settlement's ce n t r a l i z e d heating system which enabled the anthropogenic heat generation t o be r e a d i l y monitored. The measurement of anthropogenic heat spanned two s p a t i a l ar-d temporal scales. I n i t i a l l y , the energy involved i n the space heating (for the u t i l i d o r - s e r v e d portion) of Inuvik i s regressed against a i r temperature, wind speed, and s o l a r energy est a b l i s h i n g p r e d i c t i v e energy-use equations f o r d a i l y and hourly periods. The equations were w e l l correlated (r^=0.90) f o r both periods, with temperature and wind speed being the most s i g n i f i c a n t variables. I t i s suggested that once quantified, an energy-use equation might be a usef u l input to c e r t a i n urban boundary layer models (e.g. Summers, 1965) which are capable of providing heat i s l a n d i n t e n s i t i e s and mixing depths. On a smaller scale, heat loss from a si n g l e window surface was analyzed experimentally. The energy balance f o r an e x t e r i o r window surface (at the Inuvik Research Laboratory) was obtained under vrjcying atmospheric conditions ( i .e. wind speeds and cloud cover). Wind speed was s i g n i f i c a n t , i n determining sensible heat transfer from the window surface, and.valu.es f o r the heat transfer c o e f f i c i e n t are i n good agreement with those of other workers. The controls on ra d i a t i v e and convection heat losses from windows are discussed i n the l i g h t of the observational data. The p o t e n t i a l of anthropogenic heat to modify the townsite climate of Inuvik i s examined i n two ways. F i r s t l y , the influence of t h i s energy i s investigated i n regard to i t s e f f e c t on the net long-wave radiation balance. Observations indicate that the townsite net long-wave radiation values were consistently more negative than r u r a l measurements during January, 1975. I t was considered that t h i s was due to the greater emission of long-wave r a d i a t i o n from the "warmer" urban surface. A s t a t i s t i c a l l i n k between urban and r u r a l net long-wave r a d i a t i o n differences and township energy-use was obtained. This l i n k further supports the argument that the greater urban r a d i a t i o n output i s related to anthropogenic releases. Attempts to model clear sky counter-radiation revealed that the Idso and Jackson (1969) equation was most su i t a b l e . Secondly, the impact of the anthropogenic heat i n a l t e r i n g the surface energy balance of Inuvik and i t s environs i s investigated. The energy balance was assessed frem both measurements and a numerical simulation model. Energy balance comparisons between the two methods are reasonable, as are the predicted and observed heat islands i n t e n s i t i e s . With cloudless skie s , t y p i c a l measured, townsite energy balance values (Jan. 1975) were: -2 -2 net long-wave r a d i a t i o n f l u x - -39 W m , sensible heat f l u x - -7 -W m , -2 and anthropogenic heat f l u x - 46 VI m . The equivalent observed r u r a l -2 balance i s : net. long-wave r a d i a t i o n f l u x - -32 W m and sensible heat f l u x - -32 W m~2. In summary, the r e l a t i o n of urban climate to energy use i s one of in t e r a c t i o n rather than un i d i r e c t i o n a l , cause and e f f e c t . That i s , climate i n i t i a l l y forces an energy demand on an urban area. However t h i s energy demand r e s u l t s i n anthropogenic heat release which i n turn modify the urban atmosphere. The creation of a warmer urban climate a l t e r s the energy demand s l i g h t l y , creating a dynamic i n t e r a c t i o n with strong, mainly negative feedbacks. i i i TABLE OF CONTENTS Page Chapter 1 INTRODUCTION 1 (A) Statement of General Problem 2 (B) Research Objectives 4 (.C) Experimental Area and Period of Observation 6 (D) Instrumentation 6 (E) Data A q u i s i t i o n 11 Chapter 2 METEOROLOGICALLY - BASED HEAT LOAD REQUIREMENTS - INUVIK, N.W.T., 1974-1975 . 14 (A) Introduction 15 (B) Heat Transfer Theory applied to Buildings 16 (C) The Multiple-Regression Model 21 (D) Results (1) Mean Daily Values of A i r Temperature, 23 Solar Radiation, Wind Speed and Energy Use. (January-July, 1974) (2) Mean Daily A i r Temperature and Wind 40 Speed vs. Energy Consumption (November 1974-January 1975) (3) Hourly A i r Temperatures vs. Energy 41 Consumption (January, 19 75) (4) Anthropogenic Heat and Urban Climates 44 Chapter 3 THE ENERGY BALANCE OF A WINDOW/AIR INTER- 50 FACE (A) Introduction 51 (B) Heat Transfer Theory and i t s Ap p l i c a t i o n to 56 Building Surfaces (.C) Results 65 (1) Regression Models of h and Q„/L* 68 r l (2) Comparison of h Values with Previo'us 75 Work (3) Discussion of Results 78 i v TABLE OF CONTENTS Page Chapter 4 NET RADIATION IN AND NEAR INUVIK, N.W.T. 82 IN JANUARY, 197 5 (A) Introduction 83 (B) Long-wave Radiation i n the A r c t i c 83 >(C) Comparison of L* from Inuvik and surroundings 84 (1) Experimental Sites 84 (2) Results 90 (D) Modelling Clear Sky L i and L* 92 (1) Modelling L+ 92 (2) Modelling L* 102 Chapter 5 THE IMPACT OF ANTHROPOGENIC HEAT ON THE 107 SURFACE ENERGY BALANCE IN AND NEAR INUVIK, N.W.T. - JAN. 1975 (A) Introduction 108 (B) Energy Balances i n and near Inuvik, N.W.T. - 111 January 1975 (1) Energy Balance Components 111 (C) Experimental Results and Simulation 115 Comparisons for Surface Energy Balances In and Near Inuvik, N.W.T. (1) The Measured Surface Energy Balance 115 (2) Energy Balance Comparison v i a a 116 Surface Climate Simulation Model Chapter 6 SUMMARY OF CONCLUSIONS 120 (A) Introduction 121 (B) Chapter 2 121 (C) Chapter 3 123 (D) Chapter 4 124 (E) Chapter 5 125 LITERATURE CITED 127 APPENDIX 1 132 APPENDIX 2 133 v LIST OF TABLES Table Table 1-1: Table 1-2: Table 2-1: Table 2-2: Table 2-3: Table 2-3: Table 2-4: Table 2-5: Table 2-6: Table 2-7: Table 2-8: Table 2-9: Table 3-1: Table 3-2: Table 3-3: Table 3-4: Table 3-5: Caption Page Estimated Energy Savings Across Canada 5 Under Clear Skies and Calm Nights. Experimental Timetable In Inuvik, N.W.T. 5 January 1975. "Summer" versus "Winter" Wind Speeds f 33 January-July, 1974. Meteorological Factors and Heat Loss 35 Explanation. Meteorological Factors and Heat Loss 38 Explanation. Continued. 39 Daily Heat Loss Model (November 1974- 40 January, 1975). Comparison of Mean Temperatures and the 41 Regression C o e f f i c i e n t . E f f e c t of Incorporating Temperature Lag 4 3 i n Model. Hourly Heat Loss Model (January, 1975) . 44 Urban Anthropogenic Heat (Q ) and Net 46 Radiation (Q*). Comparison of Predicted vs. Actual Heat 49 Islands, Inuvik, N.W.T. Thermal Properties of Building Materials 59 and A i r . Energy Transfer i n Calm Wind Conditions. 70 Energy Transfer i n Light Wind Conditions 71 (1-2 m s~i winds) . Energy Transfer i n Medium Wind Conditions 72 (2-3 m s _ 1 winds) . Energy Transfer i n Strong Wind Conditions 73 (3-4 .5 ms _ 1 winds) . v i LIST OF TABLES Table Table 3-6: Table 3-7: Table 3-8: Table 3-9: Table 4-1: Table 4-2: Table 4-3: Table 4-4: Table 5-1: Table 5-2: Table 5-3: Table 6-1: Table A2-1: Caption Page Energy Transfers i n Intermediate Wind 74 Conditions (1.3-3.5 ms" 1). . Comparison of Heat Transfer C o e f f i c i e n t 76 Formulae. Comparison of Heat Transfer C o e f f i c i e n t 76 with Wind Speed. Influence of wind speed on Q_,LA" and Q„J 77 Percentage Contribution by Shortwave 84 (K+) and Counter Radiation (L-J-) to the Tota l Incoming Radiation Balance i n June. The Influence of Cloud Cover on L* 85 (Inuvik, N.W.T.). January Mean Monthly Net Radiation 86 (W m~ 2) f o r Three Northern Canadian Stations. Sample Comparison of Calculated L+ vs. 95 Measured L-!- under Clear Skies. Urban Anthropogenic Heat (Q^) and Net 110 Radiation (Q*). Thermal Conductivity of Various M a t e r i a l s . 113 Comparison of Probable Limits of Mean Q 114 i n Snow, Inuvik, N.W.T. Jan. 7-10, 1975. Energy Exchanges i n and near Inuvik, N.W.T. 125 January, 1975. Input Variables - Simulation Model, 135 v i i LIST OF FIGURES AND ILLUSTRATIONS Figure Figure 1-1: Figure 1-2: Figure 1-3: Figure 1-4: Figure 1-5: Figure 2-1: Figure 2-2: Figure 2-3: Figure 2-4: Figure 2-5: Figure 2-6: Figure 2-7: Figure 2-8: Figure 2-9: Figure 2-10: Figure 2-11: Figure 2-12: Caption Page An anthropogenic heat-process=>response 3 system for a settlement during polar night. Map of Inuvik j, N.W.T. and area. 7 The u t i l i d o r - s e r v e d portion of Inuvik 8 (Jan. 1975). Temperature and p r e c i p i t a t i o n means and 9 extremes - Inuvik, N.W.T. (1957-1970). Schematic T -T thermopile diagram. 12 s a . Temperature gradient through a wal l 17 cross-section. Energy balance of an A r c t i c house on 19 permafrost. Locations of Inuvik A i r p o r t and 22 Radiosonde S i t e . The u t i l i d o r - s e r v e d portion of Inuvik 24 (Jan. 1975). Comparison of wind and temperature at 25 Inuvik A i r p o r t and Inuvik Townsite (I.R.L.) Mean d a i l y energy use at Inuvik, N.W.T. 27 Jan.-July, 1974. Mean d a i l y a i r temperature i n Inuvik, 28 N.W.T. Jan.-July, 1974. Mean d a i l y wind speed i n Inuvik, N.W.T. 29 Jan,-July, 1974. Mean d a i l y s olar r a d i a t i o n i n Inuvik, 30 N.W.T. Jan.-July, 1974 . Energy use and a i r temperature graph. 32 Comparison of slopes and interc e p t s of 36 monthly T a V3. E re l a t i o n s h i p s Comparison of O and 4 hour energy use 42 lag with a i r temperature (Jan. 19, 1975). v i i i LIST OF FIGURES AND ILLUSTRATIONS Figure Figure 3-1: Figure 3-2: Figure 3-3: Figure 3-4: Figure 3-5: Figure 3-6: Figure 3-7: Figure 3-8a,b: Figure 3-9: Figure 4-1: Figure 4-2: Figure 4-3: Figure 4-4: Figure 4-5: Figure 4-6: Figure 4-7: Page 52 54 Caption Location of Inuvik Research Laboratory Inuvik Research Lab., and surroundings. . S.E. wall of Inuvik Research Iiab„ with instrument locations«. Wind d i r e c t i o n : percentage p r o b a b i l i t y f o r any wind speed during Dec«•- Feb„ (1961-1970) at the Inuvik A i r p o r t . Heat flow through a window cross-section. 62 i n polar night. Placement of net pyrgeometer over window 63 surface (Photograph). Window temperatures and L* under a H.W. wind. V a r i a t i o n of window temperature and net long-wave r a d i a t i o n with d i f f e r e n t wind speeds (S.E. winds). V a r i a t i o n of the heat, t r a n s f e r co-e f f i c i e n t with wind speed. Net pyrgeometer placement on XRL roof (Photograph). Net pyrgeometer placement, on IRL roof (Photograph). . Location of Townsite (IRL) and Hidden Lake (unsettled s i t e ) . Comparison of townsite and u n s e t t l e d long-wave r a d i a t i o n with a i r -temperature, Comparison of mean L!» and L | , • f , • meas * C c i i c . using four equations. Comparison of L l meas, fo r four A r c t i c s t a t i o n s , and L * c a J c < 66 67 79 87 88 89 91 98 100 101 Comparison of L>i and L| „ ^ meas. c a l c , under c l e a r skies using 4 A r c t i c s t a t i o n s . i x LIST OF FIGURES AND ILLUSTRATIONS Figure Caption Figure 4-8 % Comparison of L* meas. and L* ca i c -over a range of a i r temperatures at Inuvik„ N.W.T. Figure 4-9: Comparison of L* meas. and L* c a l c over a range of a i r temperatures at Resolute, N.W.T. Figure 5-1: Location of townsite and u n s e t t l e d long-wave r a d i a t i o n balance s i t e s . Figure 5-2: Heat Island Map of Inuvik, N.W.T. x AQ<NCWLEDGEMENTS I n i t i a l l y I must express my thanks to my supervisor, Dr„ T» R. Oke, fo r h i s invaluable encouragement, assistance and suggestions „ His interest at a l l stages of the study i s appreciated. Further, I would l i k e to thank Dr. J . Hay for aiding in.the preparation of t h i s thesis. I am indebted to H. Macpherson, my f i e l d assistant, who withstood the rigours of an a r c t i c winter and without whose help t h i s thesis could not have been written. Further thanks must be extended to Mr. R. H i l l , Manager of the Inuvik Research Laboratory, whose sta f f and laboratory f a c i l i t i e s were most appreciated. The author i s grateful to the Canadian Broadcasting Corporation for the.use of the i r t r a i l e r at Hidden Lake, and to the Northern Canadian Power Commission for energy-use information. The study was funded by grants to Dr. T. R. Oke from the Canada Department of Environment (Atmospheric Environment. Service) and the A r c t i c and Alpine Research Committee of the University of B r i t i s h Columbia administering funds from the Canada tepartrnent of Indian A f f a i r s and Northern Development. x i LIST OF SYMBOLS SYMBOL A Ac As a C CL CP Cs E* e h k K* Ki-ll* LI Lt L-> M DESCRIPTION area altocumulns altostratus albedo heat capacity cirrus specific heat of a i r at constant pressure cirrostratus energy use vapour pressure heat transfer coefficient. thermal conductivity net solar radiation f l u x density Solar radiation incommcj to the surface net long-wave radiation f l u x density counter radiation to the surface long-wave radiation emitted from the surface • long-wave radiation incoming to a v e r t i c a l surface long-wave radiation emitted from a v e r t i c a l surface empirical factor t seasonal temper-ature and precipitable water i n the atmosphere term (Hay, 1970) UNITS 2 ra 3 o-x J m C - I -3 J kg K rrib _7 -2 -.o-l W m C -1 ~1 W m K W ra W m -2 W m -2 W m -2 W m -2 W m -2 VI m -2 x i i SYMBOL DESCRIPTION UNITS Q * net radiaidon flux density T T "2 W m ' Q'. energy flux density ~? W ra Q a energy flux to the atmosphere TT " 2 W m QB energy flux from buildings TT ~2 Q E latent heat flux density TT ~ 2 W m Q F anthropogenic heat flux density TT ~2 sub-surface heat flux density- TT ~ 2 W m QH sensible heat flux density- W m. ^  T a air temperature °C TB building temperature °c T BW temperature of building walls °c T S surface temperature . °C T u-r temperature difference between urban and rural areas °C u wind speed m s u o wind speed of air layer over city m s 1 precLpitable water mm X distance from leading edge of city m difference i n lapse rates between rural and urban air °C rn finite difference approximation e emissivity of a surface air density kg n Stefan-Boltzmann constant VJ m 1 x i i i I N T R O D U C T I O J CHAPTER 1 2 (A) STATEMENT OF GENERAL PROBLEM Anthropogenic (or a r t i f i c i a l ) heat (Qp) can be defined as that energy derived from human a c t i v i t i e s , mainly from combustion of f o s s i l f u e l s (SMIC, 1971). Because of the combustion process, two end-products r e s u l t : (i) energy release or thermal p o l l u t i o n , and ( i i ) "material" release or a i r p o l l u t i o n . Both end-products are of significance from a climatologies! viewpoint (e.g. Atwater, 1971; Oke, 1974). Considering s o l e l y the r o l e of thermal p o l l u t i o n , the impact of t h i s energy release on urban climate has become s i g n i f i c a n t with escalating energy use. This has i n i t i a t e d i n v e s t i g a t i o n to a l i m i t e d extent i n seme mid-latitude c i t i e s (SMIC, 1971; Hage, 1972; Kalma, 1974). These studies indicate that Q„ may be important as an atmospheric energy source, p a r t i c u l a r l y i n the winter season and thus i t must be considered i n examining the causal factors i n creating an urban climate. Further examination of the problem reveals feed-back linkages between energy-use and climate. I n i t i a l l y i t i s noted that climate create an energy demand on a c i t y through space-heating requirements. Steinhart (1974) estimates that home space-heating i n the United States requires f u l l y 57.5% ( i n 1968) of the energy used i n the r e s i d e n t i a l sector. In 1970 t h i s was equivalent to 10.4% of the t o t a l energy consumption f o r the entire United States. The concentrated release of t h i s energy to the urban atmosphere i s a p a r t i a l explanation why c i t y temperatures are generally warmer than t h e i r r u r a l counterparts. In turn increases i n urban a i r temperature are li n k e d to energy requirements creating a feed-back loop. Figure 1-1 displays t h i s concept schematically, and Table 1-1 i l l u s t r a t e s the way i n which warmer urban a i r temperatures 3 URBAN/ATMOSPHERE SUBSYSTEM B u i l d i n g S u b s y s t e m •o-t h e r m o s t a t A t m o s p h e r i c S u b s y s t e m b u i l d i n g A i r i n s u l a t i o n / b u i l d i n g f u n c t i o n ( E n e rgy F l o w s ) (Temperature Response) Figure 1-1: An anthropogenic heat-process-response system for a settlement during polar night. 