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Three-dimensional radiation flux source areas in urban areas Roberts, Sarah Marie 2010

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THREE-DIMENSIONAL RADIATION FLUX SOURCE AREAS IN URBAN AREAS  by SARAH MARIE ROBERTS B.S., University of Michigan, 1999 M.Sc., University of British Columbia, 2003  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE STUDIES (Geography)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  September 2010  © Sarah Marie Roberts, 2010  Abstract  Outdoor physical scale modeling is a potentially powerful compromise between the more common numerical and observational techniques to understand urban climates, because it incorporates the experimental control of physical and numerical modeling but is subject to the real complexities associated with natural environmental forcing. An outdoor physical model of simple concrete “buildings” was constructed to simulate an “urban” array in three different configurations. Observations of both facet surface temperatures and of radiation fluxes within and above the urban canopy layer investigate the impact of surface-sensor-sun relations on measured radiation flux source areas. Field measurements from the scale model were complemented by analyses using two numerical models. The combined results guide development of a protocol to guide the optimal siting of radiation sensors in measurement projects of the urban surface energy balance. The siting protocol considers both the influence of surface structure and orientation on radiation source areas and on the streamwise dimensions of the equivalent turbulent flux source area ‘seen’ by turbulence sensors. Observed thermal patterns from the scale model compare well with those at similar fullscale urban sites. Measurements of the spatial variation in radiation fluxes reveal that measurement heights above approximately 2.5 times the mean building height generate uniform flux density patterns. An agreement index used to quantify the strength of correspondence between what a sensor ‘sees’ of an urban surface and the actual surface morphology demonstrates that measurement locations near a street intersection give results closest to those sought to represent the local scale. Relations derived to describe the measurement height at which the radiation flux source area of a radiation sensor encompasses the source area of a turbulent flux sensor, reveal the common practice of co-locating tower-based radiation and turbulence flux sensors is often not sufficient to ensure their overlap. To match radiation flux  ii  source areas to the streamwise extent of turbulence flux source areas, it is recommended that radiation flux sensors be sited so as to contain the location of the maximum turbulent flux source weight. This suggests that radiation sensor(s) should be about two- to three times higher in elevation than the turbulence sensor(s).  iii  Table of Contents  Abstract...…………………………………………………………………………………...……ii Table of Contents..........................................................................................................................iv List of Tables…………………………………………………………………………...………viii List of Figures………………………………………………………...…………………………..x List of Abbreviations and Symbols………………………………………….………………xviii Acknowledgements………………………………………………………………...…………xxiii  1  2  INTRODUCTION AND LITERATURE REVIEW…………………………………...1 1.1  Introduction………………………………………………………………………..1  1.2  Observed surface energy balance………………………………………………….2 1.2.1  The urban surface and atmosphere………………………………………..2  1.2.2  Urban surface energy balance measurements……………………………..7  1.3  Urban radiation and turbulent flux source areas…………………………………..9  1.4  Source area modeling in urban environments……………………………...…....12 1.4.1  Radiation flux source area modeling…………………………………....12  1.4.2  Turbulent flux source area modeling…………………………………....14  1.5  Rationale and research approach………………………………………………...21  1.6  Objectives………………………………………………………………………..22  PHYSICAL SCALE MODELING OF URBAN CLIMATE………………………...25 2.1  Scaling considerations…………………………………………………………...25  2.2  Geometrical similitude…………………………………………………………...29  iv  2.3  3  Dynamical similitude…………………………………………………………….30 2.3.1  Radiation…………………………………………………………………30  2.3.2  Flow……………………………………………………………………...31  2.3.3  Thermal inertia…………………………………………………………...32  A SCALE MODEL TO STUDY URBAN RADIATION SOURCE AREAS………35 3.1  3.2  3.3  Scaling considerations…………………………………………………………...35 3.1.1  Similitude………………………………………………………………...36  3.1.2  Assumptions……………………………………………………………...39  The model………………………………………………………………………..40 3.2.1  Site and operation………………………………………………………..41  3.2.2  Construction……………………………………………………………...43  3.2.3  Operational considerations……………………………………………….49  Measurements……………………………………………………………………50 3.3.1  Surface temperature measurements……………………………………...50 3.3.1.1 Measurements using infrared thermocouples……………………51 3.3.1.2 Measurements using the infrared camera………………………..51  3.3.2  Radiation flux measurements…………………………………………….54 3.3.2.1 Static radiation flux measurements………………………………54 3.3.2.2 Dynamic radiation flux measurements…………………………..57  3.3.3 3.4  3.5  Ancillary observations…………………………………………………...59  Numerical methods………………………………………………………………59 3.4.1  Surface-sensor-sun Urban Model (SUM)………………………………..60  3.4.2  Simple parameterization scheme for turbulent flux footprints…………..65  Assessment of experimental set-up………………………………………………70 3.5.1  Replicability of the model………………………………………………..70 v  4  4.2  4.3  6  Placement of sensors……………………………………………………..72  3.5.3  Sensor intercomparisons…………………………………………………78  SCALE MODEL RESULTS: SURFACE TEMPERATURE SURVEY……………82 4.1  5  3.5.2  Observed facet surface temperature……………………………………………...82 4.1.1  Comparison with full-scale observations……………………………….89  4.1.2  Comparison with numerical simulations……………..………………...92  Surface temperature of the system……………………………………………….97 4.2.1  The complete (three-dimensional) surface temperature…………………98  4.2.2  Comparison of urban surface definitions……………………………….100  4.2.3  Surface temperature dependence on sensor viewing geometry………...103  Summary of results……………………………………………………………107  SCALE MODEL RESULTS: RADIATION FLUXES……………………………..110 5.1  Uniformity of radiation fluxes………………………………………………….110  5.2  Modeled view factors…………………………………………………………...110  5.3  Reflected shortwave radiation…………………………………………………..114  5.4  Emitted upwelling longwave radiation………………………...……………….120  5.5  Net allwave radiation….………………………………………………………..124  5.6  Summary or results……………………………………………………………..129  PROTOCOL TO GUIDE EXPOSURE OF RADIATION AND TURBULENT TRANSFER SENSORS………………………………………………….………....…131 6.1  Measurement protocol for radiant fluxes……………………………………….132  6.2  SUM modeling approach……………………………………………………….133  6.3  SUM model results…………………………………………..…………………135 6.3.1  Matching facet types……………………………………………………135  6.3.2  Matching sunlit surfaces……………………………………………..…146 vi  6.4  Comparison of radiant with turbulent flux source areas………………………150 6.4.1  Matching radiation source areas to turbulent flux footprint estimates (xR)……………………………………………………………152  6.4.2  Matching radiation source areas to the maximum turbulence flux source weight function (xmax)…………………………………………157  6.5 7  Application of the protocol scheme to Urban Flux Network sites……………161  CONCLUSIONS………………………………………………………………………165 7.1  Summary of conclusions……………..…………………………………………165  7.2  Suggestions for future work…………………………………………………….167  References………………………………………………………………………………...……169 Appendices……………………………………………………………………………………..180 A  VIEW FACTOR CALCULATIONS……………………………………………..….180  B  SUMMARY OF WEATHER AND OPERATIONAL CONDITIONS…………....182  C  D  B.1  Weather conditions……………………………………………………………..182  B.2  Operational summary…………………………………………………………...182  APOGEE INFRARED THERMOCOUPLE (IRTc) IRTS-P……………………....191 C.1  Instrument description………………………………………………………….191  C.2  Instrument calibration…………………………………………………………..191  SUM MODEL OUTPUTS………………………………………………………….....194  vii  List of Tables  2.1  Indoor experiments that used an array of urban-like roughness elements……………….26  2.2  Outdoor experiments that used an array of urban-like roughness elements……………..27  3.1  Typical properties in the Built Climate Zone classes……………………………………38  3.2  Relationship between scaled elements to corresponding real-world dimensions………..39  3.3  Physical and thermal properties of the materials comprising the scale model array…….44  3.4  Surface component areas for each array configuration…………………………………..47  3.5  Sky and wall view factors for the three array configurations……………………………49  3.6  Duration and description of sampled facets corresponding to each of the sixteen periods for which an infrared camera was in operation………………………….55  3.7  Sensor specifications of the radiation sensors used in the study………………………...57  3.8  Surface geometric SUM input parameters for each scale model configuration…………65  3.9  Summary of facet temperature analysis to assess replicability of the scale model……...71  3.10  Comparison of facet surface temperature measured with the IR camera and the IRTc array……………………………………………………………………….75  4.1  TUF-3D model input parameters used in the scale model simulations………………….95  4.2  Comparison of modeled (TUF-3D) and measured facet-average apparent surface temperature for the λS = 1.25 scale model configuration………………………………...97  4.3  Surface component areas for each array configuration…………………………………..99  viii  6.1  Summary of agreement indices (AI) for the simple case of matching the proportion of three broad facet categories -- roof, wall, and road -- at sixteen radiometer positions and at six above roof-level measurement heights………………..138  6.2  Summary of agreement indices (AI) for matching the proportion of all individual roof, wall, and road surface facets at sixteen radiometer positions and at six above roof-level measurement heights…………………………………………………143  6.3  For all sunlit surfaces, a summary of the radiometer locations at which the best and poorest agreement occurs at every height……………………………………..146  6.4  Model input parameters defining atmospheric stability for the turbulence flux footprint scheme…………………………………………………………………...152  6.5  Measurement height to site a 150° FOV radiometer so as to ‘see’ out to 50%, 70%, and 90% turbulent flux footprint isopleths, for each atmospheric stability class and four surface roughness categories…………………………………..156  6.6  Measurement height (multiplier times the height of the turbulent flux to site a 150° FOV radiometer so as to ‘see’ out to the maximum source weight function (xmax), for four surface roughness categories within each atmospheric stability class….161  6.7  Basic site descriptions of a sampling of sites in the Urban Flux Network at which tower-based surface energy balance observations have been conducted……………….163  B.1  Summary of operational status, including roof treatments and operational instrument arrays for the three scale model configurations………………………………………...186  C.1  Apogee infrared thermocouple model IRTS-P specifications………………………….191  C.2  IRTc calibration coefficients……………………………………………………………193  ix  List of Figures  1.1  Schematic diagram of definitions of the urban surface…………………………………...4  1.2  Definition of surface dimensions from which nondimensional ratios are defined………..5  1.3  Schematic of the relative horizontal scales and vertical layers of urban areas…………....6  1.4  Schematic of the fluxes in the energy balance of an urban building-soil-air volume……..8  1.5  The geometrical derivation of the radiation source area…………………………………10  1.6  Conceptualization of radiative and turbulent flux source areas…………………….........11  1.7  Schematic of the source weight distribution upwind of a sensor………………………...17  3.1  Classification of the Built Climate Zones according to their perceived ability to modify local climate………………………………………………………….………37  3.2  Central Arizona landuse classifications from 2000……………………………………...41  3.3  Engineering Research Center on the campus of Arizona State University……………...43  3.4  Schematic representation showing the relative location of sensors within the λS = 1.25 ‘building’ array………………………………………………………………...45  3.5  Schematic representation showing the relative location of sensors within the λS = 0.63 ‘building’ array………………………………………………………………...46  3.6  Schematic representation showing the relative location of sensors within the λS = 0.42 ‘building’ array………………………………………………………………...47  3.7  Hemispherical photographs taken at ground level at the canyon midpoint of the three model array configurations………………………………………………….48  3.8  Example of a surface treatment applied to roofs in the λS = 0.42 model configuration….50  3.9  Installation of the Apogee IRTS-P infrared thermometers to measure x  surface temperatures……………………………………………………………………..52 3.10  Example of an infrared image used to assess surface temperatures of individual facets of the scale model……………………………………………………...53  3.11  FLIR infrared camera mounted on a tripod and positioned so as to include multiple surface facets within its FOV…………………………………………..54  3.12  Kipp & Zonen CNR1 net radiometer mounted from a tripod at the center of the array…56  3.13  The traversing mast which continually moved two arms containing four radiation sensors to twelve positions within and above the UCL………………………………….58  3.14  Area adjacent to the scale model array from which ancillary observations were conducted…………………………………………………………………………..60  3.15  Geometry used to evaluate the view factor of a surface element………………………..62  3.16  Example of the GIS input file used to represent the surface geometry of the scale model arrays………………………………………………………………………..64  3.17  Comparison of modeled and measured near-hemispherical surface temperature (Them) for each scale model configuration……………………………………………….76  3.18  Comparison of measured near-hemispherical surface temperature (Them) with modeled values (Tmod)………………………………………………………………78  3.19  Side-by-side field intercomparison of the radiometers used in the scale model study…..79  3.20  Time series of Q* observed during the radiometer intercomparison study……………...80  4.1  Diurnal variation of the surface temperature of individual vertical facets for the three scale model configurations……………………………………………………..83  4.2  Diurnal variation of the surface temperature of individual horizontal facets for the three scale model configurations……………………………………………………..84  4.3  Diurnal variation of the surface temperature of individual horizontal surfaces xi  with white roof and black roof treatments and with their corresponding vertical surfaces and for the λS = 0.63 scale model configuration…………………….....86 4.4  Diurnal variation of the surface temperature of individual horizontal surfaces, vertical surfaces, and east-west oriented 17° and 30° pitched roof surfaces for the λS = 0.42 scale model configuration……………………………………………….....87  4.5  Diurnal variation of the surface temperature of individual horizontal surfaces, vertical surfaces, and north-south oriented 17° and 30° pitched roof surfaces for the λS = 0.63 scale model configuration……………………………………………….....88  4.6  Measured surface temperatures for both the λS = 0.42 scale model configuration and the apparent surface temperatures from the Vancouver LI study site…………….....90  4.7  Normalized course of road and wall facet temperatures from the Vancouver light industrial and scale model sites………………………………………...93  4.8  Scale model measured surface temperatures plotted with corresponding TUF-3D apparent surface temperatures for the λS = 1.25 scale model configuration…………..…96  4.9  Diurnal variation of the complete (three-dimensional) surface temperature for the three scale model configurations……………………………………………………..99  4.10  Difference between TC and three alternative definitions of the urban surface temperature for the three scale model configurations…………………………………..101  4.11  Modeled directional radiometric surface temperature over the three scale model configurations…………………………………………………………………...105  5.1  Time series of individual radiation flux densities measured by the CNR1 net radiometer…………………………………………………………………………..111  5.2  Surface view factors ‘seen’ by the 160°-FOV down-facing radiometer located approximately in/above a north-south canyon and an east-west xii  canyon at heights 0.5zb to 6zb for the three scale model configurations………………..112 5.3  Vertical profiles of measured reflected shortwave radiation (K↑) at approximately 0900, 1200, and 1500 LAT from the three scale model configurations………………..115  5.4  Time series of measured reflected shortwave radiation (K↑) at four sensor heights from the λS = 1.25 scale model configuration…………………………..117  5.5  Time series of measured reflected shortwave radiation (K↑) at four sensor heights from the λS = 0.63 scale model configuration…………………………..118  5.6  Time series of measured reflected shortwave radiation (K↑) at four sensor heights from the λS = 0.42 scale model configuration…………………………..119  5.7  Vertical profiles of upwelling longwave radiation (L↑) at approximately 0900, 1200, and 1500 LAT from the three scale model configurations………………..121  5.8  Time series of modeled upwelling longwave radiation (L↑) at four sensor heights from the λS = 1.25 scale model configuration…………………………..122  5.9  Time series of modeled upwelling longwave radiation (L↑) at four sensor heights from the λS = 0.63 scale model configuration…………………………..123  5.10  Time series of modeled upwelling longwave radiation (L↑) at four sensor heights from the λS = 0.42 scale model configuration…………………………..124  5.11  Vertical profiles of measured net all-wave radiation (Q*) at approximately 0900, 1200, and 1500 LAT from the three scale model configurations………………..125  5.12  Time series of net all-wave radiation (Q*) at four sensor heights from the λS = 1.25 scale model configuration………………………………………………...…..126  5.13  Time series of net all-wave radiation (Q*) at four sensor heights from the λS = 0.63 scale model configuration………………………………………………...…..127  5.14  Time series of net all-wave radiation (Q*) at four sensor heights from the λS = 0.42 scale model configuration………………………………………………...…..128 xiii  6.1  Schematic of the radiometer locations for which the SUM model is run………………134  6.2  Stacked bar plots of the contribution of roof, wall, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at each of the 16 sensor locations for the λS = 1.25 scale model configuration………………...136  6.3  Contour plots of the agreement index for 16 radiometer locations at six heights above roof level for the λS = 1.25 scale model configuration…………………………..139  6.4  Contour plots of the agreement index for 16 radiometer locations at six heights above roof level for the λS = 0.63 scale model configuration…………………………..141  6.5  Contour plots of the agreement index for 16 radiometer locations at six heights above roof level for the λS = 0.42 scale model configuration…………………………..142  6.6  Schematic of relative locations and furthest upwind distance from an idealized measurement tower of the 50%, 70% and 90% turbulent flux footprint isopleths……..151  6.7  Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50%, the 70%, and the 90% turbulent flux footprint isopleths for convective atmospheric conditions..……….153  6.8  Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50%, the 70%, and the 90% turbulent flux footprint isopleths for neutral atmospheric conditions..……..…….154  6.9  Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50%, the 70%, and the 90% turbulent flux footprint isopleths for stable atmospheric conditions..…………….155  6.10  Measurement height of a 150° FOV radiation sensor versus R for four surface roughness categories under convective, neutral, and stable atmospheric conditions…..158  6.11  R versus measurement height of a 150° FOV radiation sensor for four surface roughness categories under convective, neutral, and stable atmospheric conditions…..159 xiv  6.12  Measurement height of a 150° FOV radiation sensor versus the turbulent flux measurement height required to encompass the maximum source weight function (xmax) under convective, neutral and stable atmospheric conditions………….160  6.13  Measurement height of a 150° FOV radiation sensor versus roughness length that is required to encompass the maximum turbulent source weight function (xmax) under stable, neutral and convective atmospheric conditions……………………162  A.1  Coordinate system used in calculating the view factor of a wall for a given point on the ground…………………………………………………………….180  B.1  General weather conditions for November 2006 observed at Phoenix Sky Harbor International Airport……………………………………………………………………183  B.2  General weather conditions for December 2006 observed at Phoenix Sky Harbor International Airport……………………………………………………………………184  B.3  General weather conditions for January 2007 observed at Phoenix Sky Harbor International Airport……………………………………………………………………185  C.1  Blackbody calibration chamber………………………………………………………...192  D.1  Surface view factors ‘seen’ by a 160°-FOV down-facing radiometer located approximately in/above an east-west canyon at heights 0.5 to 6 times the building height for the λS = 1.25 scale model configuration and at three approximate times during the