4 act to p a r t i a l l y suppress further space heating demands (i.e. giving energy savings). I t i s the interaction of these two variables, climate and energy use, that i s the central concern of this thesis. Within a progress-oriented and energy-dependent society, the impact of anthropogenic energy releases on climate are l i k e l y to become increasingly significant. The t o t a l integration of these effects may even have global climate implications (Landsberg and Machta, 1974; Kutzback, 1974). (B) RESEARCH OBJECTIVES With the above comments i n mind, certain primary objectives were considered useful research targets i n the present study. They may be summarized as follows: (1) to examine the effect of climate on space heating requirements with the purpose of delineating significant climatic variables operating to produce a space heating demand. (2) to examine the influence of Q„ on the surface energy balance, particularly directed toward explaining the heat island effect. To maximize the effect of anthropogenic heat on urban climate an arctic settlement i n mid winter was chosen as the study s i t e . The f i r s t objective was investigated at two spatial and temporal scales i n the study s i t e . I n i t i a l l y the space heating requirements of the settlement as a whole were investigated over the period of 1 year (1974). Secondly, the various methods of heat loss for a single window were examined over one month (January, 1975). The second objective included a comparison i n "urban" vs. "rural" net radiation. The period of study for this invest-igation was January, 1975 i n Inuvik, N.W.T. 5. TABLE 1-1 ESTIMATED ENERGY SAVINGS ACROSS CANADA UNDER CLEAR SKIES AND CALM NIGHTS (from Summers, 1974) City Mean Min. Temp. Average Heat Island % Energy j°Q £c) Savings Halifax -8.1 3.3 6 Montreal -13.3 6.1 10 Toronto -7.8 6.7 13 Winnipeg -22.2 5.5 7 Edmonton -18.9 5.5 8 Table 1-2 gives the dates between which each experiment was conducted. Instrument placement and testing was accomplished during the previous summer and the f i r s t week of January, 1975. TABLE 1-2 EXPERIMENTAL TIMETABLE IN INUVIK>•JANUARY 1975 Experiment Study Period (1) Heat loss frcm window at Inuvik Jan. 10 -Research Lab Jan. 31 (2) Long-wave radiation comparison in Jan. 17 -and near Inuvik Jan. 31 (3) Energy balance comparison in and Jan. 17 -near Inuvik Jan. 31 6 (C) EXPERIMENTAL AREA AND PERIOD OF OBSERVATION Inuvik (population 3500-4000) i s located just north of the A r c t i c C i r c l e i n the N.W.T. (68°N, 133°W) (See Figure 1-2). The townsite i s located on continuous perma-frost, therefore the settlement has been constructed on wooden piles to minimize disturbances to the underlying frozen ground. For this reason the u t i l i t y (heating, sewage, and water) distribution lines are situated above ground i n "utilid o r s " . The above ground u t i l i d o r distributes heat from one central heating plant (Figure 1-3). This enables townsite space heating energy use to be simply calculated. The principal data gathering month was January, 1975, although climatic information from much of the previous year was u t i l i z e d i n Chapter 2. Figure 1-4 indicates the average monthly variations i n temperature and precipitation at Inuvik (1957-1970) . Polar night exists for much of January and this condition minimizes certain equipment errors (e.g. interception of solar radiation by unshielded thermocouples), eliminates the need to monitor K* and enhances the effect of Q^ , i n the urban energy balance. (D) INSTRUMENTATION (1) NET LONG-WAVE RADIATION The net long-wave radiation balance was measured at two locations i n and near Inuvik. The pyrgecmeters were of the Funk type (Model SI, Swissteco Pty. Ltd.). Instrument specifications include (i) a tine constant of 23s, and (ii) an instrument accuracy of 5% with a typical 7 E N Z 1 E N Y * Olivier Islands -69'-T e n f L >7mi/n « n r v Island D a v i e s G i l b e r t I . i \ v\\V tv « > s p — jp VA ft D s:'b N~"!^ Z-7 ^ • .V" I v |) ''597 BEAUFORT SEA Pelly/C'" Island/ ,'' 47 Garry S y Island \ / % « H i Kendall - j , ' - Island Pullen Hooper <f-. • Island \ f ; a .„ .•jNbrt.hV' -West • v : . - - 'Point | VtMttn Pot** • « . . . Tokei Pc'nt SufTtfntf ; - Island Cabin. : Hendnckson ~ Hay ChM^ ' t i " v ' ' - R i c h a r d s j f c I s l a n d ' : ' * '.-.IslahdN"-' I--' »-.r)S^ Lang fey Cabin: r '• *-«7 r » - J » * i j C 5 b i n '•o'-y. <•'._:{ . ^ ' / ^ " N " ' * ' o Kittigazuit . (attaatfontdi 0jTuktoyaktuh 4 / I I 1 : * f Island M O U N;T.A I N S .' ^ r. I* ,1/. -4 *i E.N Z IE/ v^'."- Station ' 1--, i 'i •••• D E L T A Imivik iSco/e: \ !'>•' 1:1,000,000 Akbvik 135' X' 5 0 (O 20 , f r l^Kilomoters 134' rii -.:}.^....• -M ./ . F i g u r e 1-2: Map o f I n u v i k N.W.T. a n d a r e a . 9 TIME Figure 1-4: Temperature and p r e c i p i t a t i o n means and extremes -Inuvik,N.W.T. ( 1 9 5 7 - 1 9 7 0 ) , e l e v a t i o n 2 0 0 f t . ( a f t e r B u r n s , 1 9 7 3 ) 1 Extreme high maximum, temperature. 2 Extreme low maximum temperature. 3 Da i l y mean maximum temperature. 4 Extreme high minimum temperature. 5 Extreme low minimum temperature. 6 Mean monthly t o t a l p r e c i p i t a t i o n . 7 Monthly maximum p r e c i p i t a t i o n in 24 h r s . . 10 c a l i b r a t i o n of 1 mv per 28 W m . The pyrgecmeters were i n f l a t e d e i t h e r by a i r pumped through s i l i c a g e l as a drying agent, or simply by the r i g i d i t y of the polyethelene domes i n the col d temperatures. The dry a i r tubing was s u r g i c a l l a t e x which proved r e s i s t a n t t o breaking and cracking i n the extremely" low temperatures encountered (as low as -54°C). In addition to pygreometers equipped with transparent polyethlene domes over both surfaces, one pyrgeometer was modified to measure out-going surface long-wave r a d i a t i o n by use of a black-body cavity. This ca v i t y attachment was placed over the up-facing thermopile surface and the i n t e r i o r c a v i t y surface temperature was constantly monitored. This arrangement made i t possible t o e s t a b l i s h both the inccming and outgoing long^wave ra d i a t i v e fluxes. The l e v e l l i n g of the pyrgecmeters was checked p e r i o d i c a l l y (3-5 times per day) and the domes examined f o r transparency. The l a t t e r proved quite d i f f i c u l t t o maintain, e s p e c i a l l y during ice fog occurences when the domes became glazed with i c e or covered with blowing snow. At these times the domes were scraped cl e a r or replaced. Data gathered when the domes were omitted was discarded. (2) SURFACE AND AIR TEMPERATURES Surface and a i r temperatures were measured wit h copper-constantan thermocouples. The sensors were 20 AWG conductors, sealed i n a stai n l e s s s t e e l sheath. The thermocouple reference temperature was provided by a zener diode i n the data a c q u i s i t i o n system (section E). A thermocouple temperature difference system was also employed t o measure temperature 11 gradients between the window surface and the outside or inside a i r (see Figure 1-5) . This arrangement generates an electo-motive force which i s proportional to the temperature difference (T -T ) . The value - s a of the difference i s obtained by applying the c a l i b r a t i o n c o e f f i c i e n t f o r copper-constantan (approximately 40 V °C "S . Heat i s l a n d ( a i r temperature) observations were taken with an aspirated thermistor temperature sensor. V e n t i l a t i o n rate was maintained a t 3.5 m s ^ by an AC blower and the r e l a t i v e accuracy was considered to be 0.2°C. (Oke and East, 1971) . The sensor was housed i n a polyvinyl chloride tube and the system was attached to the roof o f a vehicle f o r mobile temperature traverses. (3) WIND SPEED Horizontal wind speeds were measured by a sen s i t i v e 3-cup anemometer (R.M. Young Co. Ltd.). The instrument's turning threshold i s 0.45 -0.55 m s \ and a distance constant (63% recovery) of 2.9 m (equivalent to 4 revolutions of the cup), according to manufacturers' s p e c i f i c a t i o n s . (E) DATA ACQUISITION The primary data a c q u i s i t i o n system consisted of a multi-channel data logger (Doric S c i e n t i f i c , Digitrend 210) with a recording accuracy of + 0.3°C or + 1 V. This u n i t monitored a l l temperature (°C) and ra d i a t i o n (mV) signals. A reference temperature of 0°C f o r copper-constantan thermocouples was incorporated w i t h i n the logger. The data were logged at 10 min. i n t e r v a l s and printed on paper tape. There were b r i e f occasions when mechanical or e l e c t r i c a l problems l i m i t e d the q u a l i t y of the data and i n these instances the data were discarded. 12 S U R F A C E C u C n C u C n T O R E C O R D E R V ' Figure 1-5: Schematic T s~T a thermopile diagram, Cu=Copper , Cn=Constantan . 13 A d d i t i o n a l recorders were used to monitor instruments a t locations other than the Inuvik Research Laboratory ( p r i n c i p a l instrumentation sit e ) or when transducer voltage outputs exceeded the voltage s p e c i f i c a t i o n s of the Digitrend system. Two.continuous s t r i p - c h a r t recorders (Honeywell Model Electronik - 194) were used, one to record wind speed a t the Inuvik Research Lab. (I.R.L.), the other to monitor net long-wave r a d i a t i o n at the " r u r a l " s i t e . The recording of the temperature traverses w i t h i n Inuvik was accomplished using a Rustrak s t r i p - c h a r t recorder. CHAPTER 2 METEOROLCGICALLY-BASED HEAT LOAD REQUIREMENTS - I N U V I K , N . W . T . , 1 9 7 4 - 1 9 7 5 14 15 A. INTRODUCTION . Estimations of heat loss (or f u e l needs) f o r buildings requires a knowledge of the complex interactions between various meteorological parameters and p h y s i c a l c h a r a c t e r i s t i c s of b u i l d i n g structure. The former provide the external controls on the heat l o s s , while the l a t t e r tend to counteract t h i s loss by the c a r e f u l choices of b u i l d i n g s i t i n g and materials. Whenever a gradient i n temperature occurs between the i n t e r i o r l i v i n g spaces of a b u i l d i n g and the cooler e x t e r i o r (ambient) a i r , heat w i l l flow through the b u i l d i n g and be l o s t to the atmosphere. The magnitude of the loss varies d i r e c t l y with the temperature gradient produced through the w a l l . The establishment of the heating degree day concept by the American Gas Association i n 1928 marked the heating industry's recognition of t h i s r e l a t i o n s h i p , and i t has since been used by f u e l companies and heating engineers to estimate probable f u e l needs and furnace requirements f o r d i f f e r e n t c l i m a t i c environments. This chapter explores these considerations as w e l l as other factors which influence the heat loading upon a b u i l d i n g . The analyses show: (a) the formulae generated may be u t i l i z e d as basic tools f o r calculating present and future f u e l requirements for the u t i l i d o r - s e r v e d portions of Inuvik, N.W.T., (b) the interactions between the various c l i m a t i c factors important i n creating heating demand, (c) that the heat loss frcm buildings r e s u l t s i n a heat gain f o r the atmosphere, and the creation of an "urban heat i s l a n d " . This i n turn influences the urban atmosphere's a b i l i t y to disperse pollutants, 16 and therefore heat loss formulae can be i n d i r e c t l y applied to models fo r p r e d i c t i n g heat i s l a n d growth or p o l l u t i o n p o t e n t i a l . B. HEAT TRANSFER THEORY APPLIED TO BUILDINGS We w i l l f i r s t review the p r i n c i p l e s of heat transfer through bui l d i n g materials. This hot only establishes which variables are most useful i n a numerical heat loss model, but also delineates the assumptions and errors associated with the p r a c t i c a l p o s s i b i l i t y of approximating actual heat flow by standard meteorological data. Since most b u i l d i n g materials can be classed as s o l i d s , thermal conduction becomes the sole method of heat transfer. For steady-state, u n i d i r e c t i o n a l conditions the heat flow i s then given by: Q = - k f f f j (2-1) -2 Q = heat flow (W m ) where, ' - 1 - 1 k = thermal conductivity (W m C ) ^ 7 = temperature gradient across the material (°C m "*").. The heat loss from a b u i l d i n g therefore i s not only a function of the temperature gradient present between the inner and outer w a l l ( c e i l i n g and roof) surfaces, but also of the a b i l i t y of the w a l l to conduct heat- Graphically eqn. 2-1 i s i l l u s t r a t e d by Figure 2-1, where materials A and C have a much higher conductivity than material B, and thus they show a much smaller temperature drop than i s represented by the i n s u l a t i n g material B. In eqn. 2-1, k refers to the bulk conductivity of the wall^ ( i . e . the mean conductivity of materials A, B, and C.) . This formulation allows the computation of heat loss from buildings i f the inside and outside surface temperatures and the thermal conductivities are known. 17 20 p /O u Inner ' Surface ^ | - 1 0 - 2 0 J A C | AT Ouffer Surface -AX F i g u r e 2-1: T e m p e r a t u r e g r a d i e n t t h r o u g h a w a l l c r o s s - s e c t i o n 18 Thermal conductivities have been tabulated f o r most ccmmon .building materials, and are available from the ASHRAE Handbook (1961) or an ecjuivalent manual. The two surface temperatures are considerably more d i f f i c u l t to e s t a b l i s h as they r e f l e c t changes i n both the outside and ins i d e w a l l temperatures. These temperatures are due to the energy balance of the two surfaces, and are a function of the i n t e r i o r and e x t e r i o r climates as w e l l as the nature of the surfaces. I t can be generally assumed that the i n t e r i o r temperature w i l l be kept r e l a t i v e l y constant (20-25°C) and consequently i n t e r i o r w a l l temperatures are not l i k e l y to fluctuate over a large range ( i f i n s u l a t i o n i s adequate). E x t e r i o r surface temperatures, on the other hand, are l i k e l y to be dcminantly controlled by the ambient a i r temperature but other processes may also become s i g n i f i c a n t (see Figure 2-2). A theoretically-sound b u i l d i n g heat loss model must incorporate as many of the terms i n Figure 2-2 as possible since a l l influence e x t e r i o r surface temperatures. Unfortunately many of these variables are d i f f i c u l t to measure. The introduction of a s o l - a i r temperature approach, which attempts to account f o r the ra d i a t i v e and oonvective processes through a single a i r temperature, i s a s i m p l i f i c a t i o n of the complex surface energy balance. I t involves the creation of a temperature gradient between the i n t e r i o r a i r temperature and a f i c t i t i o u s a i r temperature (the s o l - a i r temperature), such that the heat flow created i s equivalent to the t o t a l energy exchange that would normally occur both by r a d i a t i v e and oonvective processes. There are a v a r i e t y of s o l - a i r temperature formulae (see Hoglund et a l , 19 Energy balance of an A r c t i c house on permafrost . (Note: In mid-winter Kl and Ki are n e g l i g i b l e energy f lows as i s the energy f low through the support posts into the ground). 20 1967) depending on the complexity and accuracy desired. A l l require the measurement of parameters such as solar radiation incident upon the walls and roof and the albedo of the surfaces as well as the use of empirical formulae for determining long-wave exchanges. Although this method i s appealing, i t requires measurements that frequently are not available (i.e. solar radiation on wall surfaces). I t i s clear that some further simplification of the energy flows occuring at the exterior wall a i r interface (Figure 2-2) must be accomplished i f a practical heat loss model i s to be formulated. This requires the examination of those meteorological variables taken on a continuous basis, that are related to building energy loss. In this regard, a i r temperature, horizontal windspeed and solar radiation incident upon a horizontal surface are available through the Atmospheric Environment Service for Inuvik Airport and the nearby radiosonde site. A multiple-regression model u t i l i z i n g these variables would include an approximation of some of the key energy terras for estimating fuel consumption. Of the variables not included, evaporative effects can be considered . small i n this study since most building materials are treated to res i s t water penetration and Inuvik i s situated i n a relatively arid environment (0.4m of precipitation f a l l s annually (Bums, 1973). long-wave exchanges are also ignored, primarily because v e r t i c a l walls of a building are exposed to a long-wave radiative environment that i s reasonably i n balance. For instance, the view factor of a typical wall may include other buildings, the ground surface and other objects that are at a radiative temperature 21 similar to itself. In addition, atmospheric conditions (specifically temperature inversions) in the Inuvik area are such that a favourable counter radiation regime exists throughout much of the year. Thus i t may be argued that long-wave exchanges in this environment are small and not as cri t i c a l as other energy fluxes. C. THE MULTIPLE-REGRESSION MODEL 1. Mean Daily Air Temperature, Wind Speed, and Solar Radiation vs Energy Consumption (January - July, 1974). The variables incorporated in the model are a rationalization of the energy balance theory in terms of the available data including: mean daily temperature at Inuvik Airport, and wind speed and mean daily solar radiation measurements taken at the Inuvik radiosonde site (Figure 2-3). 22 23 These independent variables wi l l be compared against the gross energy consumption of the utilidor-seryed portion of Inuvik (see Figure 2-4). It should be noted that the meteorological measurements are only an approximation of Inuvik townsite values, but the data for the two areas tend to be highly correlated (see Figure 2-5) . The solar radiation values are for a horizontal surface rather than that ijirpinging on a vertical surface, but they serve to describe the general short-wave radiation environment and should be related to that absorbed by the building. Energy use data (E*) are mean daily values (MW) abstracted from charts, supplied by the Northern Canadian Power Commission (N.C.P.C.).. Since a change over i n heating systems was undertaken by N.C.P.C. i n August 1974, only data from January - July 1974 was available. This placed a time constraint on the analysis but this i s considered to be sufficient to analyze the annual variability. Time series of the variables for January - July 1974 are displayed in Figures 2-6 to 2-9. These graphs reveal the internal variability of each factor, and the nature of relationships between the different variables. For instance, mean daily temperature i s obviously inversely related to energy consumption but i s positively correlated with solar radiation. Consequently, solar radiation i s inversely related to energy consumption. The exact numerical formulation of relationships between these variables is the primary objective of the following section. D. RESULTS (1) MEAN DAILY VALUES OF AIR TEMPERATURE, SOLAR RADIATION, WIND SPEED AND ENERGY USE. 25 -*-20 -24* u UJ a: < UJ L U < irpori V/i'nd \ IRL W i n d \ \ 4 5 Q L U 13.6 £ to 2.7 Q Z 1.8 | iO . 9 6 12 18 Sunday J a a l 9 , 1975 24 TIME 6 12 18 M o n d a y Jon .20 ,1975 F i g u r e 2 - 5 : Comparison of wind and temperature at Inuvik Airport and Inuvik Townsite (I.R.L.) * I.R.L. temperature taken 2 m above roof. ** Standard screen temperature. ©'Height to 10 m . ©"Located 3 m above I.R.L. roof (total height of 12 m above ground). 26 A backward stepwise regression was used to deterrnine the simple and multiple regression relationships between the above mentioned variables. The regression was programmed to establish the significance of each term i n the multiple regression equation, and to remove variables which did not significantly improve the s t a t i s t i c a l relationship. The threshold level of significance was placed at 5%. Thus the derived equations include only those variables that are important i n explaining the variance of the dependent variable (energy use). Furthermore, individual plots of a l l the independent variables against energy consumption were studied for any indications of the presence of non-linear trends between variables. No systematic variation i n residuals was observed i n the energy use vs. wind speed or solar radiation graphs. However, the temperature vs. energy use graph revealed a non-linear plot (see Figure 2-10). Through a comparison of slopes test i t was shown that these temperature groups differed significantly i n slope and consequently a breakpoint of 9 MW was chosen to further define the relationship. Although natural systems do not normally have thresholds or break-points, their inclusion may enhance the operational aspect of 'a relationship by improving the productive performance of the model. Regressing mean daily temperature, wind speed and solar radiation against mean daily energy consumption for the "winter" period (>9xl0 W) yields equation 2-2. E* i n (WxlO6) = 7.82 - 0.19 (Ta) +0.20(u) (2-2) for wind speeds (u) ranging from 0-6.3 m s -^and temperatures (T ) ranging from a -40.5°C'to' 2.7°C. Relevant s t a t i s t i c s include r~ = 0.92 and a standard Figure 2-6: Mean da i l y ensrqy use in Inuvik,N.W.T. Jan . - Ju ly , 1974. 28 29 30 39fh TIME (Days) Figure 2-9: Mean dai ly solar radiation in Inuvik,N.W.T. Jan. - July ,19/4. 31 error(Sy)of 0.50 MW. Solar radiation i s found to be insignificant at the 5% level and i s eliminated from the regression equation. Of the remaining variables, T i s the most important (F-ratio = 3933) whilst u is s t i l l significant (F-ratio = 17.4), but is less useful in explaining variations in energy consumption. The "summer" model (E* < 9x10 W) yields: E* in WxlO6 = 7.45 - 0.29 (T ) (2-3) a for temperatures from -5.5 to 23°C, and wind speeds fran 0 - 6 m s \ 2 Relevant statistics include r =0.87 and Sy = 0.63 MW. Both wind speed and solar radiation were insignificant at the 5% level. In explaining the slope/intercept values and the particular terms accepted or rejected for each equation, i t should be noted that these equations originated frcm 7 months of data and that statistical problems may make certain variables important in one range and not in another. For instance, wind i s significant in the "winter" (E* >_ 9.0 MW) situation but not i n the "sunmer" (E* (9.0 MW) . This may be the result of highly variable winds in the "winter" as compared to fairly steady "summer" winds (see Figure 2-8). Thus the inclusion of wind into the "summer" model does not result in a statistical improvement since there i s so l i t t l e variation i n this component (see Table 2-1). 75.70 -/ / / ' / / / / / 12.72 -/ / / / / / I 1 •o / 2 954-r r 1/7 / 3 • / ^ / _ ' a > " O J / £ 3 6 -i / " " / / / . . . . . ... ^  3.13 -33 TABLE 2-1 'Summer" versus "Winter" Wind Speeds, January-July, 1974 Mean Standard Deviation "Summer" (E*£9.0 (MW) 3.8 ms""1 0.90 ms" 1 "Winter" (E*>9.0 (MW) 2.6 ms" 1 1.58ms" 1 Burns (1973), however, shows that normally a l l months have approx-imately the same wind speed v a r i a t i o n s , thus the wind regime during t h i s study may be somewhat abnormal. The above ccmments are made because i n t u i t i v e l y wind speed should be equally e f f e c t i v e i n removing heat a t a l l times of the year i n t h i s environment. Building roughness should be s u f f i c i e n t to y i e l d good mixing conditions i n winter as w e l l as summer, therefore, i t should be s i g n i f i c a n t i n both models. Thus although external temperature i s the dominating determinant f o r heat l o s s , and the model i s most sensitive t o i t s v a r i a b i l i t y , wind speed va r i a t i o n s can also produce marked increased i n f u e l needs at s p e c i f i c times. Solar r a d i a t i o n was found to make an i n s i g n i f i c a n t contribution t o the production of energy consumption i n e i t h e r the "summer" or "winter". This may be the r e s u l t of a number of contributing factors. For instance, i t should be r e c a l l e d that the variable used was the s o l a r r a d i a t i o n incident on a ho r i z o n t a l rather than a v e r t i c a l surface. Secondly, since i t has been established that of the selected v a r i a b l e s , temperature i s pre-eminent i n explaining f u e l consumption, additional variables must, i n f a c t , explain a s i g n i f i c a n t p o r t i o n of the remaining variance i n E* before they are accepted i n t o the model. Thus, although s o l a r r a d i a t i o n 34 produces a marginal improvement i n the predictive a b i l i t y of the model i n both temperature regimes, i t s contribution i s not s i g n i f i c a n t . F i n a l l y , i n Inuvik, aluminum f o i l frequently covers windows. The increased r e f l e c t i o n would reduce the e f f e c t of solar r a d i a t i o n i n reducing the b u i l d i n g heat demand. The outside temperature has been shown to be the single most important variable i n determining heat loss from buildings. This supports the wide spread use of degree-days as a method of calculating f u e l and furnace requirements. However, the exact form of the E* equation varies s u b s t a n t i a l l y over the two energy regimes. The temperature c o e f f i c i e n t varies from -0.29 (E**9 .OMW) to-0.19 (E*>9.0 MW). These slopes imply that heat loss i s more se n s i t i v e to outside temperatures i n warmer weather than during the "winter", because equal changes i n a i r temperature produce larger v a r i a t i o n s i n E* during the "summer". This i s also true f o r the i n d i v i d u a l monthly p l o t s of T vs. E* (Figure 2-11) . I t would appear that as monthly temperatures increase, so do the respective slope values. However, comparisons between d i f f e r e n t months or temperature regimes can only be r e a l i s t i c a l l y appraised when intercept values are reasonably close, and therefore only those l i n e s with Y-intercepts clustered at A or B on Figure 2-11 w i l l be examined. To p a r t i a l l y explain the r e s u l t that slope increases with T i t should be noted that the slope term can be viewed as a measure of the i n s u l a t i v e q u a l i t y of the buildings. A well- i n s u l a t e d structure should t h e o r e t i c a l l y y i e l d a smaller c o e f f i c i e n t than a poorly insulated dwelling, given s i m i l a r intercept values. Thus, the higher summer c o e f f i c i e n t may be the r e s u l t of a reduction i n the 35 TABLE 2-2 Meteorological Factors and Heat Loss Explanation Group (a) E*^9.0 MW ("summer") (b) E*>9.0 MW ('winter") Independent Variable(s) u K*' T+u T+u+K^  u Kl T+u T+U+K4-where: T = A i r temperature(°C ) ci u Wind speed(m s _ 2 K4- = Solar radiation(W m ) E* = Energy use (MW) r 0.87 0.01 0.07 0.88* 0.88* 0.89 0.05 0.19 0.92 0.92* *Variable does not contribute significantly to explaining variation i n energy consumption. Figure 2-11: Comparison of slopes and intercepts of monthly Ta vs E re lat ionships (A and B are referred to in the tex t ) . 37 e f f e c t i v e i n s u l a t i v e a b i l i t y of the b u i l d i n g s , (possibly r e l a t e d to more open doors and windows) and therefore the warmer a i r w i t h i n the b u i l d i n g escapes r e l a t i v e l y e a s i l y i n comparison with the winter s i t u a t i o n . A second explanation f o r the higher "summer" slope values may be r e l a t e d to a wind e f f e c t that i s s t a t i s t i c a l l y 'hidden' w i t h i n the temperature term. As Figure 2-8 and previous wind s t a t i s t i c s have shown, summer wind speeds are f a i r l y uniform. Thus i n f a c t , there may be a background l e v e l of heat loss that i s d i r e c t l y r e l a t e d to wind speed but because of i t s lack of v a r i a b i l i t y i s not s i g n i f i c a n t i n the o v e r a l l equation. This background l e v e l would represent i t s e l f i n a higher than normal slope value, and to some extent may be r e f l e c t e d i n the changing intercept values. The o v e r a l l r e s u l t s examined thus f a r (Table 2-2) compare favourably with previous work, i n p a r t i c u l a r that of Murphy (1960), shown i n Table 2-3. I t i s clear that the a d d i t i o n of a s o l a r term, e i t h e r by introducing a cloud v a r i a b l e , or by the i n c l u s i o n of solar r a d i a t i o n i t s e l f , does not m a t e r i a l l y reduce the variance i n e i t h e r model. The wind term i s apparently s i g n i f i c a n t i n Murphy's study, although no variable elimination method was used i n the regression to indicate the significance of i n d i v i d u a l variables. I n the present study, wind was s i g n i f i c a n t i n the "winter" case, but not s i g n i f i c a n t i n the "summer". -The conclusion of t h i s part of the study must be that an a i r temperature dependent, wind modified, housing heat loss model i s appropriate since 85-90% of the variance i n heat loss, can be a t t r i b u t e d to these 2 variables alone. 38 TABLE 2-3 Meteorological Factors and Beat Loss Explanation Sample Size Correlation Percent , • > T Coefficient Reduction Item Independent variable(s) . w r r 1 D D H A V 147 0.89 79 2 D EMID 147 0.90 81 3 D D B O S 147 0.89 79 4 D D B O S ( 5 ) 147 0.92 84. 5 5 D D B O S ( 2 4 ) 147 0.925 85. 5 6 v BOS 147 0.41 17 7 Saos 147 -0.31 9. .5 8 •"BL HLS 147 -0.29 8 9 p MID 147 -0.04 0 10 D D H A V + V B 0 S 147 0.92 85 11 D E k l D + V B O S 147 0.94 88 12 D D B O S + V B O S 147 0.92 85 13 D D BOS(5) + ^ B O S 147 0.945 89 14 D D BOS(24) + V B0S 147 0.95 90 15 D DMID + V B O S + I B L H L S 147 0.94 88 16 D D B O S(5 ) + V B O S + I B L HLS 147 0.945 89 17 D D B O S(5 ) + V B O S + Sos 147 0.95 90 Location subscripts: HAV - Haverhill BOS - Boston MID - Middletown BL HLS - Blue H i l l Observatory Key to independent variables: E>DHAV - Haverhill degree-days, computed by using a mean temperature obtained by averaging the maximum and minimum on consecutive days (due to the time of gas sendout). 39 D EMID ~ **i.<3,:^ljetown degree-days, computed as was DDj HAV' D DBOS~ B o s t o n degree-days, computed as was D D I i A V DD ,r. - Boston degree-days, computed by using a mean temperature obtained by averaging the temperature of the synoptic observations, 0700, 1300, 1900, 0100, and 0700 l o c a l time. D DBOS(24) ~~ Boston degree-days, computed by using a mean temperature obtained by averaging the hourly temperatures, 0800 to 0700, i n c l u s i v e . V o q - Boston mean wind speed, computed by averaging the speeds at the synoptic observations, 0700, 1300, 1900, 0100, and 0700 l o c a l time. C _ - Boston mean sunrise-to-sunset cloudiness. .BvJo L - Total d a i l y solar r a d i a t i o n received a t Blue H i l l Observatory, modified to take i n t o account the v a r i a t i o n of surface conductance with wind speed. F>MID - Middletown d a i l y p r e c i p i t a t i o n amount. (Source: Murphy (I960)) 40 2. MEAN DAILY AIR TEMPERATURE AND WIND SPEED VS.- ENERGY CONSUMPTION (November 1974 - January 1975) The time period between August 1974 and November 1974 marked a change-over in N.C.P.C.! operations. The high temperature water system which previously heated the entire townsite was thereafter responsible for heating only one loop of the utilidor network (west loop, Figure 2-4) The energy use on this loop is equivalent to roughly 2/3 of the total oonsumption. Therefore the model developed for this loop w i l l have different constants (y-iritercept) than the previous models although slope values should be fairly similar, assuming equivalent temperature regimes (see Table 2-4). TABLE 2-4 DAILY HEAT LOSS MODEL (NOVEMBER 1974 - JANUARY 1975) r 2 Sy Bange , p (MW) T (°C) (m s X) E* i n WX10 .=4.12-0.15(T )+u(0.21) 0.91 0.38 -10 to -50.5 0.5-6.3 a Again wind speed i s significant in the relation, but temperature i s the dtominant forcing function. The wind coefficient i s approximately the same as i n the previous "winter" (E*xMW=7.82-0.19(Ta)+0.20(u), for E* >9MW) . However the temperature coefficient is less, perhaps due to the more effective insulating quality of the buildings (i.e. windows and doors le f t open as l i t t l e as possible). This corresponds to the colder mean temperature for the period which makes argument intuitively reasonable (see Table 2-5) . Direct comparison however, may be somewhat misleading since i t would ignore the role of the y-intercept. 4.1 TABLE 2-5 Ccmparison of Mean Temperatures and the Regression Coefficient Time Span Mean Temperature Regression Coefficient E* 5:9.0 MW -24.0 C 0.19 Nov.-Jan. 1974/5 -31.5°C 0.15 The decrease i n the intercept value i s approximately proportional to the decrease i n size of the area served by the u t i l i d o r , therefore a direct comparison of the slope values as indicators of insulation efficiency seems reasonable. 3. HOURLY AIR TEMPERATURES vs. ENERGY CONSUMPTION (January, 1975) Because of the success of the model for mean daily values, the po s s i b i l i t y of using shorter time intervals was investigated. From the smallest time interval of the available data (hourly meteorological observations), an hourly model was prepared using data for January, 1975. The solar term was deleted because of i t s poor performance i n the daily model, and because much of January may be classed as "polar night" (i.e. K*-= 0). Tests were conducted to determine the lag time for each variable, thereby establishing the correspondence of the temperature at time " t " with the energy consumption at time "t+n" (n=l,2,3...hours). This lag-effect was ignored i n the daily models. The large amounts of data manipulation necessary to obtain hourly results necessitated the restricting of the analyses to three periods each of one day duration. From graphical comparisons (see Figure 2-12) of T^ and E*, i t would appear 42 Figure 2- j2 : Comparison of 0 and <i hour energy use lag with a i r temperature (Jan.19,1975). 43 that any lag would be on a r e l a t i v e l y short time scale. I t appears that the graph f o r zero lag follows the a i r temperature trace b e t t e r than that f o r a 4-h l a g . S i g n i f i c a n t l y , the cooler temperatures toward the l a t t e r part of January 19th r e s u l t i n increasing energy use as indicated by the zero lag data butrnot by the 4-h lag case. Therefore the lag must be reasonably short and l i e between 0-4 h. Therefore the increments "t=0", "t=l-h, "t=2-h",and "t=3-h, were obtained f o r the 3 sample days (Table 2-6). TABLE 2-6 . E f f e c t of Incorporating Temperature Lag i n Model Correlation C o e f f i c i e n t (r) f o r given lag times 0 hour 1 hour 2 hours 3 hours Jan. 6, 1975 -0.53 -0.77 -0.72 -0.72 Jan. 12/13, 1975 -0.83 -0.88 -0.90 -0.89 Jan. 24, 1975 -0.26 -0.31 -0.09 +0.22 (underlined values represent highest correlations) This table s i g n i f i e s that energy consumption i s best correlated with the previous hours' temperature. Thus a 1-h lag between changes i n a i r temperature and i t s impact on space heating demand may be implied. This r e l a t i v e l y f a s t response i s probably the r e s u l t of the small heat storage capacity of the o v e r a l l b u i l d i n g materials (e.g. average w a l l i n the Inuvik Laboratory had a heat storage capacity of 1.47 x 10 J m C ) . Table 2-7 shows the hourly model derived from January, 1975 data incorporating t h i s time lag. 44 TABLE 2-7 HOURLY HEAT LOSS MODEL (JANUARY, 1975) 2 Equation r Sy Range (MWJ T(°C) E* (MW)=5.90-0.11(T ) 0.87 0.38 -52 to -20 The small standard e r r o r value implies that t h i s hourly formulation i s approximately as accurate as the d a i l y model f o r November, 1974 - January, 1975 (Table 2-4) . Therefore i n t h i s c l i m a t i c environment i t can be used t o p r e d i c t the impact of qu i c k l y changing weather conditions on f u e l consumption. The usefulness of t h i s hourly equation can also be extended i n defining the l i m i t s of the heating equipment presently being u t i l i z e d by N.C.P.C. i n Inuvik. To maximize comfort, the heating system should be able to adjust production to cope with r a p i d l y increasing or decreasing heating demand. Cl e a r l y i t i s most c r i t i c a l f o r the heating system to qu i c k l y meet increased heating requirerrents due to dropping temperatures or increasing wind speeds. Based on the January-July, 1974 and January, 1975 data, maximum hourly temperature changes were on the order of 4.5°Ch"1. Thus the Inuvik heating p l a n t must be able to increase energy production by 1.18 x 10^ W to adequately meet the r e s u l t i n g heating -demand 4. ANTHROPOGENIC HEAT AND URBAN CIJMATES Aside.' from the usefulness of the formula derived i n the preceecling sections as p r e d i c t i v e tools f o r deterrruning heat requirements of bu i l d i n g u(m s_.) 