day…………………………………………………………………………..195  D.2  Same as D.1 except for north-south canyon……………………………………………196  xv  D.3  Surface view factors ‘seen’ by a 160°-FOV down-facing radiometer located approximately in/above an east-west canyon at heights 0.5 to 6 times the building height for the λS = 0.63 scale model configuration and at three approximate times during the day…………………………………………………………………………..197  D.4  Same as D.3 except for north-south canyon……………………………………………198  D.5  Surface view factors ‘seen’ by a 160°-FOV down-facing radiometer located approximately in/above an east-west canyon at heights 0.5 to 6 times the building height for the λS = 0.42 scale model configuration and at three approximate times during the day…………………………………………………………………………..199  D.6  Same as D.5 except for north-south canyon……………………………………………200  D.7  Stacked bar plots of the contribution of roof, wall, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at 16 sensor locations for the λS = 0.63 scale model configuration…………………………………..201  D.8  Same as D.7 except for the 0.63 scale model configuration……………………………202  D.9  Stacked bar plots of the contribution of roof, street intersection, north-, south-, east-, west-facing walls, and north-south and east-west oriented road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at 16 sensor locations for the λS = 1.25 scale model configuration……………………….203  D.10  Same as D.9 except for the λS = 0.63 scale model configuration……………………….204  D.11  Same as D.9 except for the λS = 0.42 scale model configuration……………………….205  D.12  Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at16 sensor locations for the λS = 1.25 scale model configuration, at 0900 LAT………206  D.13  Same as D.12 except for 1200 LAT…………………………………………………….207  D.14  Same as D.12 except for 1500 LAT…………………………………………………….208 xvi  D.15  Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at16 sensor locations for the λS = 0.63 scale model configuration, at 0900 LAT………209  D.16  Same as D.15 except for 1200 LAT…………………………………………………….210  D.17  Same as D.15 except for 1500 LAT…………………………………………………….211  D.18  Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at16 sensor locations for the λS = 0.42 scale model configuration, at 0900 LAT………212  D.19  Same as D.18 except for 1200 LAT…………………………………………………….213  D.20  Same as D.18 except for 1500 LAT…………………………………………………….214  xvii  List of Abbreviations and Symbols  ABBREVIATIONS AI  Agreement index  ASU  Arizona State University  BCZ  Built Climate Zone  CSI  Campbell Scientific Incorporated  ERC  Engineering Researching Building  GIS  Geographic Information System  FOV  Field-of-view  IOP  Intense observational period  IRIOP  Infrared (camera) intense observational period  IRTc  Infrared thermocouple  ISL  Inertial sublayer  LAT  Local apparent (solar) time  LPDM-B  Lagrangian Particle Dispersion Model – Backward  MBE  Mean bias error  PBL  Planetary boundary layer  PHX  Phoenix, Arizona  RMSE  Root mean-square error  RSL  Roughness sublayer  SEB  Surface energy budget  SUM  Surface-sensor-sun Urban Model  UBL  Urban boundary layer  UCL  Urban canopy layer xviii  YD  Year-day  SYMBOLS a  Surface absorptivity  A  Area (m2)  AB  Area occupied by buildings (m2)  AC  Complete urban surface area (m2)  AF  Frontal area (m2)  AH  Area of the projected plane of the radiometer  AI  Area occupied by intersection (m2)  AO  Area occupied by ground (m2)  AP  Plan area (m2)  AR  Area occupied by roof (m2)  AS  Area occupied by streets (m2)  AT  Total lot area (m2)  AV  Area occupied by vegetation (m2)  AW  Area occupied by wall (m2)  Bi  Biot number  cs  Specific heat (J kg-1 K-1)  d  Characteristic length dimension  eo  Water vapor pressure (mb)  F  Factor by which a full-scale prototype is scaled  Fo  Fourier number  fP  Turbulence source area isopleth (%)  Fsky  Fractional component of sky xix  Fwall  f  y  Fractional component of wall surface Cross-wind integrated flux footprint  F*  Non-dimensional cross-wind integrated flux footprint function  Gr  Grashof number  h  Planetary boundary layer height (m)  hcf  Convective heat transfer coefficient for a fluid (W m-2 K-1)  hks  Convective heat transfer coefficient for a solid (W m-2 K-1)  K↓  Incoming shortwave radiation (W m-2)  K↑  Reflected (outgoing) shortwave radiation (W m-2)  ks  Thermal conductivity (W m-1 K-1)  L  Obukhov length (m)  Ls  Material thickness (m)  Lsensor  Longwave radiation received by a sensor (W m-2)  Lsky  Longwave radiation from the sky (W m-2)  Lwall  Longwave radiation from a wall surface (W m-2)  L↓  Incoming longwave radiation (W m-2)  L↑  Outgoing longwave radiation (W m-2)  LB  Building length (m)  obs  Observed value  P  Fraction of total integrated turbulence footprint function  PR  Source area level (%)  r(ΩP,R)  Source area radius of a hemispherical radiometer (m)  Re  Reynolds number  Ri  Richardson number  xx  Q*  Net all-wave radiation (W m-2)  ∆QA  Net advection (W m-2)  QE  Latent heat flux (W m-2)  QF  Anthropogenic heat flux (W m-2)  QH  Sensible heat flux (W m-2)  ∆QS  Net sensible heat storage (W m-2)  TC  Complete apparent surface temperature (°C)  Tcav  Blackbody calibration cavity temperature (°C)  Them  Near-hemispherical surface temperature (°C)  Tirtc  IRTc-detected surface temperature (°C)  Tmod  Modeled surface temperature (°C)  To  Screen-level air temperature (°C)  tr  Surface transmissivity  TS  Surface brightness temperature (°C)  u  Wind speed (m s-1)  u*  Surface friction velocity (m s-1)  W  Street width (m)  X*  Non-dimensional along-wind distance  xmax  Peak location of the turbulence flux footprint (m)  xR  Streamwise dimension of the turbulence flux footprint (m)  z  Height above the surface (m)  Z  Solar zenith angle (°)  zb  Building height (m)  zd  Zero-plane displacement length (m)  zh  Height of roughness elements (m) xxi  zm  Measurement height (m)  z0  Roughness length (m)  zr  Blending height (m) Greek  α  Surface albedo  ε  Surface emissivity  ε 8−14  Atmospheric emissivity in the 8-14 µm waveband  η  Ratio of buoyant to inertial forces  κH  Thermal diffusivity (m2 s-1)  λF  Frontal area index (AF/ AT)  λP  Plan area fraction (AP/ AT)  λS  Canyon aspect ratio (zb/W)  ρs  Density of a solid (kg m-3)  σw  Standard deviation of vertical velocity fluctuations (m s-1)  φ  Dimensionless temperature response  φTOT  Total integrated turbulence footprint function  ϕtotR  Total energy received by a hemispherical radiometer (W m-2)  ΨS  View factor of sky  ΨW  View factor of walls  ΩP  Turbulence source area  xxii  Acknowledgements  This work would not have been possible without the generosity, encouragement, and inspiration of my research supervisor, Dr. Tim Oke. Through all the ups and downs and trials and tribulations over the 10 years of my graduate career, Tim was a constant mentor and teacher. Thanks are also due to the members of my supervisory committee, each of whom played essential roles in guiding me through this work. Dr. Andy Black provided the blackbody calibration chamber and helpful feedback and encouragement in the final stages of this thesis. Dr. James Voogt, in addition to having ignited my interest in urban surface temperatures on a rooftop in Marseille many years ago, fielded countless questions with seemingly limitless enthusiasm and interest in the research, as well as offered thorough and thoughtful feedback. Dr. Douw Steyn always gave practical and straightforward advice and most importantly, saw the forest for the trees at a critical time, thereby restoring my faith in the work and in myself. Various colleagues from UBC kindly contributed their time and talents at various stages of this thesis. I was fortunate to work with Devon Telford, a fantastically creative undergraduate research assistant, who was instrumental in field preparations. Ivan Liu designed and built the traversing mast used in Phoenix. Trevor Jones, with his unwavering patience, friendship, and desire to convert the world to SASS, assisted in data processing. Scott Krayenhoff kindly provided TUF-3D simulations and assistance with MATLAB. Andreas Christen assisted in a wide range of questions pertaining to radiometer calibrations and flux source area modeling. Thanks also to Lori Daniels, whose open door as a mentor, strategist and sounding board was always appreciated. I’m incredibly grateful to the amazing staff in the Department of Geography (in particular Stephanie Lambiris, Sandy Lapsky, and Lorna Chan), who were always able and willing to lend a helping hand in all administrative matters. My fellow urban climate group members through the years – Andres Soux, Scott Krayenhoff, Iain Stewart, and Ben Crawford – were always available to answer questions, bounce around ideas, and drink beer. Colleagues from Arizona State University generously provided essential logistical support in the field component of this research. Jay Golden, Joby Carlson, Rahul Bhardwaj, and Todd Otanicar from The National Center of Excellence on Sustainable Materials and Renewable Technologies were invaluable in assuring technical support (including the use of a FLIR infrared camera), site access, and imperative midday youtube and lunch breaks. Thanks are also due to Rick Martorano for going out of his way to facilitate unrestricted access to the Engineering xxiii  Research Building and to ASU Research Support Services, for their help in troubleshooting the traversing mast. The support and friendship of others in Tempe (Tony Brazel, Winston Chow, James Voogt, Carolyn Beeson, Jaime Adams, and Michael Barlage) also ensured the success of the field project. Funding for this research has been provided to Dr. T.R. Oke by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Personal funding for this project was provided by University of British Columbia Graduate Fellowships, Teaching Assistantships in the Department of Geography, Research Assistantships through an NSERC Discovery Grant (T.R. Oke) and my family. The unwavering support of my amazing friends helped me to persevere through the most difficult periods of this research. Thanks are especially due in this regard to Stephanie Meyn, Trevor Jones, Wren Montgomery, Andres Soux, Kathy MacRae, Michael Barlage, Shane McCloskey, Amanda Stan, Sonya Powell, George Richards, Karis Sengara, Gerald Mills, and Jayme Walenta. And finally to my parents and sister, who always knew when not to ask how it was coming along, never questioned my decision to pursue this work, and who were always my fiercest supporters, I can hardly begin to express my debt of gratitude. In so many ways, I simply could not have done this without you.  xxiv  Chapter 1  INTRODUCTION AND LITERATURE REVIEW  1.1 Introduction Although