0 to 10 45 they also have wider applications in urban micro-climate. In the absence of advection, the urban energy budget i s given (e.g. Oke, 1974) by: L*+K*+QF = QH"K}E+QG (2-6) or Q*+QF = QH-K2E-K)G -2 where, L* = net long-wave radiative flux density (W m ) -2 K* = net short-wave radiative flux density ( W m ) -2 Q_ = anthropogenic heat flux density (W m ) r -2 Qrr = sensible heat flux density (l^m ) H -2 0_ = latent heat flux density (W m ) -2 Q = sub-surface heat flux density (W m ) -2 • - Q* = net all-wave radiative flux density [tJm ) In the winter i n many mid-latitude cities, the magnitude of i s comparable to Q* or even K*, and thus i t s impact on urban climate i s potentially substantial. 46 TABLE 2-8 Urban Anthropogenic Heat (0^ ,) and Net Radiation (Q*) City Area Population Q F Q* (W m 2) (W m 2) (a) Montreal (1961) Summer Winter Year 78 1.1 57 153 99 92 13 52 0.6 11.8 1.9 (b) Vancouver (1970) 112 0.6 Summer Winter Year 15 107 0.1 23 6 3.8 19 57 0.3 (after Oke, personal communication) Table 2-8 displays the variation of Q f and Q* i n summer and winter for two Canadian locations. The importance of Q p i n the urban energy balance i s particularly significant i n the case of Montreal i n winter. Although other factors besides space heating contribute to the a r t i f i c i a l heat minimal, i n comparison to space heating demand, formula such as equations 2-3 and 2-4 could be u t i l i z e d . The estimation of anthropogenic heat production i s not only important from an energy balance standpoint but i s significant i n other urban climatic applications. In recent years, many researchers (Ieahey and Friend,(1971); Hage, (1972); and Kalma, (1974)) have used a model originally designed by Surrrtiers (1961) to predict urban heat island growth and urban mixing depths. A key equation (2-7) derived from this model i s used to predict the heat island intensity. flux, i n certain urban areas where industrial and cormercial uses are 47 where, <iT =heat island intensity (°C) -2 Qp + H =sensible heat flux to the atmosphere (W m ) -(includes 0_) r <* = difference i n lapse rate between rural and urban. area (°C m x=distance from leading edge of urban area (m) U q= wind speed of a i r layer over city (m s -3 f = density of a i r (kg m ) c = specific heat of a i r (J kg ^ C "*") Consequently for settlements where space heating doirrinates the Qp+jj term, the heat island w i l l be a function of space heating requirements. The previous sections have demonstrated, Q can be adequately quantified r for 'Inuvik, given wind speed and a i r temperature, so that equation 2-7 can be rewritten: (2-8) AT = 2*x (T(X-i) +-u ( X 2 ) + ( X 3 ) ^ u-r x o ^ J u o c P where, T = a i r temperature. (°C) 2 A = urbanized area (m ) and X l ' 2^ a n < ^ X3' n e e < ^ t o ^ determined from local data. X^ not only includes the constant term from the original energy use formula but also any other anthropogenic heat terms. I t should also be noted that Summers assumes that Q„,t,=Q1_, which implies that QI7 i s zero. This has p a r t i a l l y been supported by experimental evidence (Summers, 1965), although more recent evidence i s not as conclusive (Yap et a l . , (1969); 48 Roberts et al., (1970)). fevertheless the assumption that Q„ i s zero implies that wind speed , air temperature, and rural lapse rate are the only variables needed to determine the urban heat island. If the urban lapse rate i s assumed to be adiabatic, (i.e. Q =0) then<*is determined r i solely by the rural lapse rate which can be obtained from radiosonde, minisonde, or rural tower data. Therefore, in cases where space heating is the dofninant input to Q_, heat islands can be calculated i n the manner of equation 2-8. This formula has the advantage of having a physical base, and yet has fairly simple input parameters, once the original building energy use formula has been identified. The heat island predicted by the model refers to that temperature difference encountered at street level. However, there i s certain evidence to indicate that perhaps, when building heights and densities reach a c r i t i c a l level, a decoupling of street level and roof top air layers may occur, as indicated by some Vancouver, B.C. heat island data (Oke, 1975) . In Inuvik, N.W.T., where the combination of low heights but wide spacing of buildings, this decoupling i s assumed to be absent and heat islands predicted by this model are those for street-level air. Testing the model i s possible at a primitive level since heat island traverses were recorded during the study period. However, because of instrumentation problems, only 5 traverses are considered useful for the present analysis. Table 2-9 shows the magnitude of the various parameters in the Summers1 model calculation, as well as the measured heat islands. 49 TABLE 2-9 Comparison of Predicted vs. Actual Heat Islands, Inuvik, N.W.T. 2 x Calculated Observed Date (1975) Q F -2 (W m u ) (m s Wind ( C/lOOm) "H Direction (m) u-r (°C) AT u-r (°C) Jan.;; Yl. 23.2 2.8 S 1.8 460 0.44 2.0 Jan. - 21 20.9 4.0 SE 1.0 920 0.29 0.7 Jan. 22 20.5 2.0 SE 1.2 920 0.45 0.8 Jan. 24 21.9 3.1 SE 2.7 700 0.48 0.5 Jan. 27 23.2 0.4 E 1.2 700 0.94 0.7 1 obtained from Jan. 1975 prediction rrodel-equation plus e l e c t r i c a l energy use (monthly data frcm N.C.P.C). 2 obtained from Inuvik radiosonde ascents. CHAPTER 3 THE ENERGY BALANCE OF A WINDOW/AIR INTERFACE 50 51 (A) Introduction The processes by which heat i s l o s t from buildings can be obtained by investigating the energy flows occurring a t t h e i r e x t e r i o r surfaces. Whereas the preceding chapter was p r i m a r i l y concerned with establishing semi-empirical relationships between meteorological variables and heat l o s s , t h i s chapter i s oriented towards a f u l l e r examination of the heat transfer processes operating at an i n d i v i d u a l b u i l d i n g surface. Because of the d i f f i c u l t i e s i n instrumenting an entire b u i l d i n g , the convective and r a d i a t i v e responses of a s i n g l e window were investigated i n r e l a t i o n to various meteorological influences. The objectives of t h i s section include: (1) the cetermination of a heat transfer c o e f f i c i e n t . (2) examination of the v a r i a b i l i t y of the r a t i o , CL/Q*, (sensible heat flux/net r a d i a t i o n heat flux) with changes i n certain atmospheric parameters; s p e c i f i c a l l y , wind speed (u) and cloud cover (n). Figures 3-1 and 3-2 show the location of the study b u i l d i n g , the Inuvik Research Laboratory (I.R.L.), located i n Inuvik, N.W.T. Tne r e l a t i v e l o c a t i o n of the study window i s also indicated i n Figure 3-2 (on the SE w a l l of the I.R.L.), but other measurements were also taken on the NW w a l l , i n a s i m i l a r w a l l p o s i t i o n (see Figure 3-3) . Figure 3-3 shows the SE w a l l and the l o c a t i o n of the instruments. A net pyrgecmeter was located one window to the l e f t of the temperature sensors. The SE w a l l o r i e n t a t i o n was chosen because i t i s usually the windward w a l l of the b u i l d i n g during the winter months, (Figure 3-4), and therefore the problem of wake turbulence behind the b u i l d i n g was minimized. 53 Figure 3-2: Inuvik Research Lab. and surroundings. 54 Wind Speed INSTRUMENT LOCATIONS O Not Pjrgeome!ers 2.3 4.6 m i S.E. wall of Inuvik Research Lab. with instrument, locat ions. 55 N Figure 3-4: Wind d i r e c t i o n : percentage p r o b a b i l i t y fo r any wind speed during Dec.-Feb.(1961-1970) at the Inuvik A i r p o r t . (Note: Dec . -Feb . records 29% calm) ( a f t e r Burns,1973) 56 The I.R.L., l i k e most structures b u i l t on permafrost, was constructed on wooden p i l e s to prevent b u i l d i n g heat from penetrating to the frozen ground and adversely a f f e c t i n g the bearing strength of the s o i l under-l y i n g the b u i l d i n g . The a r e a l dimensions of the I.R.L. (14m wide x 32m long and 9.5m high) i s t y p i c a l of those along Mackenzie Road and D i s t r i b u t o r Street. The height i s important i n r e l a t i o n to net r a d i a t i o n and counter-radiation measurements because of view factor considerations (See Chapter 4) . (B) Heat Transfer Theory and i t s Application to Building Surfaces The methods involved i n delineating heat loss from buildings require the determination of energy flows occurring a t the e x t e r i o r surface of the b u i l d i n g . This not only indicates instrumentation requirements but also i s useful i n estimating errors associated with each energy transfer. In the case of a window surface i n Polar night, a balance must be maintained between the anthropogenic heat f l u x (Q_) from inside the b u i l d i n g and the pathways through which i t i s l o s t to the atmosphere, namely r a d i a t i o n (L*), or convection (Q ), as i l l u s t r a t e d i n Figure 3-5. Evaporation has been ignored because of the dryness of the environment and the apparent lack of water on e x t e r i o r window surfaces, and heat storage i n the window volume ( A Q ) has been assumed to be n e g l i g i b l e . The v a l i d i t y of t h i s assumption w i l l be discussed l a t e r . Thus the net energy balance of the window can be w r i t t e n : "ST °H + L * Ideally the independent measurement of each variable i s required, but both t h e o r e t i c a l and instrumentation deficiencies d i c t a t e that Q„ H 5 7 can be only roughly approximated. This i s due to problems related to defining the turbulent heat flux, particularly the atmospheric diffusion parameter. This necessitates that Q T form a residual term after Q_ and L* have been accurately determined and i s therefore calculated as Q.. = n 1. Heat Transfer Through a Window Surface (G_) r From the preceding framework, the only heat flow through the window surface i s Q F and this can be estimated by the method introduced i n the previous chapter. Therefore, recalling equation (2-1), we can equate the loss of Q_ to.,the conductive flux, v i z : Q = -k(AT). The conductive F F CTTx) heat transfer through the window can be determined i f the temperature gradient ( A T / A X ) i s measured, andk i s determined from tables. This equation requires that.interior and exterior surface temperatures are recorded and that a l l flew i s uni-directional and steady-state. If these conditions are not met, an over- or under-estimation of heat flow w i l l occur due to heat storage i n the intervening glass layer. Because of the complex nature of heat flow equations where directional and non-steady-state conditions prevail, an approximation to (2-1) i s necessary. Further, this approximation requires two assumptions; either a) external and internal temperatures throughout the test periods are f a i r l y constant (i.e. the window i s i n "steady-state"), or b) that the heat storage capacity i s small compared to actual heat flow, so that any over- or under-estimation i s s t i l l relatively small i n comparison to the t o t a l energy flow. Generally condition (a) i s sought, but where this i s not possible, the heat storage capacity must be considered. 58 The heat storage capacity (AQg) can be investigated by considering the divergence of Q_ with distance. From equation (2-1) : r b dx dt . u x; where, dT , , ... . . ,o -1. = temperature change with time ( C ) C = volumetric heat capacity (J m ^ °C V For a derivation of equation 3-1 see Appendix 1. Hence, i f both C and dT are small, then the varia t i o n s i n heat dt storage both w i t h i n the window and through time, are small, and steady-state conditions are approached. The reasonableness of t h i s f o r the b u i l d i n g and the environment under study i s investigated below. From blueprints of the study b u i l d i n g the p r i n c i p a l s t r u c t u r a l components of the b u i l d i n g were obtained. Table 3-1 shows the density, s p e c i f i c heat, heat capacity and thermal conductivity f o r glass as w e l l as the w a l l construction materials involved. The l a t t e r are displayed f o r comparison values. Using the heat storage values f o r glass from Table 3-1 i n conjunction with anticipated window Q_ values, l i m i t s can be placed on the allowable r time variations i n the surface temperature (dT/dt) i f heat storage errors are to be avoided. The average heat transfer, Q_ = -k (dT/dx), given r t y p i c a l i n t e r i o r and e x t e r i o r window temperatures (10°C i n s i d e , -30°C -2 -2 outside) r e s u l t s i n a heat loss approximately equal to HOW m + 30W m . Therefore dT/dt can be obtained by rearranging equation (3-1) as follows: dT =.dQ F/dx = 1 1 0 + 3 0 / Q Q Q 5 , Q J , ,0^.-1 dt —•= ~ t cc / mCs = 48 + 13 C h C 1.66 (xlO ) — 59 TABLE 3-1 Thermal Properties of Bu i l d i n g Materials and A i r MATERIAL DENSITY(p) SPECIFIC HEAT (c ) HEAT CAPACITY (C) THERMAL P CONDUCTIVITY (k) (kg m"3) ( J k g " 1 V 1 ) ( J m~3 V 1 ) (W m"1 V 1 ) Glass 2483 670 1.66 x 10 6 42.8 Gypsum 6 board 1500 1049 1.57 x 10 17.4 Insulation 150 835 1.25 x 105 3.47 Wood 480 1885 9.02 x 10 5 7.65 1.2 1010 1.21 x 10 3 0.025 A i r (Source: B. Jenrdngs (19 70)) This assumes two panes of glass each 0.0025m th i c k , and that the intervening window a i r has a n e g l i g i b l e heat storage capacity i n comparison with glass (Table 3-1). The sol u t i o n implies that surface temperature changes of 48 + 13°C h 1 w i l l r e s u l t i n a heat storage term equal t o the t y p i c a l heat transfer i t s e l f . In the present study, i f measurement accuracy i s w i t h i n 10% (see instrumentation section, Chapter 1) of the t o t a l heat flow, t h i s necessitates that surface temperature changes vary no more than 4.8 + 1.3°C h 1 . Therefore, data were not analyzed i n cases where a combination of i n t e r i o r and e x t e r i o r temperature va r i a t i o n s yielded changes i n glass temperature of more than a 4.8°C h 1. These l i m i t s placed on the temperature change in d i c a t e that the "allowable" temperature v a r i a t i o n on the window surface i s further a function of the i n i t i a l gradient heat -2 flow through the window (Qp) . Thus when i t approaches 140W m (the 60 upper l i m i t ) , the "steady-state" condition w i l l change to 6.1°C h 1 rather than 4.8°C h Further, a reduction i n the conductive heat f l u x w i l l have the opposite e f f e c t , and a reduction i n the allowable dT/dt w i l l occur. Pursuing a s i m i l a r approach to that j u s t presented, the c r i t i c a l outside temperature variations f o r walls can also.be calculated. From the blueprints, the thickness of each of the major w a l l cortponents was measured. In conjunction with the respective heat storage capacities of the materials (Table 3-1), the mean storage capacity i s : -P i n =0.01 (1.57xl0 6) + 0.15(1.25xl0 5) + 0.02(9.02xl0 5) c w a i l : 0.18 = 29.6 x 10 4 J m~3 °C - 1 Experimental evidence indicates that average heat losses through the I.R.L. -2 walls was 13.0 + 4W m , given t y p i c a l i n t e r i o r and e x t e r i o r w a l l temp-eratures. Accordingly, from (3-1) : dT _ dC>/dx dt - C = 13 + 4/0.18 , — j- = 0.88+ 0.27 C h 29.6 x 10 Thus 0.88 +.0.27°C h 1 i s the e x t e r i o r or i n t e r i o r temperature change which w i l l create a heat storage value equivalent to the t o t a l heat flow through the w a l l . Further, the accuracy of the t±ierrrorneters and recording equipment must be able to resolve temperature changes to w i t h i n 10% of t h i s value i f "steady-state" conditions are to be assumed. Therefore, i t i s apparent that attempts to measure heat loss through the theory j u s t presented i s not applicable to walls because i n t e r i o r / e x t e r i o r dT/dt 61 values are cxarmonly greater than 0.088^C h J~. 2. Net Long-wave Radiation (L*) and Building Heat Transfer . The heat loss from the e x t e r i o r surface of the b u i l d i n g must now be p a r t i t i o n e d between ra d i a t i v e and turbulent heat transfer mechanisms. The net r a d i a t i o n component i n t h i s environment includes (a) r a d i a t i o n input to the b u i l d i n g surface frem the ground surface, other buildings, and the sky i n the form of long-wave emission from these surfaces (L«~), and (b) the long-wave loss from the b u i l d i n g surface (L-*) . These two flows, as shown i n Figure 3-5, constitute the net long-wave r a d i a t i o n balance, L*. The windows are r e l a t i v e l y small and hence to properly measure L* the net pyrgeometer must be f i x e d as close as possible to the window surface to avoid view factor errors. These errors would ar i s e i f the r a d i a t i o n impinging on the net pyrgeometer does not originate from the glass alone. The average window view factor calculated f o r the net pyrgeometer placement shown i n Figure 3-6 i s roughly 0.85 ( i . e . approximately 15% of the t o t a l L -> f l u x originates from non-glass surfaces surrounding the windows). 3. Theoretical and P r a c t i c a l Requirements f o r Calculating a Heat Transfer C o e f f i c i e n t (h) f o r Building Surfaces)  From the i n i t i a l energy balance framework discussed at the beginning of t h i s chapter, (Q_ = L* + Q u), i t i s c l e a r that Q„ can be solved as the r ri n difference of CL and L*. To further solve f o r the heat transfer co-F e f f i c i e n t (h), Q„ i s expressed i n a s i m i l a r form to that used f o r conduction n as shown i n equation (3-2): 62 Exterior Of B u i l d i n g L* <k : <— —> I W i n d o w C r o s s Section J B u i / d i n g I n f e r i o r 1 1, Q n ^ A Q c Figure 3 - 5 : Heat f low through a window c r o s s - s e c t i o n i n po lar n i g h t . Note: A Q S represents the heat storage term w i t h i n the window volume. 63 Figure 3-6: Placement of net pyrgeometer over window surface. 64 Q H = h(T s - T a) (3-2) where , h - heat transfer c o e f f i c i e n t (W ra T - T = difference between surface temperature (T ) and the s a ambient air- temperature (T ) ( C). s a Therefore, incorporating the known energy transfers: h = Q p - L* (3-3).. ( T s - V The c o e f f i c i e n t can be further refined by l i n k i n g i t to wind speed (u), since (3-3) h i s closely r e l a t e d to the d i f f u s i v e a b i l i t y of the a i r . The r e l a t i o n s h i p between u and h can be generated i f h i s calculated from (3-3) over a range of wind speeds. Although the above methodology allows the c a l c u l a t i o n of h i f the appropriate measurements are a v a i l a b l e , other p r a c t i c a l considerations i n t h i s study must be handled i f accurate analysis i s to ensue. Simultaneous timing and data f i l t e r i n g must be achieved i f spurious re l a t i o n s h i p s are not to occur. Most problems deal with the wind speed term sinoa i t was continuously measured and not mechanically integrated and consequently i t s format d i f f e r s s u b s t a n t i a l l y from the temperature and r a d i a t i o n terms (see instrument section, Chapter 1). The wind flow around buildings i s exceptionally complex (Halitsky, 1962) and hence f o r most s i t u a t i o n s , roof wind speeds w i l l be non-representative f o r a l l wind dir e c t i o n s . In t h i s study i t was decided to only use data when winds from S, SE and E directions occurred. Only frcm these directions would winds s t r i k e the study w a l l a t a favourable (a) Wind Speed/Direction F i l t e r 65 angle-of-attack. Although roof l e v e l winds and window measurement l e v e l winds are seldom i d e n t i c a l , because of the lack of close dwellings and the r e l a t i v e l y smooth topographic fetch from these directions (see Figure 3-1, map of Inuvik) they are l i k e l y to be s i m i l a r . Wind d i r e c t i o n was established from a i r p o r t records with d a i l y observations made i n Inuvik. (b) Steadiness of Wind F i l t e r P r a c t i c a l d i f f i c u l t i e s a r i s e from, the timing of the two data logging systems. The r a d i a t i o n and temperature measurements are only to with i n + 3 min. of the wind speed recorder. This necessitates f a i r l y steady winds i f the wind speed a t time t i s to be compared with r a d i a t i o n and temperature measurements made a t time t+3min. Therefore, highly, flu c t u a t i n g winds were f i l t e r e d from the data to prevent spurious comparisons. Since p e r f e c t l y steady winds were d i f f i c u l t to obtain, some v a r i a b i l i t y about a mean wind speed was allowed. Fluctuations w i t h i n + the square root of the 10 min. mean wind speed (integrated by hand) , were a r b i t r a r i l y considered "steady", and thus, f o r example with a mean wind speed of 2.7m s \ fluctuations of + 1.1m s 1 were accepted. This method, i n conjunction with the wind d i r e c t i o n f i l t e r , resulted i n a suitable data base f o r cetermining the heat transfer c o e f f i c i e n t of the study window. (C) RESULTS The data are f i r s t analysed to i l l u s t r a t e the magnitudes of the energy flows and t o see i f there was a lag i n response between the energy transfers and changes i n wind speed. Figures 3-7, 3-8(a), and 3-8(b) display the fluctuations of L*, e x t e r i o r window temperatures (on the NW and SE sides 66 CO J O a m a z P LLI CC cc LU a LLl I— O o 2: 2.0 1 0 0 2 5 -27 =- -29 1910 2 0 0 0 T ' ' 2 1 0 0 ' (Jan.14,1975) F igure 3-7: Window t e m p e r a t u r e s and L* u n d e r a N.W. w i n d . o a w i n d s p e e d ( IRL r o o f ) . L* ( S . E . w indow) A t e m p e r a t u r e on S . E . window o t e m p e r a t u r e on N'.W. window 57.5 ^ q t— < 6 5 . — < C \ 1 cc 'E ;62-5 § ~ 1 O 6 0 . § 2 2 0 0 A-c -67 Figure 3 - 8 a , b : V a r i a t i o n of window temperature (•) and net- long-wave r a d i a t i o n (o) with d i f f e r e n t wind speeds (A ) , (SE winds) . 68 of the building) and wind speed. These figuxes indicate that changes in wind speed almost immediately create a response i n the exterior window surface tempera-bore resulting, i n an immediate modification to the radiative balance of the window. ;• Figure 3-7, with NW winds, clearly demonstrates the "lee" or sheltering effect of the building. Since SE window temperataores generally follow the trend of wind speed, but are warmer than NW window temperatures. The temperature and wind speed' fluctuations are in-phase with each other, whilst temperatures and radiative balance are decidedly out-of-phase. This phase relationship i s probably a function of increasing exterior window temperatures being associated with increased radiative loss (assuming that incoming radiation to the window i s relatively constant) . 1. Regression Models of h and QH/L* Initially hourly values of the f u l l data base were investigated. This was necessary because cloud cover influences are significant i n certain portions of the following analysis and cloud values were only available on an hourly basis from the Inuvik Airport. Tables 3-2 to 3-6 display the energy flows and related terms for five arbitrary wind speed classes. Q_ and L* values were obtained from measurerrent, and Q solved for as a residual (Equation 3-2) . The transfer coefficient, h, was cetermined frcm equation 3-3. ____ The ratio QIT/L* reflects the comparative iinportance of the turbulent H and radiative energy loss pathways. A ratio of greater than unity signifies that convective exchanges dominate; whilst a ratio less than unity 69 indicates that r a d i a t i v e e f f e c t s are most important. From Tables 3-2 to 3-6, perhaps the most noticeable trend i n the data i s the increase of h with wind speed. Hourly wind data were used to develop a predictive model of the heat transfer c o e f f i c i e n t . Linear regression of 97 hourly data points (see Figure 3-9) y i e l d s : h = 7.55 + 4.35(u) (3-4) where: u = wind speed i n m s ^  (0<u-c5.0m s "S and h has the units W m~2 °C, with r 2 = 0.83 and = 2.70W n f 2 °cf1. A 10 minute time i n t e r v a l model resulted i n more data points (470) and the equation: h = 7.69 + 4.52(u) (3-4a) with r 2 = 0.85 and S, = 2.69W m~2 °C - 1. h A s i m i l a r regression of the r a t i o Qri/L* with wind speed (u) and cloud cover (n) resulted i n the hourly equation: QI7/L* = 0.62 + 0.44 (u) + 1.2 (n) (3-5) "ft 2 where n = cloud cover i n tenths, with r = 0.59 and S Q^/L* = 0.75. Si m i l a r l y f o r 10 min. i n t e r v a l s : Q/L* = 0.70 + 0.44(u) + 1.3(n) (3-5a)' H 2 with r =0.59 and S(QH/L*) = 0.79. (Note: where needed, n was interpolated between hourly cloud cover values. 70 TABLE 3-2 ENERGY TRANSFER IN CALM. WIND CONDITIONS S/E Window Date (1975) Time Sky Cover Wind2 4 4 L* V L ! , (LST) (in lOth's) (m s 1) -2 (W m XW m~ •2 -ZXW m (W m j Jan. 12 2100 0. 0.0 143. 57. 86. 10.1 1.51 2158 0. 0.0 139. 50. 81. 8.8 1.40 2305 0. 0.0 137. 60. 77. 8.1 1.28 Jan. 13 2403 0. 0.0 136. 57. 79. 9.3 1.38 0101 0. 0.0 141. 55. 86. 9.3 1.56 0159 0. 0.0 144. 52. 92. 10.8 1.77 Jan. 16 1607 2.0 0.0 137. 72. 65. 7.6 0.91 1705 2.0 0.0 137. 65. 74. 8.1 1.04 1901 • 2.0 0.0 133. 63. 70. 7.5 1.11 2000 2.0 0.0 137. 67. 70. 7.2 1.04 Jan. 15 2106 0.0 0.0 132. 75. 57. 5.8 0.76 2204 0.0 0.0 131. 76. 55. 6.1 0.72 Jan. 21 0100 7.0 0.0 92, 32. 60. 9.9 1.90 0158 9.0 0.0 93. 37. 56. 9.2 1.50 0256 9.0 0.0 89. 46. 33. 5.7 0.72 0404 1.0 0.0 90. 57. 33. 5.9 0.58 0502 1.0 0.0 95. 65. 30. 4.8 0.45 Jan. 31 1859 0.0 0.0 112. 64. 48. 6.8 0.75 1 Inuvik Airport 3 Qp= -k(^) 5 solved by^residual 2 I.R.L. roof (3m) 4 ^ A S U R E D B Y N E T QR ~ Q F L * pyrgeometer 6 H = Q*J, _ T 71 TABLE 3-3 ENERGY TRANSFER IN LIGHT WIND CONDITIONS (1-2JH S winds) SE Window Date(1975) Time (LST) Sky Cover 1 (in 10th's) . 2. Wxnd_ (m s 3 4 1 % - 2 L * - 9 ) (Wm ) (W m " V - 2 ) (Wm Z •,6 h -2 ) (W m Jan. 13 1549 2.0 1.00 130.5 40.5 90.0 12.3 2.21 1902 4.0 1.56 129.5 44. 85.7 16.3 1.95 Jan. 15 1259 0.0 1.13 144.5 46.5 98. 14.6 2.1 1348 0.0 m m m m m m 1703 0.0 1.35 138. 59.5 78.5 12.5 1.31 1801 0.0 1.35 133.5 63.0 70.5 10.8 1.11 Jan. 18 1805 5.0 1.58 118.0 49.0 69.0 11.6 1.41 Jan. 24 1055 8.0 1.80 94.5 38.5 56.0 14.4 1.45 1204 9.0 1.58 93.5 33.5 58.0 14.6 1.74 Jan. 28 1704 4.0 0.90 99.5 55.5 44.0 9.7 0.80 1802 4.0 1.13 103.0 51.0 52.2 14.1 1.02 1900 3.0 1.35 101.5 41.0 60.5 16.3 1.47 1958 6.0 0.90 98.5 37.5 61.0 14.8 1.84 2100 8.0 1.35 97.5 39.0 58.5 13.6 1.52 2158 10.0 0.78 95.5 34.5 61.0 13.3 1.78 2256 9.0 1.35 93.0 33.0 63.0 12.9 1. 82 2413 7.0 1.35 94.5 33.5 60.0 13.3 1.79 Jan. 27 1157 3.0 1.13 112.0 55.5 56.5 14.7 1.01 72 TABLE 3-4 ENERGY TRANSFER IN MEDIUM WIND CONDITIONS (2-3m s _ 1) SE Window Date(1975) Time (LST) Sky 1 Cover ( i n 10th's) Wind, M s Gradient (W m ) (W m O i l ) (W m 2 h -2 ) (W m ) Jan. 17 1406 1.0 2.50 136. 50. 86. 14.4 1.72 1504 2.0 2.02 134. 53. 81. . 14.0 1.54 1552 2.0 2.50 132. 53. 79. 15.0 1.48 1758 1.0 2.25 136. 56. 80. 14.9 1.45 1905 1.0 2.70 134. 53. 81. 15.8 1.52 2004 1.0 2.70 134. 46. 88. 15.8 1.90 Jan. 18 1400 5.0 3.15 123. 22. 101. 18.6 4.55 1458 5.0 3.15 123. 35. 88. 16.9 2.54 1557 6.0 2.91 120.5 34. 87. 16.9 2.55 1656 5.0 2.48 119.5 40. 79. 14.5 1.97 Jan. 19 503 4.0 1.8 104. 38. 66. 12.9 1.72 601 8.0 2.48 88. 32. 55.. 16.2 1.72 700 8.0 1.8 83.0 28. 55. 16.8 1.97 758 3.0 ' 2.92 84. 33. 51. 15.8 1.55 Jan. 22 2257 2.0 2.90 85. 34. 51. 24.8 1.48 2404 3.0 2.70 87. 36. 51. 20.2 1.42 102 3.0 2.70 87. 36. 51. 20.3 1.41 Jan. 24 1458 3.0 3.15 113.5 20. 93.5 19.5 . 4.78 1606 2.0 2.92 98. 30.5 67.5 15.6 2.21 1704 2.0 2.70 106.5 41. 65.5 15.5 1.63 1742 2.0 3.38 103.5 40. 63.5 16.7 1.57 1900 2.0 3.15 95.5 36.0 59.5 21.0 1.64 1958 2.0 1.80 104.5 39.0 65.5 14.8 1.68 2056 2.0 1.80 111.0 45.0 66.0 13.5 1.45 Jan. 26 1658 10.0 2.92 86.0 20.0 56.0 21.6 2.74 1756 10.0 2.50 99.5 27.0 72.5 26.7 2.68 1913 10.0 3.15 87.0 24.0 63.0 24.9 . 2.58 2001 10.0 3.38 90.0 25.5 64.5 24.6 2.52 73 TABLE 3-5 ENERGY TRANSFER IN STRONG WIND CONDITIONS -1, (3 - 4.5 in 1 ) SE Window Date (1975) Time Sky" Wind Qf Cover L* -1 -2 -2 (i n lOth's) (m s ) (W m ) (W m ) V h -2 -2 (W m IW m °C _ 1) Jan. 18 455 8. 3.38 126. 22. 104. 21.4 4.06 602 10. 4.05 124. 19. 105. 25.2 5.59 701 10. 3.16 122. 24. 98. 22.0 4.10 750 10. 3.84 124.5 21.5 103. 28.6 4.80 859 10. 4.05 123. 22. 101. 26.9 4.67 957 3. 4.05 123.5 36.0 87.5 25.4 , 2.45 1045 . 4. 3.60 123.5 36. 87.5 22.2 2.45 Jan. 21 1600 9. 3.84 88. 22. 66. 16.5 3.05 1658 9. 4.30 84.5 22.5 62. 27.3 2.74 1757 8. 4.31 84. 17. 67. 24.6 3.96 1855 7. 3.60 84.5 24. 60.5 21.6 2.55 Jan. 22 2055 1. 3.60 90.0 34.5 55.5 22.1 1.60 2159 1. 3.82 86. 34.0 52. 27.6 1.55 2247 2. 3.60 84.5 33. 51.5 26.5 1.57 Jan. 23 406 9. 3.15 84.5 17.0 67.5 22.5 3.91 504 9. 3.38 82. 17.0 65. 27.5 3.82 Jan. 24 1802 2. 3.38 97.5 37.5 60.0 19.7 1.59 Jan. 27 104 10. 3.60 91. 22.0 69. 30.6 3.11 202 10. 3.38 89.5 21.5 68. 28.4 3.20 74 TABLE 3-6 . ENERGY TRANSFERS AT INTERMEDIATE WIND CONDITIONS (1.3 - 3.5 m s" 1) SE Window Date (1975) Time S k y 1 Wind 2 Q p 3 L* 4 h 6 QR/ LST Cover _ 7 _ ? _ 2 -2 " i ( i n 10th's) ( m s .) (W m ) (W m ) (W m ) (W m c - i ) Jan. 17 1602 2.0 2.46 133. 54. 79. 15.0 1.46 1700 2.0 1.35 134. 64. 70. 10.0 1.08 Jan. 18 103 3.0 3.60 131. 26. 105. 20.7 3.96 201 6.0 2.92 127.5 22. 105.5 20.0 4.77 258 6.0 3.13 122. 21. 101. 22.6 4.72 35(5 7.0 3.13 125.5 26. 99.5 19.6 3.80 Jan. 21 2209 9.0 2.70 81. 21.5 59.5 19.9 2.76 2257 9.0 1.80 81. 23. 58. 18.1 2.49 2356 9.0 2.92 83. 17. 66. 22.5 3.88 Jan. 22 104 10.0 2.46 79.5 21. 58.5 19.6 2.76 202 9.0 3.13 79. 21. .58. 20.8 2.84 300 9.0 2.46 77. 18. 59. 19.1 . 3.22 75 U t i l i z i n g the CL/L* equation, certain applications can be addressed. For example, with good mixing conditions ( winds of 5 m s "S and radiative losses at a minimum (overcast skies), convective losses dominate. An upper l i m i t of four times as much energy may be lo s t by convective means i n these conditions compared with radiative losses. At the other extreme, the lower convective/radiative l i m i t of the window i s less than 1.0, under clear skies with calm winds. I t should be noted that the exact numerical representation of equation 3.5a i s li k e l y to be related to the convective and radiative environment i n which the building i s situated and this w i l l change with the nature of the building and i t s surroundings. For instance, i n areas where other buildings or terrain features control radiative exchanges and cloud variations become less significant i n the overall radiation balance (e.g. i n deep urban canyons), the co-e f f i c i e n t of cloud cover may be expected to become smaller. Similarily, where convective exchanges are enhances, (e.g. by increased building roughness), the u coefficient may be expected to increase. The location of the study site on a particular wall may also produce different co-effi c i e n t s i f view factors and other effects are significantly different. Nonetheless, the concept of expressing convective and radiative transfer by parameterizing two easily measured variables i s appealing and warrants more consideration. 2. Comparison of h Values With Previous Work Table 3-7 shows the comparison between the h vs. u relation found i n this study and that found by other investigators. The agreement i s good 76 SOURCE . (1) Jennings (1970) TABLE 3-7 COMPARISON OF HEAT TRANSFER COEFFICIENT FORMULAE WIND SPEED RESTRICTION SURFACE TYPE EQUATION very smooth h = 7.82 + 3.50(u) (2) Jennings smooth wood h = 8.9 + 3.71(u) (1970) and plaster (3) Jennings cast concrete h = 10.7 + 4.96(u) (1970) and smooth brick (4) Schaak (1965) (5) McAdams (1954) (6) Schaak (1965) (7) Nicol (1977) rough surface h = 6.05 + 4.08(u) rough surface h = 6.2 +• 4.26 (u) ro l l e d surface h = 5.82 + 4.02(u) window surface h = 7.69 + 4.52(u) (present study) NOTE: u = m s" 1 h = W n f 2 0 C _ 1 none none none <5 m s <5 m s -1 <?5 m s -1 <5.5 m s -1 TABLE 3-8 . COMPARISON OF HEAT TRANSFER COEFFICIENT WITH WIND SPEED (USING. THE ABOVE EQUATIONS IN TABLE 3-7) ; :  EQUATION (1) (2) (3) (4) (5) (6) 11.3 12.6 15.7 10.1 10.4 9.8 (7) (present study) 11.2 (8) (equation 4 with mass velocity) 11.8 WIND SPEED (m s _ 1 ) 3 5 18.3 19.5 25.6 18.7 18.9 17.8 20.6 20.5 25.3 27.4 35.5 26.4 27.5 25.9 30.0 30.5 NOTE: a l l units i n W m 2 °C 1 77 TABLE 3-9 INFLUENCE OF WIND SPEED ON Q_, . L * and QL_ F H TIME F r i . Jan. 24 (W m 2) L * (W m"2) QP. -2 (W m ) WIND SPEED1 (m s ) 2037 2046 2056 2106 2166 2126 2136 2146 112 110 111 110 110 110 112 112 45 45 45 52 59 62 60 60 67 65 66 58 51 48 52 52 2.7 2.7 2.6 0.5 0.3 0.0 0.5 0.4 Sat. Jan. 25 2206 91 2215 87 2225 86 2235 95 2244 98 2254 99 2304 93 2313 91 56 58 60 59 53 37 31 28 35 29 26 36 45 62 62 63 0.5 0.5 0.37 0.5 1.0 3.2 3.7 4.0 78 considering the dissimilar methods used to establish the relationship. For instance, the development of formulae 4 - 6 i s the result of wind tunnel studies i n which a ve r t i c a l l y heated plate was exposed to a turbulent a i r flow. The plate was heated 25 - 39°C above the ambient a i r temperature, which was fixed at 21°C. Heat loss was measured by the amount of energy necessary to maintain the fixed plate temperature. The equation developed from the present studyy with natural wind speed conditions around a building, gives very similar results (see Table 3-8). I t should be noted that Sdhaak (1964) has suggested that since mass velocity rather than linear velocity i s the variable i n the forced convection equation, a density correction should be made i f the a i r temperature differs materially from 21°C (70°F). Using his correction factor, this modification increases h by 10% (see equation (8) of Table 3-9) / which i s very similar to the measurements from this investigation. In general agreement with other formulae i s within 5-10%. 3. Discussion of Results An interesting implication of equation (3-5a) (Q^/L* = 0.70 + 0.44 (u) + 1.3 (n))is that for increasing wind soaeds, only the ratio Q„/L* n changes; the t o t a l heat loss (Q_) remains the same (see Table 3-9). r Intuitively this would seem contradictory since i t should be expected that t o t a l heat loss would increase as wind speed increases, since heat diffuses more rapidly away from the building i n these conditions. This i s probably the result of the radiative heat loss term which i s a function of the window surface temperature and acts as a negative feedback control on the to t a l heat loss. Thus as QT. increases L* decreases because of 7.0-S-?«?0 - r . <-o u. •O' O cc' ~> 13.0-- r — / i i —I -7.0-7/ i n ///"/ fn \ /1111 i11 /11 / /11 /1 \i in it in UTi 11111in 11111111 \ i /1111111\ 11111111 I\I i /111111 \ / i/////77\ 0 0.76 1.75 . , 2.74 3.73 _4.72 ' WIND SPEED (m's1) " Figure 3 -9 : ' Variat ion of the heat transfer coeff ic ient with wind speed. Note: Number (1,2,3 or 1) indicates the number of data points at that location. 