currently only a small fraction of the Earth's land is considered urban, spatial coverage and density of cities are expected to rapidly increase in the near future. The United Nations estimates that by the year 2025, two thirds of the world population will live in cities (cited in Uitto and Biswas, 2000). The past few decades have been witness to increasing focus paid to gaining an understanding of and appreciation for how urban areas influence weather and climate systems at local, regional, and global scales all over the world, in both developed and developing countries (Grimmond, 2005). Surface and atmospheric environments are modified through the process of urbanization, leading to the creation of distinct urban climates. Resulting climatic features unique to the urban environment (e.g., the urban heat island, urban-induced wind circulation, enhanced downstream precipitation patterns, park breezes) are ultimately due to differences in the budgets of heat, mass, and momentum between the urban and pre-urban landscape (Grimmond et al., 2004). Knowledge of the spatial and temporal variability in urban surface-atmosphere exchanges is prerequisite to the understanding, prediction, and possible mitigation of urban climate effects (Grimmond et al., 2004). With the overall objective of better resolving urban areas and their impacts in weather and climate models, scientists employ a multitude of observational and numerical methods, with tower-based direct measurements of surface-atmosphere fluxes and turbulence chief among the observational tools. Complications and measurement uncertainties associated with such campaigns aside, these measurement campaigns have proven invaluable in advancing our general knowledge base. In the context of radiative and turbulent flux source 1  areas, the research program comprising this thesis seeks to address some fundamental issues of scale and representativeness that are most often associated with conducting tower-based micrometeorological flux measurements over complex urban terrain. Through numerical and physical scale modeling studies, this work will culminate in a more comprehensive understanding of urban turbulent and radiative flux source areas as well as a series of suggested guidelines for ensuring maximum utility in flux observations.  1.2 Observed urban surface energy balance Ideally, differences in the surface energy budget (SEB) between the urban and pre-urban landscape at a particular location are used to assess the impact of urban development. Pre-urban observations are difficult to attain, so comparisons between urban and rural landscapes are often used instead (Lowry, 1977). A significant number of urban surface energy balance studies over the past decade focus on inter-urban differences in the surface energy balance (e.g., Christen and Vogt, 2004; Grimmond et al., 2004; Offerle et al., 2006a) by mounting measurement systems on tall towers at one or two sites within a city. This approach presupposes a representative sample from a large enough area that the small-scale complexity of cities is blended into a spatial average. More recent developments have been made in intra-urban observations (e.g., Offerle et al., 2006b), as it is recognized that spatial variability in surface cover characteristics such as building density and morphometry and fraction of impervious and vegetated surfaces can vary as much within cities as between cities. Grimmond and Oke (2002) showed that such surface characteristics are important controls on the observed SEB.  1.2.1 The urban surface and atmosphere Prerequisite to understanding the nature of urban surface-atmosphere exchanges and surface properties and conditions is the proper specification of the urban surface (Voogt and Oke, 1997). 2  The urban surface is important from a climatological perspective, for it is at the surface where sources and sinks of heat, mass, and momentum are located. Surface properties and conditions determine the partitioning of the radiant energy received at the surface. This energy partitioning is the ultimate driver of conditions within the lowest layers of the urban surface-atmosphere climate system. Depending on the scale of the processes to be studied or modeled, the position of observation, and the application of the measurements, several definitions of the urban surface are commonly used. For example, ground-based observations may not include roof surfaces (Figure 1.1a) while a measurement position from above the urban system may not include vertical (wall) surfaces (Figure 1.1b). The urban surface can also be conceptualized as a plane at roof level that treats the canopy as a ‘black box’ (Figure 1.1c), a plane at screen-level that coincides with standard measurements of air temperature (Figure 1.1d), or a plane corresponding to the level of zero-plane displacement (i.e. ‘effective surface’ defined by extrapolation of above roof profiles down to their apparent source in the canopy layer; Figure 1.1e). Ideally, however, the ‘complete’ urban surface area comprises the boundary between the air and every element comprising the surface system (Figure 1.1f). Urban areas are inherently complex, containing a three-dimensional surface structure which includes built and vegetated components, all of which should be considered when formulating the complete urban surface. The complete urban surface area AC can be approximated by adding the three-dimensional areas of vegetation (AV), buildings (AB), and exposed ground (AO): AC = AV + AB + AO  (1.1)  Common length scales such as the height of roughness elements (zH), street width (W), and building length (LB) are used to characterize the geometric patterns, spacing, and density of built  3  elements (Figure 1.2). Grimmond and Oke (1999) define common non-dimensional ratios to characterize surface morphometry: canyon aspect ratio, λS = zb/W; plan area fraction (density of  B. A.  C.  D.  F. E.  Figure 1.1 Schematic diagram of definitions of the urban surface. (a) ground-level, (b) bird’s-eye view, (c) rooftop (black box), (d) surface (screen level) observed, (e) zero-place displacement, (f) complete. Source: Modified after Voogt and Oke (1997)  elements) λP = AP/ AT; and frontal area density λF = AF/ AT, where AT is the total lot size. Threedimensional building footprints are often derived from information obtained from aerial  4  photography, foot surveys and planning databases. The three-dimensional surface cover of vegetation (e.g., trees, shrubs, bushes) can be calculated by using a series of simple shapes such as cones (coniferous species; Li and Strahler, 1985), ellipsoids (Campbell and Norman, 1989;  Figure 1.2 Definition of surface dimensions from which nondimensional ratios are defined to characterize urban surface morphometry. Source: Adapted from Grimmond and Oke (1999).  Voogt and Oke, 1997), cylinders, and spheres (deciduous species; Goel, 1988) to represent tree forms or it can be estimated using aerial photography, remote sensing imagery or side-ranging lidar. For practical reasons, the complete urban surface considered in observational studies does not usually include elements with length scales less than those of a building or tree (Voogt and Oke, 1997). Measurements of urban surface-atmosphere exchanges also require an appreciation for the climatic scales and vertical layers comprising the system (Figure 1.3). At the mesoscale, urban impacts occur at the scale of the whole city, typically tens of kilometers in extent (Figure 1.3a and 1.3b). The local scale corresponds to an urban neighborhood (horizontal length scale ~102– 5  104 m) with similar surface cover, building density, and activity (Figure 1.3c). The microscale (Figure 1.3d) extends from less than one meter to hundreds of meters, corresponding to individual buildings, roads, trees, courtyards, lawns, etc. (Oke, 2006).  Figure 1.3 Schematic of the relative horizontal scales and vertical layers typical of urban areas. (a) mesoscale “dome”, (b) mesoscale “plume”, (c) local scale, (d) microscale. Source: Modified after Oke (1997).  Within the planetary boundary layer (PBL), the height of the urban boundary layer (UBL) grows with increasing fetch. The rate at which this growth occurs depends on surface roughness and stability (Figure 1.3b). The UBL contains the inertial sublayer (ISL), also called the constant flux layer, where shear stress is nearly constant with height and Monin-Obukhov similarity theory is valid (Christen, 2005). Beneath the ISL lies the roughness sublayer (RSL), an area that 6  extends from the ground to the blending height, zr (Figure 1.3c). The blending height occurs where the influences from individual roughness elements vanish as a result of turbulent mixing. The lowest part of the RSL is referred to as the urban canopy layer (UCL), which extends from ground up to the mean height of the main roughness elements (trees, buildings), zH (Figure 1.3d; Oke, 1987). Within the roughness sublayer exchange processes and turbulence statistics are vertically and horizontally inhomogeneous and are not fully understood. Since most urban dwellers spend much of their lives within this layer and because this is where most emissions take place, there is a pressing and continued need to understand and parameterize exchanges in the RSL (Christen, 2005).  1.2.2 Urban surface energy balance measurements Oke (1988) gives the surface energy budget (SEB) for a volumetric ‘black box’ at the local scale, the bottom of which is the sub-surface depth at which zero net heat flux occurs over the period of concern (Figure 1.4). The upper bound of the volume extends to the top of the UCL, or better still the top of the RSL, which should be the minimum measurement height for turbulent fluxes (Oke, 2004): Q * +QF = QH + QE + ∆QS + ∆Q A  [W m-2]  (1.2)  where Q* is the net all-wave radiation through the top of the volume, QF is the anthropogenic heat contribution from within the volume, QH and QE are the respective turbulent fluxes of convective sensible and latent heat through the top of the volume, ∆QS is the net sensible heat storage by the volume, and ∆QA is the net advection through the sides of the volume. Net all-wave radiation Q* is the most important term of the surface energy budget because it represents the limit to the available energy source or sink for the system (Oke, 1987). It is the difference between all incoming short- and longwave radiation (K↓ and L↓ respectively) and all outgoing short- and longwave radiation (K↑ and L↑ respectively). Net horizontal 7  advection ∆QA is typically neglected in the measured SEB, as it is assumed that measurements conducted at sites  Figure 1.4 Schematic of the fluxes in the energy balance of an urban building-soil-air volume. Source: Meyn and Oke (2009).  with extensive horizontal fetch do not include non-characteristic contributions from outside the volume. QH and QE are usually directly measured with fast-response eddy covariance techniques. The direct measurement of ∆QS is practically impossible due to the myriad materials and threedimensionality of urban systems so this term is often expressed as the residual from direct observation of the other terms in Eq. 1.2 or is parameterized as a function of Q* (Roberts et al., 2006). Anthropogenic heat QF is usually omitted from the observed urban energy budget, because it is assumed that some of the anthropogenic heat flux is included in the measured Q*, QH, and QE terms as plumes of warm air and water vapor released by vehicles and building vents, thermal infrared radiation from the warmer urban setting, and alterations to the heat conducted into and out of buildings (Grimmond and Oke, 2002). When the storage heat flux term is calculated as a residual, however, any anthropogenic heat flux that warms the building-soil-air volume should be prescribed (Grimmond et al., 2004).  8  Measurements conducted above the RSL (Fig. 1.3) detect the blended integration of microclimate effects at the local scale (Oke, 2004). These measurements assume sufficient fetch over a relatively homogeneous surface for an equilibrium boundary layer to have grown up to the measurement height. If zm is the chosen measurement height, the minimum fetch requirement over homogeneous terrain is very approximately given as 100 (zm – zd), where zd is the zero-plane displacement length (Oke, 2004). The use of a height-to-fetch ratio of 1:100 for urban areas is based on the fact that urban areas tend towards neutral stability (due to enhanced thermal and mechanical turbulence and large roughness; Bottema, 1997). Ensuring the measured turbulent and radiative flux signals originate from an area of homogeneous fetch is critical, for it implies that each term of the SEB applies to the same surface.  1.3 Urban radiation and turbulent flux source areas The surface area containing the effective sources and sinks contributing to a given measurement point is termed the ‘source area’ of those measurements (Schuepp et al., 1990) and defines the “spatial context of the measurement” (Schmid, 2002). It is the portion of the surface fetch from which an instrument derives its measured signal. The source area is a function of the sensor location and the characteristics of the process (e.g., radiative transfer, turbulent eddies, etc.) transporting surface properties to the sensor (Oke, 2004). There are two distinct flux source areas to consider when conducting SEB measurements: those arising from upwelling radiation exchanges and those derived from turbulent transport. The source area for upwelling radiation fluxes (short- and longwave radiation and/or surface temperature detected by an infrared thermometer) is a function of a sensor’s location and field-of-view (FOV), as well as the underlying surface structure (Voogt and Oke, 2003). The surface area sensed by a down-facing hemispherical (FOV = 180°) radiometer parallel to the ground is a circular disk shape with the sensor located at the center (Figure 1.5). Although the 9  radiometer is exposed to radiation from the entire underlying surface extending to the horizon, the majority of the flux contribution is found directly beneath the sensor.  Figure 1.5 The geometrical derivation of the radiation source area. The source area level PR is the ratio of the projection of the source area onto the lower hemisphere and then onto the radiometer plane (AΩ), to the projection of the entire hemisphere onto the radiometer plane (AH). Source: Schmid (1997)  As illustrated in Figure 1.5 and by Reifsnyder (1967), a down-facing hemispherical radiometer measures upwelling radiation from the entire ground-surface, as projected to the lower hemisphere. From Lambert's law, the total energy received at the radiometer, ϕtotR, is proportional to the area of its normal projection onto the radiometer plane (AH) and not to the surface area of the hemisphere. Similarly, the energy received from a finite circular source area is proportional to its central projection onto the hemisphere and the normal projection onto the radiometer plane (AΩ). The source area level (or view factor, PR) is therefore defined by the radius of the source area, r(ΩP,R), and by the sensor height, zm (Schmid, 1994):  PR =  r (Ω P , R ) 2 ϕ P, R = ϕ totR r (Ω P , R ) 2 + z m 2  (1.3)  10  Alternatively, Schmid et al. (1991) and Reifsnyder (1967) rewrite (1.3) to use a prescribed view factor PR (e.g., 50%, 90%, 95%, etc.) to approximate the source area of upwelling radiation fluxes: r (Ω P , R ) = z m (  1 − 1) 2 PR  (1.4)  For quantities that depend on turbulent diffusion processes (e.g. scalar fluxes such as water vapor and sensible heat fluxes), the source area of influence depends on the surface structure and the local meteorology of the location and is therefore spatially and temporally dynamic. Unlike radiation flux source areas, turbulent flux source areas are not symmetrically distributed about the sensor location but are instead generally elliptical in shape and aligned in the upwind direction from the tower (Figure 1.6; Oke, 2004).  Radiation source area isopleths  z  Turbulence source area isopleths  Sensor ■ □  y  x  50% 50% 90% 90%  Wind  Figure 1.6 Conceptualization of radiative and turbulent flux source areas. The 50% and 90% circular (corresponding to radiative fluxes) and elliptical (corresponding to turbulent fluxes) isopleths indicate the area from which 50 or 90% of the measured signal originates. Source: Oke (2004)  11  While the majority of upwelling radiation reaching a sensor originates from directly below the sensor, this is not the case for a turbulent quantity. Turbulent transport requires a distance for diffusion to carry the property up to the sensor level (Schmid, 1991). At some short distance upwind from the mast, surface sources and the state of turbulence are capable of having an impact the sensor signal. As one moves further away their impacts rise to a peak, and then decay at greater distances upwind. The shape of the total turbulent source area is elliptical and its dimensions (including the distances to the point of initial influence on the sensor, the point of peak influence and the furthest extent of influence) depend on the measurement height, surface roughness, and atmospheric stability (Pasquill, 1972). This so-called ‘footprint’ of the turbulent flux measurement defines the spatial context of the measurement and is now well understood over spatially homogenous surfaces. While there is a generally good and thorough understanding of the surface-layer relationships used to describe turbulent exchanges over homogeneous and smooth surfaces, such relations do not hold in heterogeneous environments. Over a homogeneous surface, the horizontal position of a turbulent flux sensor is irrelevant, because fluxes from all parts of the surface are, by definition, equal. Most of the earth’s surface including urbanized terrain is not, however, considered homogeneous (particularly at smaller scales) and the measured flux signal over such heterogeneous surfaces depends on which portion(s) of the surface has the strongest influence on the sensor.  1.4 Source area modeling in urban environments Much attention has been given to the challenges associated with conducting flux measurements over homogeneous and patchy terrain and much care taken to develop models which estimate flux footprints. Given the level of complexity inherent in turbulent processes, it is not surprising that the majority of work on the topic has focused on developing turbulent rather than radiative flux source area models. . 12  1.4.1 Radiation flux source area modeling Equation (1.4) is a straightforward expression to calculate the two-dimensional perimeter of the surface area from which a specified proportion of the upwelling radiation fluxes originate. Unlike the number of input parameters necessary to generate estimates of turbulent flux source areas, the boundaries of radiation flux source areas over non-urban sites depend only on sensor height and field-of-view. Recent work by Soux et al. (2004) and Kanda et al. (2005a) suggests that for urban terrain this is an over-simplification that under-represents its true nature. Urban surfaces are complex and three-dimensional, constructed of a myriad of materials and orientations. The geometric complexity together with the location of the sensor, dictates the relative proportion of facets contained within the FOV of a downward-facing radiometer. The facets actually involved in surface-atmosphere emissions include the walls and ground, the roofs and surrounding vegetation each of which can be sunlit or shaded. Therefore, to achieve a spatially representative sample of the complete surface, the field-of-view of the radiation sensor should contain a reasonable proportion of each surface facet. It is conceivable that the location of the radiation sensor could introduce unfair bias into the measurements. For example, if the sensor is mounted too high, the measured signal will incorporate more roofs/roads than are actually representative of the complete surface, and if mounted too low, the instrument’s FOV may be overly dominated by walls. In this sense, radiative flux source areas are highly dependent on sensor placement, and both the surface and solar geometry. Complex urban surface structures, in combination with resultant surface-sensorsun geometries, give rise to methodological problems in interpreting remotely-sensed urban surface temperatures (Roth et al., 1989). Further, improper incorporation of the surfaces contained within the radiometer’s FOV potentially jeopardizes proper evaluation of urban surface temperatures and the surface energy balance (Soux et al., 2004). 