80 the cooler surface temperature created by the enhanced mixing conditions (or vice-versa), and the t o t a l heating demand remains r e l a t i v e l y con-servative. I t should be noted, however, that heat can be l o s t from buildings i n two main modes. I n i t i a l l y , conductive losses through windows or walls must be considered and t h i s i s b a s i c a l l y the approach taken i n the present study. Secondly, heat may be l o s t by mass leakage of warmer a i r out of (or cooler a i r into) the b u i l d i n g through i l l - f i t t i n g doors or windows., or through simple door and window openings. Thus, although evidence developed from t h i s study indicates that wind speed has l i t t l e e f f e c t on the f i r s t of these methods of heat l o s s , i t could w e l l influence the heat loss by the second means, e s p e c i a l l y through the cladding oriented normal to the wind flow. This conclusion should be experimentally examined more cl o s e l y however, since i t implies that heat loss v i a changing wind speeds i s not affected by i n s u l a t i o n thickness, but i s rather a function of the a i r tightness of the structure. This i s i n basic disagreement with tables of w a l l c o e f f i c i e n t s (k) and wind speed commonly shown i n engineering heat loss texts (e.g. Jennings, 1970). Appl i c a t i o n of the QK/L* r a t i o can also be envisioned f o r engineering design factors f o r maximizing energy conservation, and also i n elucidating urban climate processes acting a t the b u i l d i n g / a i r interface under d i f f e r e n t c l i m a t i c conditions. For instance, a convectively-dominated heat loss regime means that the urban a i r w i l l increase i n temperature d i r e c t l y because of t h i s heat transfer, whereas i n a radiatively-dominated heat loss regime, the a i r w i l l only warm i f the r a d i a t i o n i s re-absorbed. Such 8 1 r a d i a t i v e f l u x divergence raay occur i n the lowest layers of the atmosphere with calm conditions at night., Equally important i n urban heat i s l a n d development i s the rate of urban v e n t i l a t i o n , which, together with the rad i a t i v e and convective heat releases, determines the gain of heat by the urban a i r . For example, i n a s i t u a t i o n where convective heat tr a n s f e r i s dominant and v e n t i l a t i o n i s strong ( i . e . high wind speeds), there w i l l be a low net accumulation of heat i n the urban atmosphere. When r a d i a t i v e release i s maximum (calm, clear s k i e s ) , atmospheric temperature increases w i l l become a function of (1) the long-wave absorptive q u a l i t y of the atmosphere and (2) the sky view factor of the urban b u i l d i n g surfaces. The r e l a t i v e importance of each w i l l determine heat i s l a n d formation and magnitude, and therefore becomes a function of the minimum r a t i o of Q H / L * -CHAPTER 4 NET RADIATION IN AND NEAR INUVTK, N.W.T. IN JANUARY, 1975 82 83 To properly analyse the effects of anthropogenic heat release (QF) on the rMcro-climate of Inuvik, N.W.T., i t s ' magnitude must be compared with the other possible energy flows - Q„, Q*, 0_ and 0_. Net radiation rl ti Cj can normally be considered to be the forcing energy flux to the climate system, thus i t s ' accurate deterriLination and v a r i a b i l i t y are most inf l u e n t i a l i n predicting the resulting climate of an area. Thus before the energy balance analysis i s accomplished (Chapter Five), the net radiation environment of Inuvik and environs i s examined for January, 1975. This chapter investigates: (1) a townsite versus "rural" comparison of Q* (actually the net long-wave balance, L*) and (2) modelling the long-wave balance and i t s components. (B) LONG-WAVE RADIATION IN THE ARCTIC Although the long-wave radiation regime of the ar c t i c has not been well documented, there are sufficient studies (Marshunova, 1961; Vowinckel and Orvig, 1964) to indicate that the long-wave balance i s of considerable importance. This i s particularly true during polar night when counter-radiation (Li ) i s the only radiative energy source, but even during the summer months i t s ' contribution outweighs solar radiation (see Table 4-1). During polar night the net radiation balance i s sl i g h t l y negative (Table 4-3). The atmospheric temperature p r o f i l e i s inverted, thereby increasing counter-radiation (Li ) whilst surface losses are riunimal as a result of cold surface temperatures. The addition of clouds (i.e. increasing the effective emissivity of the atmosphere) the surface radiation balance becomes positive even i n the absence of solar energy. This i s v e r i f i e d 84 TABLE 4-1 Percentage Contribution by Shortwave (K •V ) and Counter Radiation (L<H to the Total Incoming Radiation Balance i n June . Latitude (N) 65° 70° 75° 80° 85° 90° % 40 36 32 31 31 31 L * % 60 64 68 69 69 69 (after Orvig, 1970) i n Table 4-2 and by work of Vowinckel and Orvig (1964) . I t would appear that clouds make the winter inversion most effective i n terms of the long-wave surface balance and aid i n creating a radiative balance that i s only s l i g h t l y negative (see Table 4-3). It may be inferred that because of the small amounts of radiative energy i n the winter i n this environment, the other energy exchanges (i.e. QR, and 0^) are l i k e l y to be small or negligible (see Chapter 5) . (C) COMPARISON OF L* FROM INUVIK AND SURROUNDINGS (1) Experimental Sites The net long-wave balance was investigated i n Inuvik during January, 1975. Although solar radiation was present, toward the lat t e r part of the month, measurements i n this analysis do not include solar influences This was accomplished by only using data from times when the sun was below the horizon (polar night). 85 TABLE 4-2 THE INFLUENCE OF CLOUD COVER ON L* (INUVIK, N.W.T.) Time L * ( 1 ) Cloud Cover ( 2 ) Jan. 16/17, 1975 (W m ) Cloud Type/lOth's coverage 2159 (LST) -49 Ci/1 2257 -45 Ac/1, Ci/1 2404 -39 Ac/2, Ci/1 0102 -43 Ac/2, Ci/1 0200 -44 Ac/1, Ci/1 0258 -7 Ac/4, Ci/1 0406 +14 Ac/9 0504 +10 Ac/9 0602 +7 Ac/8 0700 +4 Ac/8 0758 +8 Ac/6 (1) measurement taken on I.R.L. roof (average of 2 net pyrgeometers) ' ( 2 ) f r o m Inuvik Airport 86 TABLE 4-3 January Mean Monthly Net Radiation (W m ") for Three ferthern Canadian Stations Baker Lake, N.W.T. Marld Bay, N.W.T. Whitehorse, Y.T. Year 60°N, 96°W) (76°N, 119°W) (60°N, 135°W) 1972 -23 -21 -13 1973 -17 missing -14 1974 -16 -14 -19 1975 -9.5 -20 -15 (source: Monthly Record, 1972-75.) (a) Inuvik Town Site Measurements of long-wave radiation were made with three net pyrogemeters mounted approximately 3.5 m above the Inuvik Research Laboratory (I.R.L.) roof, (see Figure 4-1 and 4-2). One pyrgeometer was modified to measure only outgoing long-wave radiation (L4- ) , and the other pyrgecmeters provided an average net long-wave flux. (b) Non Settled (Rural) Site This s i t e was located near Hidden Lake to the NE of the' Inuvik s i t e (Figure 4-3). A net pyrgeometer was used to measure L* and was located 15-20 m away from a Canadian Broadcasting Corporation t r a i l e r used to house the data recorder. The net pyrgeometer was located 1 m above the snow surface i n a vegetation free area. The instrument was installed . on Jan. 17, 1975 and comparisons with the Inuvik s i t e data are available to Jan. 30, 1975. 87 Figure 4-2: Net pyrgeometer placement on IRL roof (looking north) 90 (2) Results Figure 4-4 displays a comparison of L* for the Inuvik and non-settled sites for Jan. 26 and Jan. 27, 1975. The differences are generally small -2 (5-10 W m ) but the L* trends are consistent between the two sites. In absolute magnitude the divergence may be explained by differences i n the surface temperature at the two sites. Emissivity differences are not considered significant and the view factors for both surfaces are similar. Assuming that i s equivalent for both sites, which i s reasonable since the sites are separated by only 900 m and urban effects on Lv (in the absence of ice fog) are probably negligible, the Lv difference can be equated to surface temperature differences of roughly l°C/4 W m 2 at the temperatures prevailing. This indicates that during the time period for which Figure 4-4 was derived, surface temperatures were generally 1°C to 3°C warmer on the I.R.L. roof than on the non-settled site surface. The increase i n Lt results i n a more negative net radiation balance for the I.R.L. roof. Further analysis reveals that intersite differences in the long-wave balance (A L*) are s t a t i s t i c a l l y relatable to a i r temperature. The resulting inverse relation i s not strongly correlated (r = 0.34), but i s significant at the 1% level. This correlation with a i r temperature further implies that A L* may be positively correlated' to energy use within Inuvik (Chapter 2). Thus as a i r temperatures decrease, energy use increases' and differences i n the long-wave balance of the two sites increase. Maximum AL* values of 20 W m were recorded. This i s equivalent to a 5 C -2 surface temperature difference, however this decreased to 2-6 W m at times of lesser energy use. These energy findings support the i n i t i a l 91 4 - 4 0 TIME un., Jan.2.6 Mon..,Jan.27 f i gu re 1 - 1 : Comparison of townsite and unset t led long-wave r a d i a t i o n with a i r temperature. n- o a i r temperature fC ) . < . unset t led s i t e (Hidden La(:e). o o townsite ( I K L ) . 92 suggestion that L* differences are surface based. (D) Modelling Clear Sky and L* Measurement i s the preferred method f o r obtaining the long-wave r a d i a t i o n components. Where t h i s i s not possible, other approaches must be u t i l i z e d including r a d i a t i o n charts and empirical formulae (S e l l e r s , 1965). Due to c e r t a i n d i f f i c u l t i e s i n calculating L l by charts, t h i s section w i l l deal with the t e s t i n g of four L l formulae. Further, having established the most su i t a b l e means of emp i r i c a l l y calculating L l makes i t possible to develop an L* formula, based on certain assumptions f o r computing . (1) Modelling L l The estimation of counter r a d i a t i o n (LI ) under clear skies i s possible using a v a r i e t y of empirical and semi-empirical equations. They a l l have a basic form involving the black body r a d i a t i o n from the sky, modified by an e f f e c t i v e e m i s s i v i t y term. The use of an e f f e c t i v e emissivity i s an attempt to quantify the atmospheric nraisture and temperature influence on the incoming long-wave f l u x . (a) Counter r a d i a t i o n Formula (i) Brunt Equation (1932) Brunt (1932) suggested an equation for estimating L^ as follows: L l =cri 4 ( a + bVe) c a l cm - 2 rrdn - 1 (4-1) a where: e = vapour pressure (mb) T = a i r temperature at screen height (K) -10 -2 -1 -4 C = 0.813 x 10 c a l cm min K 93 A variety of values for the constants a and b exist depending on the location for which the constants were derived. However Sellers(1965) suggests mean values of a = 0.605 and b = 0.048 which compare well with those calculated by Budyko (1958)(a=0.61 and b = 0.050) . These values also agree with those obtained by Rusin i n Antarctica (Zillman, 1967). In the present study the Rusin values were used (a = 0.60 and b = 0.048) because they were derived at a i r temperatures of 0°C to -70°C. I t should be indicated that practical d i f f i c u l t i e s arise i n determining the vapour pressure because standard Atmospheric Environment Service (A.E.S.) equipment f a i l s at temperatures below -40°C (personal coirmunication, A.E.S., Inuvik, N.W.T.) . Because the amount of water vapour i s extremely low, the measurement accuracy of the instruments involved must be very high to discern the actual vapour pressure. However the Brunt equation u t i l i z e s the square root of e multiplied by a small constant (0.048) . Thus errors i n e can be very large at these temperatures and the resultant effect on the calculated w i l l be small. With this understanding, IA was calculated using Inuvik Airport screen temperatures, (ii) Swinbank(1963) Attempting to improve upon the Brunt formula, Swinbank (1963) derived the following equation which i s solely dependent on a i r temperature: L i = 53.1 x 10~ 1 4 T 6 (Wm~2) (4-2) The data sources used to generate equation (4-2) were a l l either tropical or mid-latitude (Indian Ocean, Aspendale and Kerang, Australia) and thus this equation lacks high latitude v e r i f i c a t i o n . 94 ( i i i ) Idso and .Jackson (1969) Idso and Jackson (1969) derived what they considered to be an universal clear.sky L4- model, based on data from Pt. Barrow, Alaska; Phoenix, Arizona; and Aspendale and Kerang, Australia. Their equation i s : L|=crT 4 (1-0.261 exp (-7.77(10~4) (273-T)2) (W m~2 ) (4-3) (iv) Hay (1970) Hay (1970) developed the following counter-radiation formula using a range of Canadian sites: = -2.5109 + 39.37 (ii)* - 0.7284(Lt) - 6.789 (M) cal cm"2 day" 1 where: u' '= precipitable water (cm) -2 -1 L f - outgoing long-wave radiation (cal cm day ) M= seasonal temperature and precipitable water term (see Hay, 1970). This formula has the apparent advantage of u t i l i z i n g total atmospheric precipitable water rather than screen vapour pressure, however at Inuvik i n winter, this term becomes negligible. Further, M attempts to describe the seasonal variations i n L4 that arise due to a i r mass changes (i.e. accounting for v e r t i c a l variations i n temperature and water vapour when screen a i r temperatures are similar) . This value however, i s not applicable to this study because of the short time period over which i t was carried out. (b) Discussion Hie comparison between L^ c a^ c , by the four methods and I ^ a s from the I.R.L. roof s i t e i s given i n Figure 4-5 and Table 4-5. I t i s apparent that a l l the models except for the Idso and Jackson equation 95 TABLE 4-4 SAMPLE COMPARISON OF 'CALCULATED L i ® VS. MEASURED L^S® UNDER CLEAR SKIES . Measured „ : Brunt Swinbank Idso/Jackson Hay Date Time L l (W m ) (W m ) (W in ) (W m~2) (W m ) Jan. 12 1903 94 87 60 106 98 12 2100 108 87 60 106 98 11 2200 118 101 75 148 107 9 2305 127 104 79 146 117 10 0005 136 105 81 148 121 17 1855 148 125 104 165 134 17 2004 159 119 96 161 134 31 1859 171 125 103 165 141 22 2006 182 130 147 181 163 ® a l l calculated L values from Airport derived valued ®® measured valued are spot values 96 have underestimated Ll . .. Causes for these discrepancies are varied meas.. c and any explanation must investigate each model individually, with particular emphasis on the geographic location and temporal aspects of the data used to develop the particular model. For instance, Swinbank's L l equation uses only low and mid-latitude data. This i s significant when one examines the inverted atmospheric temperature structure which overlies much of the arc t i c during polar night. Using an argument similar to that of Paltridge (1970) , this mderestimate of L j r B a s ' can be explained by examining screen vs. "centre of gravity" temperature changes in the atmosphere. For example, in lapse conditions, screen height temperatures effectively overestimate the average "centre of gravity" atmospheric radiative temperature since temperature i n this case declines with altitude. The reverse situation occurs with an inversion (temperature increasing. with height) and an underestimation of average atmospheric radiative temperature occurs. Thus although Swinbank's data i s nocturnally based and consequently biased toward s l i g h t inversion conditions, the A r c t i c — temperature inversions are more extreme and may result i n an underestimate of L l by this formula. The typical correction factors given by Paltridge (1970) for inversion -2 conditions are only on the order of 10 W m , however the Swinback formula underestimates LI -by much more than this in the present study. I t .4' calc. could be argued that i n the ar c t i c this correction value would increase r (due to stronger A r c t i c inversions than would be present over Aspendale, Australia or over the Indian Ocean), but i t i s unlikely that this would -2 account for 50 W m which i s the descrepancy applying to Figure 4-5. 97 Swinbank's formula therefore i s not appropriate for high latitude use i n mid-winter since mid-latitude "centre of gravity" corrections s t i l l do not y i e l d suitable results. The Brunt equation (as used i n this study) should not need correction, since the constants u t i l i z e d are based on Antarctic data. However as Figure 4-5 displays, the formula s t i l l yields calculations which under-estimate Li . Hay's L| formula seems to be an improvement (Figure 4-5) which may be attributable to the fact that this model i s based on Canadian data and includes sites of geographic proximity to Inuvik, N.W.T. Furthermore, actual IA measurements were not u t i l i z e d to generate Hay's equation (4-4) but rather Elsasser chart calculations. Thus a "centre of gravity" explanation for the calculated under estimation of L | i s not v a l i d since v e r t i c a l temperature variations are already incorporated. However this approach assumes that Elsasser chart calculations are equivalent to the measurement of Li which i s uncertain. Unlike the above models, which underestimate , i n comparison with clear sky L\ , the Idso calc. meas. and Jackson equation yields results that overestimate Li , especially at ''low" values of L+ ( ^ -150 W m ) . As with the Brunt model, the Idso and Jackson model has high latitude ve r i f i c a t i o n and consequently the effect of the inverted temperature structure occuring i n a r c t i c winter should already be incorporated. This makes the assumption that '.the "cold sky" Li calculations u t i l i z e d by Idso and Jackson, originated under inversion conditions. This i s very probable considering the lew surface temperatures at Pt. Barrow (source of Idso and Jackson L^ calculations) during the L| 98 COUNTER RADIATION (Wm ) F i g u r e <1-5: C o m p a r i s o n o f mean 1.1 p , ^ , c . and Li . u s i r g f o u r m e a s . c a l c . J e q u a t i o n s ( o - S w i n b a n k ( 1 9 6 3 ) , x - B r u n t ( 1 9 3 2 ) , » - H a y ( 1 9 7 0 ) and o - i d s o and J a c k s o n ( 1 9 5 9 ) ) . N o t e : S u b s c r i p t e d numbers r e f e r t o t h e number o f h o u r s c o m p o s i n g e a c h moan . 99 measurement period. Explanation of the overestimate of the idso and Jackson formula can therefore be i n terms of a different v e r t i c a l temp-erature structure over the Inuvik area (in Jan. 1975) i n comparison to typical temperature present at Pt. Barrow i n the Idso and Jackson data. For instance, i f average inversion intensities were weaker over Inuvik (compared to Pt. Barrow) , i n t u i t i v e l y this would lead to less L {• given identical screen temperatures. Although temperature soundings were not obtained for the period i n which the Pt. Barrow data were taken, averages (for 7 years) of inversion at Pt. Barrow reveal that v/inter seasonal inversion thickness i s significantly greater than for many :Arctic stations (U.S. Navy, 1963). S t i l l i t should be noted that divergence i n to calc. -2 Li i s relatively small ( <15 W m ) and further explanation must meas. be handled with care. Since the Idso and Jackson formulae results i n the best estimates of clear sky L^ , further analysis was developed using this formula and data from other Arctic stations. The individual points are displayed i n Figure 4-6 and the mean values i n Figure 4-7. I t becomes apparent that i n agreement with Figure 4-5 the Idso and Jackson formulation overestimates , i n spite of the fact that i t underestimated the original data ( i n Figure 4-4). In general, the comparisons are satisfactory, although the -2 agreement i s definitely better at higher values of L| {Lb > 160 W m ) . At values below this, the agreement becomes poorer although f u l l confirmation i s lacking due to insufficient data from sources other than the present study. Although the difference between Li „ and L^ . '. i s small 1 3 meas. calc. -2 i n energy terms (10-20 W m ) i t i s of interest and warrants further study. 100 COUNTER RADIATION (Wm2)c?.!c F igure 4 - 6 : Comparison of U p , e a s _ v s . U c a 1 c . ( f r o m Idso and J a c k s o n , 1969) f o r four A r c t i c s t a t i o n s ( x - R e s o l u t e , N.V.'.T. (mean d a i l y v a l u e s : 1953-1972) , & - P t . Barrow A laska (hour l y values i n 1957-58,t'.at.her and T h o r n t h w a i t e ) , ' - I n u v i k , N.W.T. (hour ly va lues : Jan . ,1975) a n d A - P t . Barrow, A laska (mean of 130 h a l f hourly va luos t Idso and J a c k s o n , 1969) . 101 C O U N T E R RADIATION (W m > c a | c . F i g u r e 4 - 7 : C o m p a r i s o n o f LJ V S hi , . under c l e a r r i n e a s . c a l c . s k i e n (mean v a l v a r , ) u s i n g f o u r A r c t i c s t a t i o n s ( H - P t . B a r r o w , A l a s k a ( M a t h e r and T h o r n t h w a i t e , 1957/58, h o u r l y s p o t v a l u e s ) , V- P t . B a r r o w , A l a s k a ( I d so and .'Jackson, 1969 - each p o i n t i s 130 1/2 h o u r m e a n s ) , A - Resolute,N.W.T. ( 1 9 6 3 - 1 9 7 2 mean d a i l y v a l u e s ) •- I n u v i k N.W.T. (Jan.1975 s p o t h o u r l y v a l u e s ) ) . N o t e : S u b s c r i p t r e f e r s t o t h e number o f d a t a p o i n t s t h a t w e r e ' u s e d i n e a c h mean. 102 In surrmary, the analysis just presented indicated the Swinbank clear sky i A formula to perform poorly i n this environment, unc^estimating L I ' by as much as 50%. The Brunt and Hay equations are more useful, although they also underestimate L ^ . In addition, instrumental d i f f i c u l t i e s may hamper data collection for these formula and thus i t i s suggested that the Idso and Jackson formula i s best u t i l i z e d i n this environment because of the relatively good results obtained and the simple input requirements. (2) Modelling L* (in polar night) If i t can be assumed that the snow surface radiates as a black body at the screen height a i r temperature, then u t i l i z i n g Idso and Jackson's L formulation, we may write: L* = c r T 4 - c r T 4 ( 1 -0.261(exp -7.77(10~4) (273-T)2) W m~2 (4-5) The i n i t i a l assumption (approximating the surface long-wave loss by •4 T ) i s reasonable since fresh snow emissivities range from 0.95 - 0.99 (Sellers, 1965). Further surface to screen temperature differences may be small, within 1-2°C (average Jan. values, Vowinchel, 1966) and thus assuming the ground to radiate at screen temperatures i n this -2 environment creates a maximum error of 8-10 W m . This was confirmed experimentally by analysis of the cavity-equipped pyrgeometer results which showed that the I.R . L . roof surface was generally cooler but only within the range already stated (1-2°C). Equation (4-5) further indicates that as screen temperatures decrease, L* becomes less negative. This theoretical result i s the consequence of L^ approaching Li- as colder temperatures occur, since the expression: 103 0.261 (exp (-7.77 (10~ 4) (273-7) 2)->0 i n e q u a t i o n (4-5). This r e s u l t i s evident i n the January, 1975 Inuvik data (Figure 4-8) although the e f f e c t i s not as pronounced as equation (4-5) might in d i c a t e . The Lieske and Stroschien data used by Idso and Jackson (1969) are a l s o included. In the present study, the f a i l u r e of the model to p r e d i c t a more negative net long-^wave r a d i a t i o n balance can be explained by the . o r i g i n a l over-estimation of Id> (Figures 4-6 and 4-7) . These graphs show that in. the range of temperatures from 223-233°K, i s overestimated by 20-25 W m 2. A t "warmer" temperatures (>. 250°K) the model pr e d i c t s L* w e l l and comparisons with equations 4-4 and 4-5 reveal that the model compares favourably with) a c t u a l measurements. Explanation of the Pt. Barrow, Alaska data i s more d i f f i c u l t since these points were used to generate the o r i g i n a l Idso and Jackson formula. Thus i f L* ' < L* , , i t would seem to s i g n i f y that LV i s i n error and i s greater than expected. This requires the surface to be warmer than the a i r temperature which seems contradictory to the t y p i c a l winter s i t u a t i o n . In f a c t , an increase i n surface tenperature of 7-8 °c i s necessary to explain these higher negative L* values. meas. Si m i l a r analysis of the Resolute data (Figure 4-9) indicates a high degree of s c a t t e r , but a s i m i l a r trend i s apparent. Further analysis to examine which of the component terms ( i . e . cind/or JA ) i s i n error i s not possible since i n Figure 4-6 was determined by the r e s i d u a l of L*-cr T . I n t u i t i v e l y i t i s anticipated that the counter r a d i a t i o n term i s a t l e a s t accurate and Figure 4-6 and 4-7 i n d i c a t e that the model overestimates act u a l Li . Thus a s i t u a t i o n s i m i l a r to the I.R.L. example may be present (where the general estimation of L* i s the r e s u l t of an L-l overestimation) . 104 233 243 253 Z63 A I R TEMPERATURE ( K ) Figure 4-8: Comparison of !,*• and L* , over a range metis. calc. J of air temperatures at Inuvik,N.W.T.(Jan.1975) with cloudless s k i e s . ( x - Inuvik,H.W.T.(hourly spot values); V - Pt.Barrow,Alaska(from Idso and Blad,1971). 105 A I R T E M P E R A T U R E ( K ) F i g u r e 4-9: C o m p a r i s o n o f L* and L* , o v e r a 1 meas. c a l c . r a n g e o f a i r t e m p e r a t u r e s a t Resolute,N.W.T. w i t h - c l o u d l e s s 0 s k i e s . ( x - Resolute,H.W.T. (mean d a i l y I,*); A P t .Barrow , A l a s k a (from I d s o and B l a d , 1 9 7 1 ) . °The s k y i s c o n s i d e r e d c l e a r i f 19 h o r more a r e c l e a r i n 24 h .Other 5 h may n o t e x c e e d 1/10 C i , A s , A c , o r Cs . 106 However i t i s not possible to conclusively determine with the present information. In summary, the estimation of L* by equation 4-5 i s not very encouraging. However definite conclusions are d i f f i c u l t to assess, since the data sets available are limited and their internal v a r i a b i l i t y i s large. For instance, a s l i g h t modification to for the Inuvik data would have resulted i n a good comparison, of L* and L* , whereas the internal 3 meas. calc. v a r i a b i l i t y of the Resolute data indicates that such an approach equation 4-5 i s too simple. Thus, contrary to the rrodelling of clear sky LV , which gave reasonably good results, modelling clear sky L* i s more complex and requires further work. CHAPTER 5, THE IMPACT OF ANTHROPOGENIC HEAT ON THE SURFACE ENERGY BALANCE .IN AND NEAR INUVTK, N . W . T . - J A N . 19 107 108 (A) INTRODUCTION A knowledge of sixrface energy flows i s a necessary constituent i n any process-oriented climatic analysis since i t i s through changes i n the surface energy balance that variations i n commonly measured variables such as temperature and humidity arise. The surface energy balance i n the absence of advection can be expressed: i9* = Q H ± Q E ± Q G . (5-i) where: positive fluxes indicate toward surf ace energy flews and negative fluxes indicate a surface energy loss This balance i s applicable to any surface where other energy sinks (i.e. snowmelt) or energy, sources (i.e. heat frcm rainwater) are not present. While many rural surfaces typify this situation, urban energy balances include an additional term, CL, such that: Jb Q* + Q F = Q H + QE-+ Q G (5-2) -2 where: Q_ = the anthropogenic heat flux (W m ) r The significance of this new term i n the energy balance i s dependent upon a number of factors. Clearly i t s ' importance i s irdnimal i n urban areas where energy consumption i s low and solar loading i s high. (e.g. sub-tropical urban areas such as Los Angeles i n Table 2-8). Conversely, because of the inverse relationship between Q* and QL, as Q* becomes smaller 0_ increases (see Table 2-8, Table 5-1). t This chapter examines: (1) clear sky energy exchanges i n both Inuvik and a non-settled site near Inuvik (see Figure 5-1) 109 JSP, U - 5 / • 4A • | K * i I S//V /^:*>1 «^V.^ C<c>*'-<'4^ \ « f J Y,. ^X.--^v^ T V V 1 \ S i " W W ' ./0^YT^ ' * .'* Figure 5- t.iic,->hion of townsite and unsettled radiation ba3ance s i t e s , C"! io c i r c l e at th.V I . R . L . indicates the area seen by the lower • _ surface of thr< net pyrgeometer (i.e. view C a r t e r ) . : V The c i r c l e at the unsettled s i t e does not ri> •? 3 5 X c ropresent th.- surface .-ro., seen by --his net pyrgeo- i meter, tmt o n l y indicates its loc.it inn.) Z 110 (2) the effects of the energy balance differences on a i r temperature differences between these sites, thereby creating an "urban heat island", and (3) the change i n energy flows and the temperature response due to Q_ • through a numerical climate - simulation model. TABLE 5-1 Urban Anthropogenic Heat (Q_) And Net Radiation (Q*) r City Area Pop. G_ Q* Q_/Q* (km2) xlO 6 (Wm~2) (W m~2)  (a) Cold Winter Climate Montreal (1961) 78 Summer Winter Year (b) Mild Winter Climate Vancouver (1970) 112 Summer Winter Year 0.6 57 92 0.6 153 13 11.8 99 52 1.9 15 107 0.1 23 6 3.8 19 57 0.3 (after Oke, personal communication) I l l (B) ENERGY BALANCES IN AND NEAR INUVIK, N.W.T. - JANUARY, 197b Ideally to define the magnitude of the energy flews within Inuvik,. N.W.T. and i t s environs, each term i n the energy balance should be measured. In this study, equipment and time constraints precluded a complete measurement programme of urban and non-urban surface energy balance components. Consequently assumptions and approximations were invoked to supplement available measurements to enable a simplistic energy balance comparison to be carried out. The purpose was to i l l u s t r a t e the possible influence of the input of anthropogenic heat i n this otherwise low energy system, rather than to define accurately each energy term individually. (1) Energy Balance Components (a) Measured Q* and Calculated CL The respective surface energy balance of the two sites are given by equations 5-1 and 5-2, v i z : Q* = Q A + Q E + Qg (non-settled) Q* + QF = QH + QE + QG (townsite) The formulation of equations 5-1 and 5-2 requires steady state conditions (i.e. no advection) which can be approximated i f skies remain clear and no sudden changes i n a i r mass (i.e. changes i n a i r temperature or humidity) are observed. These criteria, were applied to the available Q* and CL data to deterndne those suitable for analysis. After f i l t e r i n g , three p a r t i a l days of data (between Jan. 17 and Jan. 31) were selected, giving a total of 29 hourly measurements. Tine 29 values of Q* and the computed Qp form 112 the core of the energy balance calculations and comparisons developed i n the remainder of the chapter. The Q* and 0_ fluxes have already been dealt with i n d e t a i l (chapters 2 and 4) and only brief explanation i s necessary. An__opcgerdc heat release was considered to be the sum of e l e c t r i c a l energy consumption plus the space heating requirements of the west loop of the Inuvik u t i l i d o r system divided by the appropriate land area. This yields an average value for Q_ i n the west loop of the u t i l i d o r system which was subsequently r increased because the building area/land area ratio i n the v i c i n i t y of the I.R.L. (see c i r c l e i n Figure 5-1) was roughly two times higher than the average ratio for the rest of the west loop sector. The accuracy involved i n this method of calculating 0_ i s further limited because i t assumes that an average Q^ , exists for a l l buildings despite possible differences i n building construction (i.e. insulation thickness) and building function (i.e. frequency of door openings and closings). Considering the building specifications (of I.R.L.) this would probably result i n an overestimate of building heat loss. However, on the other hand, not a l l anthropogenic heat release has been included, (e.g. heat emissions from t r a f f i c and fuel consumption for heating houses not connected to the u t i l i d o r ) . These errors are to some extent offsetting and hence do not unduly bias the calculations. The data were gathered at the sites and i n the manner described i n Chapter 4. 113 (b) Assumptions Regarding the Magnitude of 0_ and CL I n t u i t i v e l y we antici p a t e Q can be neglected a t both, s i t e s since v i s u a l evidence of sublimation ( i . e . f r o s t on trees and buildings) was not observed during t h i s time period and evaporation must be n e g l i g i b l e a t the low temperatures encountered (e.g. L i l z e g u i s t (1956) and Mather (1958)). Estimates were made of the energy released from condensation of water vapour from urban combustion sources (mainly automobile) i n Inuvik f o r Jan. 1975, following procedures outlined by Benson (1969). The r e s u l t s confirmed the view that t h i s energy source could be neglected. Use of equations 5-1 and 5-2 assumes that Q G a t both s i t e s w i l l be n e g l i g i b l y small. I n t u i t i v e l y t h i s assumption i s j u s t i f i a b l e since snow depth throughout Jan. 1975 ranges from 0.80 - 1.00 m over both the townsite and non-settled s i t e s . The snow was not w e l l compacted and hence i t s thermal conductivity can be considered small (Table 5-2) so that i t may be assumed to act as an i n s u l a t i n g layer over the ground surface. Thus subsurface heat flow w i l l be assumed not to play a s i g n i f i c a n t r o l e i n the surface heat balance of e i t h e r s i t e . TABLE 5-2 Thermal Conductivity of Various Materials M a t e r i a l Thermal Conductivity (W m"1 °C "1)  Snow = d r y 1 (0.2 gem'"3) 0.151 2 —3 Snow = wind packed (0.35 gem ) 0.26 Water 1 0.57 Ouartz 3 8 7 1 Smithsonian Met. Tables (1966 " ' 2 M i l l e r (1956) I c e 3 2.2 3 S e l l e r s (1965) I 114 This hypothesis i s further supported by experimental data gathered i n Inuvik (Jan. 7 - Jan. 10, 1975) v i a a thermocouple d i f f e r e n c i n g system between the snow surface and a depth of 0.2 m a t a distance of 10 m from the east w a l l of the I.R.L. i n a t o t a l snow depth of approximately 0.8 m. The r e s u l t s during c l e a r weather, revealed a s l i g h t temperature gradient i n t h i s upper snow layer with heat flow directed toward the surface. The average gradient (from 44 spot readings y i e l d e d a temperature gradient of 0.6°C/0.2 m (or 3°C m" 1). Adopting t h i s gradient i n conjunction with the probable l i m i t s of thermal conductivity (Table 5-2) permitted the c a l c u l a t i o n of the l i k e l y range of subsurface heat flow (see Table 5-3). TABLE 5-3 Comparison of Probable Limits of Mean 0, i n Snow*, Inuvik, N.W.T. Jan. 7 - 10, 1975  Snow Type . Thermal Conductivity (k) Q G  (W m"1 °C~1) (W m~2) Dry (0.2 g cm 3 ) 0.15 0.45 Wind packed (0.35 g cm"3) 0.26 0.^ 78 * This c a l c u l a t i o n assumes a gradient of 3°C m ^ and u n i d i r e c t i o n a l and steady-state heat flow. Furthermore, using the most extreme gradient values recorded -2 during t h i s period, r e s u l t s i n a maximum Q_ of 2.3 W m . This i s almost n e g l i g i b l e i n an environment where cl e a r sky Q* values were -30 to -40 'W m~2. These assumptions are given further support by Wendler (1969). With < 0.5 m snow cover during a period of c l e a r s k i e s near Fairbanks, Alaska, both the evaporative and subsurface heat f l u x e s comprised but 115 -2 ~7 a small portion of the surface energy balanoa ( Q ^ = 5 W m ., Q = 51 W m ", Q = 4Wm , and Q * - 61 W m ). Assuming Q _ = Q _ = 0/ townsite and non-settled energy balances now reduce to the simple form: 0* ^  Q r r (non-settled) (5-3) n and, Q * + Q & Q R (townsite) (5-4) ^ EXPERIMENTAL RESULTS AND SIMULATION COMPARISONS FOR SURFACE ENERGY  BALANCES in and near INUVIK, NWT. (1) The Measured Surfane Energy Balance Averaging the 29 "steady state", clear sky hourly values of Q * and Q _ , the simplistic energy balance for the townsite (I.R.L,) resulted in: r Q * + Q F + Q H = 0 -39 +46 + Q r = 0 (W m~2) rl -2 and therefore: Q r = -7 W m , which indicates that the surface sensible heat flux i s small and i s directed away from the surface. In other words, the relatively large value outweighs the negative radiation balance, creating a surplus of energy at the surface. The surplus is lost to the overlying air, as a sensible heat flow which via mixing w i l l raise the air temperature. The average unsettled (C.B.C. trailer) energy balance was: Q * + Q H - 0 -32 + Q „ = 0 (W m~2) x i -2 so that, Q r T = -32 W m H Thus in the unsettled area, away from the influence, of Q f the negative radiation balance must be compensated for entirely by sensible heat flow from the relatively "warm" atmosphere to the "cold" surface. 