13  There are very few schemes which tackle the challenge of estimating the exact population of urban surfaces within the FOV of given sensor. One tool was introduced by Soux (S3MOD, 2000) and further tested by Soux et al. (SUM, 2004) and refined by Voogt (2008). The SurfaceSensor-Sun Urban Model (SUM) was originally born out of the necessity to better estimate the directional variation of upwelling thermal radiation (thermal anisotropy; Voogt, 1995) and predicts the total surface area contained within the measured signal of a sensor of known FOV pointing in any direction when placed at any point in space above a specified, but simplified, urban surface array. The model calculates the view factors of all surface components (walls, flat roofs, and ground) within the sensor FOV, and then determines whether the facets are sunlit or shaded. Similar to the SUM model, Kanda et al.’s (2005a) simple theoretical radiation scheme explicitly considers the three-dimensionality of urban surface geometry and is demonstrated to be an improvement over two-dimensional models. Representing the urban structure as an infinitely extended regular array of uniform buildings, the model can easily and quickly calculate, for any time and location, view factors of the six faces (roof, ground, and four vertical walls) comprising the surface, the sunlit-shaded distributions, as well as the integrated canopy albedo. Despite their potential in helping to guide the placement of sensors in observational programs, these models have yet to be wholly exploited for practical use in the field. Despite the potential measurement and analysis complications that can arise as a result of complex surfacesensor-sun relations, the SEB literature reveals little attention paid to the source areas of measured Q*. Observational and numerical studies of urban thermal anisotropy have addressed the general issue of source areas in the context of investigating complete urban surface temperatures but the effort has not yet been fully extended to tower-based SEB campaigns.  14  1.4.2 Turbulent flux source area modeling Originating from concepts of internal boundary layer growth (resulting from flow re-adjustment to a one-dimensional crosswind discontinuity; Elliot, 1958), turbulent flux footprint models are derived from basic principles. They range greatly in complexity, each with their own strengths and drawbacks. The most recent methods can be classified into three categories: stochastic Lagrangian approaches, analytical solutions to the advection-diffusion equation, and large-eddy simulations. Pasquill (1972) was the first to draw attention to the problem of accounting for the spatial context of measurements by developing his concept of effective fetch, which considers a horizontal homogeneous flow field perturbed by surface patchiness, i.e. two-dimensional irregular inhomogeneity. He treated the source area of influence downwind from a surface element as an inverted Gaussian diffusing plume of a scalar emitted by a surface source. Surface elements were regarded as an array of individual momentum sinks, rather than momentum sources. His model assumes uniform regional surface roughness and stability, allowing for Gaussian diffusion in both the vertical and lateral directions. The dimensions of the approximately elliptical source area depend on sensor height, surface roughness, and atmospheric stability. Pasquill provided results for stable, neutral, and unstable conditions and at a range of receptor heights (his Table 2). The inverted Gaussian plume assumption, though flawed in its original form (e.g., dispersion is not Gaussian in the vertical), remains to this day an explicit or implicit basis of flux footprint models (Schmid, 2002), as will be demonstrated in the discussion which follows. Another basic assumption of Pasquill’s inverted plume model - that the region is characterized by uniform roughness and stability - is in fact one of its major drawbacks, as the mere suggestion of ‘surface patchiness’ implies discontinuities in surface roughness. Even if that homogeneity assumption were to hold over a particular surface, the likelihood of such an ‘ideal’ 15  surface occurring in nature is small. Most surfaces are naturally inhomogeneous (e.g. urban areas, forests, mixed agricultural crops) and therefore surface-atmosphere turbulent exchanges vary considerably over a range of scales (Schmid, 1990). Accordingly, most long-term flux measurement programs have evolved from focusing on “ideal” homogeneous environments to more realistic, heterogeneous ones. Gash (1986) expanded Pasquill’s effective fetch idea to estimate the effect of a limited fetch on evaporation measurements. To do so, he applied an analytical solution to the basic advection-diffusion equation to derive an equation for the vertical concentration gradient at sensor height, as caused by evaporation from a uniform infinitesimal strip (he assumed neutral stability and constant wind velocity with height). From this, Gash was the first to develop the “F-fraction effective fetch” or cumulative effective fetch, which expresses the proportion of the measured flux originating from sources within a limited fetch to the total flux originating from sources in an unlimited fetch (expressed as a percent; Gash, 1986). In so doing, he was able to estimate the error of the measured signal (as the difference in flux contribution from the two fetches) as a simple function of roughness length and measurement height (assuming constant wind speed and changes in evaporation at the edge of the surface under study, as well as no discontinuity in roughness at the upwind edge of the surface under study; Gash’s Eq. 12). Schmid and Oke (1990) combined the ideas of Pasquill’s (1972) two-dimensional area bounded by a footprint function isopleth and Gash’s (1986) cumulate effective fetch to develop a reverse plume model to estimate the “source area” of a point measurement. The source area concept considers more specifically the region of the surface with the greatest impact on a sensor mounted at a given height. They defined the source area to be “the integral of the source weight function over a specified domain”, where the source weight function describes “the relationship between the spatial distribution of surfaces sources (or sinks) and a measured signal at height in the surface layer” (Schmid, 1994). In other words, the footprint or source weight function 16  provides information on the relative weights of individual point sources and is approximated by the continuous distribution from a continuous point source of a passive scalar (Schmid, 2002; Figure 1.7). Similar to Gash’s (1986) argument, Schmid and Oke (1990) showed that the source area, ΩP, is bounded by a footprint isopleth (fP) where P is the fraction of the total integrated footprint function φTOT contained in the source area. The Schmid and Oke (1990) model uses a  Figure 1.7 Schematic of the source weight distribution upwind of a sensor. Isopleths bounded by cooler colors indicate a greater source contribution to the measured signal. Source: Modified after Schmid (1994)  gradient-diffusion (K-theory) model that allows for the specification of surface-layer scales and can be used for concentrations and fluxes, requiring only slight adjustments between the two. The footprint isopleth for passive scalar concentration estimates is estimated from a plume dispersion model (Gryning et al., 1987). For source areas of passive scalar fluxes, Schmid (1994) adapted Horst and Weil’s (1992, see below) analytic flux footprint expressions and, in so doing, expanded the range of stability over which the model can be applied. Schmid et al. (1991) used 17  the source area model of Schmid and Oke (1990) to show that measurements performed over heterogeneous terrain (in their experiment, a suburban area of Vancouver) grow more spatially representative with increasing source areas. Another important analytic model was proposed by Schuepp et al. (1990), who used several approaches to solving the advection-diffusion equation (although primarily Gash’s (1986) suggestions are considered) to develop a differential footprint model (for the flux of a passive scalar under neutral conditions, Schmid, 2002). This scheme comprised of existing analytical solutions that are compared to stochastic Lagrangian trajectory simulations of flux profiles in conditions of local advection. In addition, results from one set of analytical solutions were compared to aircraft-based flux measurements taken over an isolated island. While good agreement was found between the analytic solutions and the measurements, the authors realize that numerical simulations do not form an absolute ‘truth’ against which analytical predictions can be compared and in fact, draw attention to the differing assumptions between the schemes. The authors also highlight the simplicity and ease of application of the analytical scheme (their Eqs. 9 and 10) but then also state that its applicability to only neutral conditions with a constant wind speed with height is severely limiting. Wilson and Swaters (1991) cited Schuepp et al.’s (1990) identification of “a pressing need for manageable analytical solutions capable of giving order-of-magnitude predictions of upwind areas most likely to affect a point measurement at a given height” that “specifically include the effect of stability” as a driving force behind the development of their Lagrangian stochastic footprint model. This approach is an alternative to the analytical solutions discussed above in that it represents the diffusion of a passive scalar by the trajectories of a finite number of particles that are completely independent of one another (Schmid, 2002) and describe the diffusion with a Lagrangian stochastic differential equation (Kljun et al., 2003). In addition to further exploring the footprint function, Wilson and Swaters also consider the distribution of 18  “contact distance”, which they define as “the distance since a particle observed aloft last made contact with the surface.” To do so, they first lay out a Lagrangian framework (assuming Gaussian turbulence) that considers the diffusion of a scalar through the planetary boundary layer in four configurations: a single infinitely-deep layer, a single layer of finite depth, two distinct homogeneous layers (surface layer and mixed layer; Figure 1.2), and two heterogeneous layers (again, the surface and mixed layers). By developing simple analytical expressions for both the footprint and the contact distance in each scenario, they show that the contact distance generally extends to much further distances upwind of the measurement point than the traditional footprint (Wilson and Swaters, 1991). Horst and Weil (1992) also address some limitations of Schuepp et al.’s (1990) work in their footprint model, which is a more realistic analytic dispersion model that considers various atmospheric stability conditions and a varying wind speed with height (Schmid, 2002). The authors show that the dependence of the flux footprint on crosswind location is identical to the crosswind concentration distribution for a unit point source and then use their analytic model to estimate the crosswind-integrated flux footprint in the atmospheric surface layer. An approximate vertical concentration profile equation was used to derive the crosswind-integrated flux footprint. It was found that the flux footprint depends primarily on z/zm, which is a measure of the vertical dispersion from a surface source. The z variable then serves as a surrogate to explicitly consider the dependence of the crosswind-integrated flux footprint on downwind distance, thermal stability, and surface roughness. Similar to Schuepp et al.’s work (1990), Horst and Weil (1992) use a Lagrangian stochastic dispersion model as a comparative tool in order to explore the sensitivity of their scheme. They fit their analytic model to simple empirical curves, to facilitate ease-of-use in the field. The Horst and Weil model (1992) was later applied by Amiro (1998) in an innovative fashion to investigate patterns of evapotranspiration source contributions during a field study in a 19  boreal forest. The resulting “footprint climatology” is essentially an illustrative map identifying surface sources within the landscape from which water vapor could likely have originated. Such an operational use for a footprint model was deemed by the author to be a useful way to garner important information about a study area during a long-term measurement project. Amiro also investigated the impacts of different footprint averaging times and found that longer averaging times increase the spatial area in the analyses. Accordingly, he advocates a thorough quantitative knowledge of footprint estimates, as subsequent flux analyses can be adjusted to include only those contributions from the desired sectors of the landscape. Such stratification measures are widely in use today. Of all the models considered above, not one considers heterogeneity in the flow and turbulence fields in both the vertical and horizontal directions. Pasquill (1972), Gash (1986), Schmid and Oke (1990), Schuepp et al. (1990), and Horst and Weil (1992) all assume homogeneity in both directions while Wilson and Swaters (1991) allow for just vertical inhomogeneity. Kljun et al. (2002, 2003, and 2004) sought to address this obvious drawback with their tool, the Lagrangian Particle Dispersion Model – Backward (LPDM-B). Their model is a versatile three-dimensional Lagrangian stochastic dispersion model that, given appropriate velocity statistics, can predict flux and concentration footprints in any turbulence and surface regime from measurement heights within and above the surface layer. Results from LPDM-B simulations are in good agreement with results from Kormann and Meixner’s (2001) analytical model. A particularly useful extension of this work is development of a simple parameterization scheme for flux footprints that is applicable over a range of stabilities and receptor heights from near the active surface to the middle of the boundary layer (Kljun et al., 2004). The simple, nondimensional parameters stem from applying a scaling procedure (Stull, 1988) based on a few basic variables (surface friction velocity u* , standard deviation of vertical velocity fluctuations  20  σw), which are derived from common turbulence measurements. Results from the simple parameterization scheme show good agreement with those from the LPDM-B model. Regardless of the type of footprint model considered, there are a few general features amongst them that determine their relative utility. For example, although Lagrangian stochastic models or large-eddy simulations facilitate reliable calculations, they are computationally expensive and not well-suited for use in long-term flux measurement campaigns. On the other hand, analytic models, while founded on solutions to the advection-diffusion equation (K-theory) and therefore easy to compute, are often not valid in most real-world conditions (e.g., over a range of stabilities and surface roughnesses). With this in mind, investigators are advised to choose a footprint model which best suits their measurement needs. It is important, however, to bear in mind that Pasquill’s original effective fetch paper was published just over thirty years ago, at a time when much of the focus of micrometeorology was on homogeneous surfaces. Since that time, focus has shifted to more realistic and heterogeneous surfaces and, in tandem with huge advances in computing methods, we now have a more comprehensive understanding of boundary-layer processes. Even with our enhanced understanding of such processes, however, investigators working within urban environments have been slow to adapt footprint schemes to urban settings, much less develop urban-specific tools. Urban researchers are increasingly using computational fluid dynamic models developed for use in the urban environment to better understand flow and dispersion around arrays of obstacles. Although still in its relatively infant stages of development, researchers are already applying this powerful tool to predict mean flow, turbulence statistics, and pollution dispersion in urban areas, and to evaluate the effects of obstacles within a known array (Baik, 2005). In relation to the research topic in the present study, it is the latter application that is particularly promising.  21  1.5 Rationale and research approach Urban source area modeling has been under-studied yet it is potentially of significance because it is critical to questions regarding the interpretation of surface-atmosphere energy balance observations. The lack of attention is due to a host of factors, including: a limited understanding of surface-atmosphere exchanges within the urban canopy layer (aside from air quality issues), difficulty in resolving the three-dimensional urban surface in numerical models, and limits in computational resources. Explicit mention or discussion of source area estimates in reporting measured urban SEB is seldom undertaken. This is not to say that such analyses are not performed, but that perhaps the general concept of adequate fetch is merely assumed. Neglecting to report such information has the potential to impede seriously the transferability of data and the ability to make inter-site comparisons (Grimmond, 2005). Most of the previous work on the general topic of source areas treats radiative and turbulent flux source areas as discrete arguments and models estimating these source areas are designed specifically for use over relatively simple surfaces, such as low-canopy vegetation stands. Moreover, a fundamental assumption in conducting urban SEB measurements is uniform Q* over the spatial scale of interest. The notion of homogeneous net radiation is critical when interpreting a measured SEB, as it implies that, regardless of the spatial complexity of the active urban surface and the nature of energy partitioning at that surface, non-stationary turbulent flux source areas consistently originate from areas with similar energy forcing. Scale modeling is a constructive tool to further understand the nature of radiative flux source areas and the three-dimensional surface temperature field of a simple urban form. The experimental control afforded by outdoor scale modeling simplifies the onerous task of achieving an adequate spatial sample at a full-scale urban site.  22  1.6 Objectives The overall objectives of this thesis are to aid the measurement and interpretation of surfaceatmosphere energetic and radiation fluxes. It will demonstrate the potentially negative consequences that arise from improper or insufficient consideration being given to incorporating the appropriate aggregate of active surfaces contained in the measured signal. Through the integration and expansion of current methods, this work seeks to serve past and future urban climate studies by ensuring more appropriate observation methods and interpretations of measured urban SEBs. It aims to develop a set of integrated protocols that will serve as a standard analysis scheme or universal methodology for surface-atmosphere flux studies. Specific objectives of this work are to: 1. Design, construct, and test an outdoor scale model of a simplified urban form to model three-dimensional surface temperature patterns and radiation flux source areas at the local scale. 2. Develop a protocol to guide the measurement of three-dimensional radiation flux source areas in urban environments. Drawing upon an established sensor view model, the aim is to devise a technique to assess which surfaces are contained within the upwelling source area viewed by radiation sensors exposed at a given location. Further, to assess the suitability of that mix to represent the radiation budget for a local area. 3. Combine the radiation flux source area analyses with an established turbulent flux source area model to enable direct comparison of the spatial extent of the two flux source area types. 4. Suggest a protocol to guide the placement of radiation and turbulent flux sensors in a field array that is sensitive both to the properties of the instruments and the surface structure of the local site. 23  Following the principles to achieve similitude in scale modeling outlined in Chapter Two, the scale model design and observation approach are summarized in Chapter Three. Results from the scale modeling experiment are presented in two chapters. First, a comprehensive investigation into the urban surface temperature is given in Chapter Four. These results are compared with full-scale urban observations and numerical simulations. Chapter Five focuses on the spatial and temporal variation of measured terms in the surface radiation budget. Chapter Six concerns the final three objectives outlined above and the main conclusions are briefly summarized in Chapter Seven. Additional data analysis methods, instrument descriptions and calibration, and operational conditions are included in appendices.  24  Chapter 2  PHYSICAL SCALE MODELING OF URBAN CLIMATE  Field data acquired in real cities provide valuable information critical in the development of a comprehensive understanding of complex urban surface-atmosphere interactions. These data, however, are largely site-specific and therefore are rarely transferrable to other sites and climate regimes. Numerical modeling of urban climate involves simplification of the physical domain as well as the governing processes, so validation of these models can be challenging, because equivalent real-world configurations are often difficult to find (Mills, 1997). Initially used by engineers interested in dispersion and architects or urban planners studying design theories, physical scale models have been used extensively in the study of urban climate, because they allow systematic investigation of the relations between the surface and physical processes both within and above the urban canopy (Kanda, 2006). Indoor and outdoor scale modeling experiments (see Tables 2.1 and 2.2 for a partial listing) that focus on a range of processes (e.g., turbulent flow, energy balances, local transfer coefficients) and urban configurations have usefully provided the physical parameters needed to construct numerical models (Kanda, 2006).  