116 (a) Measured Urban Heat Islands One result of the altered townsite energy balance i s the production of s l i g h t l y warmer a i r temperatures. Figure 5-2 i s a typical Inuvik "heat island" map based on observations with clear skies. This map reveals a heat island of approximately 1.7°C. The difference i n temperature between the C.B.C. and I.R.L. sites gives a value of 1.5°C. Heat island traverses were recorded on a t o t a l of 10 days, however due to instrumental d i f f i c u l t i e s , only 5 were thought to be useful i n the present analysis. The average heat island for these 5 days was 0.9°C with a maximum of 1.9°C and a-minimum of 0.4°C (between the I.R.L. and C.B.C. t r a i l e r s i t e s ) . (2) Energy Balance Comparison via a Surface Climate Simulation Model Numerical modelling represents an alternative, and independent method of assessing the energy balance and temperature response of the two sites. The ore-dimensional, time dependent model used here i s based upon equilibrium temperature theory, and was developed by Myrup (1969) and further modified successively by Outcoit (1972a), Oke (pers. comm.) and Oke and Hertzmann (pers. conmj . A more detailed description of the model appears i n Appendix 2 . The model input consisted of two data sets, one describing the townsite, the other the non-settled s i t e . Of the 16 input variables only Q_ and roughness length were thought to be substantially r different between the two sites. Thus energy balance and surface temp-erature differences w i l l be a function of those two variables. For each environment, the model output includes the diurnal energy balance, a s o i l temperature matrix, and a heat island (generated by subtracting the 117 Ffgure 5 -2: Heat is land map of Inuvik, R.H T (Date: Jan. £7,3975, Ti : - : » : lK lO - i f i jb (L-S T } Sl:y:clcv.r, Kind: calm to l inht (from L/Sf). 118 unsettled s i t e surface temperatures from those calculated for the townsite surface). These calculations allow direct comparison between: (1) simulated vs. measured and calculated energy exchanges and, (2) simulated vs. measured heat islands. I t should be noted that due to the lack of a solar forcing function at Inuvik during polar night, the simulated energy flows show no diurnal variation. (a) Simulated Inuvik Townsite (I.R.L.) Energy Balance^ Using the input parameters given i n Appendix 2 the simulated surface energy balance for the townsite was: Q* + Q p + Q H + QE•+ Q G = 0 (-29.2) + 46.0 + (-16.4) + 0.0 + (-0.4) = O (W iff 2 ) This i s to be compared with that from the preceding analysis: Q* + Q F + Q H = O (-39) + (46) + (-7) =0 (W m"2) The e a r l i e r assumption that Q_ and Q are negligible i s supported by the simulated energy flows. The differences between the two balance estimates arise with respect to Q* and the residual term, Q . I t should be noted that the model uses equation 4-5 based on Idso and Jackson's (1969) L i formula which was shown to underestimate i n Chapter 4. Considering this, the divergence i n absolute energy amounts i s small, and the direction of energy transfers are consistent between the two approaches. Both approaches i l l u s t r a t e the significance of 0_ i n this low energy system. (b) Simulated Non-Settled Site Enerqy Balance The simulated energy balance i n the absence of Q p and with a smaller 119 roughness length i s much different from the townsite energy balance: Q* + Q H + Q E + Q G = 0 -25.7 + 24.8 + 0 + 0 . 9 = 0 (W m~ 2). This compares to the measured energy balance i n the non-settled s i t e : Q* + Q H = 0 -32 + 32 = 0 ( W rrf 2) Again the Q* i s underestimated by the model, but i n absolute energy terms, the agreement i s satisfactory. Again the simulation reveals that QQ~ °' 3 1 1 ( 1 t h e r e f o r e shows the balance for this site consists almost e n t i r e l y of two terms, Q* and Q . The radiative loss i s compensated for by turbulent transfer of sensible heat, Q , toward the surface from the "warm" a i r to the cold surface. (c) Simulated Urban Heat Island As a result of energy balance differences between the two sites, the simulation model predicts an urban heat island of 2.0°C. Although measured heat islands indicated an average value somewhat smaller than t h i s (0.9°C), these were based on a i r temperatures at a height of approximately L 5 ra and when extrapolated to the surface, a 2°C heat island i s not unreasonable. CHAPTER 6 SUMMARY OF CONCLUSIONS 120 121 (A) INTRODUCTION The overall titrust of this thesis has been anthropogenic heat release, i t s estimation, and i t s impact on the urban climate of Inuvik, N.W.T. Estimation of anthropogenic heat release (Qp) spanned two spatial scales; frcm heat loss through a single window surface (Chapter 3), to the more general heat output from Inuvik as a whole (Chapter 2). The impact of Q_ was assessed i n relation to the net long-wave radiative energy flux (Chapter 4) and i t s influence on the energy balance of Inuvik (Chapter 5) . I t i s clear from this study that the relation between urban climate and energy use i s one of interaction rather than unidirectional cause-and-effect. Climate i n i t i a l l y forces an energy demand on an urban area. This demand results i n anthropogenic heat release which thermally modifies the urban atmosphere. The creation of a warmer climate returns to alter the energy demand sl i g h t l y , and so forth. This chapter examined the role of climatic parameters on daily space-heating demand i n Inuvik, N.W.T. A theoretical heat loss analysis was considered i n the delineation of potentially significant climatic variables. A i r temperature (T ), and wind speed (u) , and solar radiation a (K^ ) were ident i f i e d to be the most pertinent variables based both on them av a i l a b i l i t y , and their importance i n the theoretical model. Because of s t a t i s t i c a l inter-oorrelations, solar radiation was found to be insignificant at the 5% level, while temperature was found to be the dominant variable i n a l l cases, with wind speed becoming significant i n certain months. Space-heating demand models were developed for the utilidor-served portion of 122 Inuvik using data from the f i r s t half of 1974 (Jan. - July, 1974). A secondary model (Nov. 1974 - Jan. 1975) was also established because of a change over i n N.C.P.C. (Northern Canadian Power Commission) operations i n the latter part of 1974. Thus a smaller portion of. Inuvik (west loop of the utilidor) was studied. Successful development of multiple regression models on the daily time scale (r = 0.90), subsequently led to the development of an hourly model. The hourly heat loss equation proved to be almost as well correlated (r = 0.87) as the daily models, i f 1 h-lag i n a i r temperature was incorporated. This model was used to define the limits of the heating equipment presently being used by N.C.P.C. i n Inuvik. To maintain comfortable i n f e r i o r l i v i n g conditions, i t was calculated that N.C.P.C. must be able to generate an increase of 1.0 x 1 0 i n one hour (for the west loop of the util i d o r ) to offset the maximum cooling observed i n the 1974 a i r temperature data. The p o s s i b i l i t y of using these equations as input to an urban boundary layer model was il l u s t r a t e d . Although calculation of areally-averaged anthropogenic heat release (Q_) through regression equations i s r e l a t i v e l y simple (after the i n i t i a l heat load formula has been developed) care must be taken to ensure that i t relates only to energy output which can be climatically predicted. Thus i t s use i n boundary layer models may be restricted to non-industrialized c i t i e s with high heating demands. Nevertheless the predictability of urban heat islands and mixing depths from a i r temperature, wind speed and rur a l lapse rate data i s appealing. 123 (C) " QiAPTER 3 The third chapter examined heat loss from a single window surface based on experiments performed at the Inuvik Research Laboratory (I.R.L.). From theoretical analysis, three energy flows were considered significant i n describing heat loss from the windows'exterior: (1) the gradient flow (conduction) of anthropogenic heat (Q_) from the inte r i o r window surface to i t s exterior surfaoa, (2) the radiative loss (Q*) and (3) the convective loss (QrT) . With negligible long-wave radiative transfer r l through the window Q_ could be equated to the thermal conduction through the glass. Thereby i t was possible to solve for Q p with only a knowledge of the thermal characteristics of the building materials and the interior and exterior surface temperatures. Q* was measured directly, and Q was solved for by residual. In addition the wind speed (u) and the temperature gradient from the exteriors surface to the a i r (T - T ) were measured. o a This permitted calculation of the heat transfer coefficient h (h - 0 -Q* /T c - T ) and an equation relating h and u (h = 7.69 + 4.52 (u) W n f 2 °C - 1) . o a Values of h derived from this equation agreed to within 10% of others developed under controlled conditions. The h analysis provided confidence i n the relative accuracy of the calculated energy flows, and enabled the development of a model for estimating the r a t i o QT/Q* (Q„/Q* = ° - 6 2 + 0.44(u) + 1.2(n), where n = cloud coverage i n tenths) . Thus a knowledge of u and n i n conjunction with the energy flow through the window (Q ), enables the calculation of the other energy loss terms, Q • and Q*, (i.e. Q R = QF/(Q*/QH) +1 smd Q* = Qp/QH/Q*) + 1) . The significance of the wind speed and cloud cover 124 c o e f f i c i e n t s to other urban or r u r a l areas i s not yet c l e a r . For instance, the b u i l d i n g (sky view factor and roughness regime w i l l e f f e c t the r e l a t i v e importance o f Q* and i n the t o t a l heat l o s s , and t h i s may vary considerably from s i t e to s i t e . I t was also noted that the Q^/Q* equation implies that increases i n wind speed do not influence t o t a l heat loss but rather r e s u l t i n adjustments i n the method of heat transfer through Q H and Q*. This i s i n c ontradiction to c e r t a i n engineering approaches t o c a l c u l a t i n g heat loss from bui l d i n g s and demonstrates the need f o r further research. (D) CHAPTER 4 Chapter four investigates long-wave r a d i a t i o n balance differences (L* = I> - L t ) i n and near Inuvik, as w e l l as the p o t e n t i a l f o r modelling Li and L* i n the A r c t i c . Differences i n net long-wave r a d i a t i o n between the townsite (urban) and surrounding unsettled (rural) areas were small -2 (5-10 W m ). However the townsite values were consistently lower ( i . e . more negative). This was thought to be due t o the greater emission of L t from the "warmer" urban surface. Further analysis revealed that these i n t e r s i t e differences were s t a t i s t i c a l l y l i n k e d t o a i r temperature. The strong c o r r e l a t i o n of a i r temperature and energy use (Chapters 2 and 3) i n d i r e c t l y supports the explanation that L* differences are due to the surface e f f e c t s of urbanization. Four c l e a r sky counter r a d i a t i o n ( L i ) formula were tested using the measured Li values (73 spot readings) as the b a s i s f o r comparison. Results revealed that the Idso/Jackson (1969) Li formula i s most suitable 125 for this environment due both to i t s apparent accuracy, and i t s simple input requirements. Swinbank's (1963) formula proved to be the least appropriate, underestimating L\- by as much as 50%. The Brunt (1932) and Hay (1970) equation yielded intermediate values (See Table 4-5) . Modelling L*, using a black body a i r temperature value for l A i n conjunction with the Idso and Jackson formula, resulted i n estimates of L* that were not as encouraging as the comparisons. However the limited data set used for this analysis r e s t r i c t s the generality of conclusions. (E) CHAPTER 5 This chapter discusses anthropogenic heat release i n Inuvik and i t s . e f f e c t on simple energy balance models formulated for the Inuvik area. Using experimental evidence i t was assumed that i n Jan. 1975 the energy balance at the townsite could be approximated by Q* + Q p + = 0, and similarly the rur a l energy balance could be represented by: Q* + = 0. These balances were evaluated using measured and calculated input data. Further townsite/unsettled comparisons were obtained using a numerical climate - 'simulation model which computes energy fluxes v i a equilibrium surface temperature theory. Table (6-1) displays townsite/unsettled energy balance comparisons produced by the two approaches. 126 TABLE 6-1 -2 Energy Exchanges i n and Near Inuvik, N.W.T. January 1975 (W m ) (1) Townsite Q* + Q p + 0^ + QE + QQ= 0 Measured and calculated -39 + 46 - 7 + 0 + 0 = 0 Simulated - 2 9 + 4 6 - 1 6 + 0 + 1 - 0 (2) Unsettled Q* + QR + QE + QG = 0 Measured and calculated -32 + 32 0 + 0 = 0 Simulated -26 + 25 + 0 + 1 = 0 Note: negative values are losses and positive values are gains for the surface. The model also predicts that the altered townsite energy balance should increase townsite a i r temperatures. This was v e r i f i e d by a i r temperature traverses. 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Note #87, 142-159. 132 APPENDIX 1 Derivation of dQ = C (dT) frem Q = k (dT) ^7 (dt) (dx) Given that Q_, = k,(dT) represents the flow of heat passing through an i n t e r i o r wall/window surface, and Q_„ = k„(dT)„ i s the flow through t Z Z 7 - 5 — \ z (dx) 2 the exterior surface of the wall/window, then: d0_ = (P_ 9 - 0_J = (k_(dT) - k,(dT) ). ' n tz t± A(6x)2 1 ( d x ) 1 If Qp^ = ' i t . can be assumed that the temperature distribution i n the wall i s steady and heat flow i s constant. I f CL^ = / then the temp-erature distribution has changed and the wall i t s e l f i s either gaining or losing heat. This gain or loss i s proportional to the heat capacity of the materials and the actual temperature change over time. Numerically this can be written: dQ = C(dT)dx, or dQ = C (dT), where C = volumetric heat capacity (dt) dx (dt) • (J m 3' °C "*")', C = p 0^ where f - material density (kg m 3) and c p= the specific heat of the material (Jkg "S , and dT = actual temperature o - l d t change ( C s ) . 133 •Appendix 2 The simulation of the surface energy balance which forms the basis of t h i s model was o r i g i n a l l y constructed by Myrup (1969) and was extended for computer application by Outcalt (1972a). The model i s based on equilibrium temperature theory which states that for a given set of environmental conditions, a unique surface temperature exists which s a t i s f i e s the conservation of energy at the earth's surface. Energy flow i s considered to be restricted to the v e r t i c a l and, thus advection effects are not included i n the model. Further only clear sky conditions can be simulated by the model. Given the constraints of clear skies and no advection, the model has performed adequately a t a number of different geographic scales, from the simulation of ice needle events i n Vancouver, Canada, to modelling thermal plume development i n the r c t i c (Outcalt, 1972a),(Outcalt, 1972b). Outcalt (1972b), considers that the model "reasonably mimics nature". The modelling of thermal contrasts of sea ice and terrain features i n the a r c t i c (Outcalt, 1973) resulted i n predicted surface temperatures that approached measured surface temperatures. Consequently a reasonable l e v e l of confidence i n the models' a b i l i t y to simulate the a r c t i c environment seems j u s t i f i e d . The model assumes that energy flow across a surface i s conservative, such that a balance i n the major energy sources and sinks i s formed, Q* = QtT + Q_ + Q_. • Further, i t i s assumed that i n conjunction with certain H E G adjustable environmental boundary conditions, these energy flows can be expressed as a function of an unknown surface temperature. Constrained by stipulated boundary and input conditions, the model "searches" via a 134 halving i t e r a t i o n for an equilibrium surface temperature which sa t i s f i e s the given conditions. The 16'input or boundary conditions used i n the present study are given i n Table A2-1. for each site-. The computer output displays 36 hourly sets of surface energy balance conponents and equilibrium temperature values. The•time-step between computations i s 0.5 h r e a l time. In addition, a s o i l temperature matrix i s generated. In the present case, because of the r e s t r i c t i o n of polar night (e.g. solar input i s n i l ) , energy values are .constant i n magnitude and direction with time. Thus the simulated diurnal energy balances can be represented by a single numerical balance. 135 TABLE A2.-1 Variable Townsite Unsettled! Variable Townsite Unsettled! Variable Townsite Unsettled Variable Townsite Unsettled INPUT VARIABLES-SIMULATION MODEL Latitude Solar Declination Pressure Prec. Water Albedo <2) (2) 1008.8 mb 2.0mm ' (2) (2) 1008.8 mb 2.0mm ' 03) 'C3>-68.3 °N -23.4^  68.3°N -23.4° ( 1 ) Dust Particles Radius Vector Qp_ Vapour Pressure Wind Speed 0) (3) 0.98372 0.98372 .(1) (1) 46 W m 0 W m (2) 0.25 mb ' 3.2 m s -1 (2) 0.25 mb (2) 3.2 m s -1(2) Air Temp. Shadow Ratio Soiljrhermal Diffusivity Wet Fraction -28.4°Cf2) .', --28.4°C(2) - ( 3 ) (3) . . ,„-6 2 -1(4) 0.4x 10 m s ' 0.4xl0-6m2 s" 1 { 4) 0.0 0.0 (6) (6) Soil Heat Capacity Roughness, 668800. J m 3C 1 ^ 0.89 m (5) 668800. J m 3 C -1(4) 0.14 m (5) (2) (3) (4) (5) (6) Smithsonian Met. Tables (1966). Calculated under clear skies in Inuvik in Jan.,1975 from Airport records or Inuvik (IRL) data. Estimated (insignificant since no solar radiation). Average of values quoted in literature for slightly packed dry snow. See Sumpton (1975). Estimated. 

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