2.1 Scaling considerations At the most fundamental level, a scale model involves comparison between objects with similar geometry but different size. The model is a scaled down version of a larger prototype, which is typically described as full-scale (Richards, 1999). For benefits to be gained from scale modeling it is necessary that similarity exists between the model and the full- scale prototype on which the model is based. Correspondence between the geometric, thermal, and dynamical characteristics of a scaled model to that of a prototype is referred to as model similitude (Imbabi, 1991). When 25  Table 2.1 Indoor experiments that used an array of urban-like roughness elements. Authors  Target  Roughness Element  Alignment  O'Loughlin and Macdonald (1964) Counihan (1971) Cook (1976) Wedding et al. (1977) Hussain and Lee (1980) Raupach et al. (1980) Oke (1981) Osaka and Mochizuki (1987) Hoydysh and Dabberdt (1988) Murakami et al. (1990) Dabberdt and Hoydysh (1991) Baechlin et al. (1991) Theurer et al. (1992) Davidson et al. (1996) Meng and Oikawa (1997) Peterson (1997) Rafailidis (1997) Hall et al. (1998)  Flow Flow Flow Flow & dispersion Flow Flow Radiative cooling Flow Flow & dispersion Flow Flow & dispersion Flow Flow Flow & dispersion Flow & dispersion Flow Flow Flow & dispersion Nocturnal cooling in urban parks Flow in street canyons Flow Flow Flow in street canyons Transfer coefficient Flow Flow Flow Transfer coefficient Bottom heating and flow  Cubes Blocks Lx/zh=1.67 Blocks Lx/zh=1.0, 2.0 Blocks Lx/zh=4.0 Blocks Lx/zh=0.5-4.0 Cylinders Lx/zh=1.0 Blocks zh/Lx=0.25, 0.5, 1.0, 2.0, 3.0, 4.0 2-D canyon λS=1.0 Blocks Lx/zh=2.67, Ly/zh=8.0 Cubes Cubes, blocks Lx/zh=2.67, Ly/zh=8.0 Blocks Lx/zh=1.0, Ly/zh=3.2 2-D canyon Lx/zh=0.8, λS=1.6 Cubes Cubes Cubes 2-D canyon Lx/zh=1.0+pitched roof top λS=1.0, 2.0 Cubes  Staggered Staggered Staggered Normal Normal Normal. staggered Normal 2-D canyon Normal Normal Normal Normal 2-D canyon Normal, staggered Staggered Staggered, random 2-D canyon Normal  Spronken-Smith and Oke (1999) Baik et al. (2000) Uehara et al. (2000) Hagishima et al. (2001) Kastner-Klein et al. (2001) Barlow and Belcher (2002) Macdonald et al. (2002) Cheng and Castro (2002) Uehara et al. (2003) Narita (2003) Liu et al. (2003)  Two geometries, with/without trees, three sizes, five surface materials 2-D canyons λS=1.0, 1.5, 2.0, 2.4, 3.0 Cubes Cubes zh/Lx=0.38, 0.75, 1.13, 1.5 2-D canyon λS=1.0 2-D canyons λS=0.19-0.75, 0.19-1.52, 0.44-1.44, 0.25-2.0 Cubes Cubes, random blocks Cubes Blocks Lx/zh=1.0, Ly/zh=1/6-5.0 2-D canyon λS=0.67, 0.83, 1.7  2-D canyon Normal Normal, staggered 2-D canyon 2-D canyon Normal, staggered Staggered Normal Normal 2-D canyon  26  Table 2.2 Outdoor experiments that used an array of urban-like roughness elements. Authors  Target  Roughness Element  Alignment  λP  λF  Aida (1982)  Albedo  Concrete cubes zh=15 cm, λS =Lx/zh =1.0  Normal  0.25, 0.5  0.25, 0.5  1:8 scale model houses  Staggered  0.05  2-D canyon λS=1.0 2-D canyons λS=0.375, 0.5, 0.67, 0.75, 1.0, 2.0  2-D canyon  Voogt and Oke (1991)  Landscape treatments, interior temperature Longwave radiation balance  Swaid (1993)  Radiative-convective interaction  Davidson et al. (1995)  Flow and dispersion  Mills (1997)  Interior temperature  Macdonald et al. (1997, 1998)  Flow and dispersion  Hanna and Chang (2001)  Flow and dispersion  McPherson et al. (1989)  Mavroidis and Griffiths (2001) Richards and Oke (2002)  Normal  0.04 - 0.44  Normal  0.06 - 0.44  0.06 - 0.44  Staggered  0.0 (plate)  0.028, 0.117  0.16  0.16  Normal  0.096  0.1  Normal  0.096  0.1  Concrete cubes zh=15 cm  Normal  0.25  0.25  Concrete cubes zh=15 cm Rows of concrete blocks  Normal Normal  0.11 - 0.69 0.21  0.11 - 0.69 0.21, 0.42  Wooden cubes zh=0.2 cm, λS=4.0, 2.0, 1.0, 0.5 Steel cubes zh=1.12 m, zh/Lx=1.0, Ly/zh=1.0, 2.0, 4.0 2 plates; 0.81(Lx) x 0.2(zh) m, 2.4(Lx) x 2.4(zh) m  Urban dew deposition  1:8 scale wooden houses Containers 2.42(Lx) x 12.2(Ly) x 2.54(zh) m Containers 2.42(Lx) x 12.2(Ly) x 2.54(zh) m  Yee and Biltoft (2004)  Flow and dispersion  Kanda et al. (2005a) Pearlmutter et al. (2005)  0.111  Cubes zh=1.15 m  Flow and dispersion  Kanda et al. (2005b)  Normal, staggered  2.2(Ly) x 2.45(Lx) x 2.3(zh) m  Flow and dispersion  Vernath et al. (2003)  Energy balance, transfer coefficient Albedo Energy balance  2-D canyon  Normal, staggered Normal  0.111  27  similitude is achieved, mathematical relationships exist between parameters at both scales so that scaled data are transferable to the full scale (Richards, 1999). Depending on the objective of modeling, different types of similitude may be stressed more than others. For example, the importance of geometric similarity is emphasized when investigating processes related to building density such as the relationship between urban structure and albedo (Aida, 1982; Kanda et al., 2005a), building density and interior temperatures (Mills, 1997), or urban nighttime cooling rates (Oke, 1981; Spronken-Smith and Oke, 1999). When airflow and dispersion characteristics of different urban geometries are to be examined, the priority is to achieve similitude of boundary layer depth and of Reynolds and Richardson numbers close to those at full scale. Because scaling criteria are interdependent, conservation of one type of similitude is often in conflict with another and a degree of compromise is necessary in model design (Richards, 1999). Even so, partial similitude can achieve meaningful results (Barozzi et al., 1992). In his review of progress in the scale modeling of urban climate, Kanda (2006) identifies two general categories of physical similitude required in scale modeling of the real (full scale) urban environment: geometrical and dynamical. Geometrical similitude is the more feasible of the two and is generally accomplished simply by ensuring the array of roughness elements is scaled to approximately match the relative size and spatial distribution of real-world urban surface elements. Dynamical similitude in reduced-scale modeling requires three criteria to be satisfied: (1) similitude of radiation, (2) similitude of flow, (3) similitude of thermal inertia. Following Kanda’s (2006) framework, a general discussion of scaling criteria can be separated into two parts: those dealing with similitude in the physical domain (Section 2.2), and those with dynamical similitude (Section 2.3) of the model.  28  2.2 Geometrical similitude The spatial dimensions of a scale model should be in the same proportion as the full-scale prototype, scaled by a factor, F. By extension, length is scaled by F, area is scaled by F2, volume by F3, and ratios of proportion (i.e., canyon aspect ratio, frontal area density, sky view factor, etc.) should remain the same in the model as at the full-scale (Imbabi, 1991; Richards, 1999). Consideration must also be given to the appropriate spatial scaling of environmental gradients such as temperature, radiation, and turbulence. Parczewski and Renzi (1963) point out that for two geometrically similar objects the ratio of the temperature gradient between any two points on the model to the temperature gradient between corresponding points on the full-scale prototype is constant. Oke (1981) found that temperature gradients in the model are commonly accelerated and greater than those at the full-scale and that the mean temperature of the model is higher. Even so, this definition for the scaling of the temperature field is often preferred to the alternative view that absolute temperatures between the model and prototype should be identical. When the primary process is conductive, convective, and/or radiative, similitude often requires the model to be infinite in some dimension. Physical models, however, are finite, which implies the potential for undesirable edge effects of the model must be considered. In the case of conduction, the dimensions of the body, the rate of conduction, and the time frame over which conduction occurs dictates the size of model required to avoid edge effects at a central measurement location (Richards, 1999). For convection, the size of the model should incorporate the area containing the portion of the sensor signal that is well adjusted to the flow. In order to match real-world boundary conditions, the upwind fetch of the model should be long enough produce an internal boundary layer height at least 10 times greater than the obstacle height (Bottema, 1997). Few indoor experiments are able to satisfy this requirement for such extensive fetch (Kanda, 2006).  29  Radiation studies also require that the horizontal dimensions of the source area of influence be contained within the limits of the model, in order to avoid abnormal sinks or sources at the edges of the model (Aida, 1982). Similitude of shortwave radiation in the vertical dimension is a function of the number of reflections of shortwave radiation needing to be modeled. The canyon structure (i.e., orthogonal walls and ground of finite width and infinite length) of a basic urban configuration allows for the straightforward calculation of the number of shortwave reflections that occur before exiting through the canyon top. The requirement for an infinitely long canyon is impractical in a physical scale modeling exercise. Arnfield (1976) and Voogt (1989) found that for a canyon to behave radiatively as if it is infinite, the canyon length must be greater than eight times the canyon height and width. An alternative approach is to ensure similitude of sky-view factor ΨS. The advantage of this method is that ΨS can be easily assessed numerically (Steyn and Lyons, 1985) or through the analysis of hemispherical photography (Steyn, 1980; Blennow, 1995; Chapman et al., 2001).  2.3 Dynamical similitude Achieving model similitude of physical processes such as radiative exchanges, convection/flow, and thermal inertia/conduction is typically a more challenging objective than achieving geometrical similitude. Ensuring that the nature of the primary process under study is correctly replicated in the model requires careful consideration of the boundary conditions of the model.  2.3.1  Radiation  The characteristic length scale of radiation (10-7 – 10-4 m) is considered negligible when compared to the linear scale of even a small scale model (Oke, 1981) hence similitude of radiation always exists for both indoor and outdoor scale models. Outdoor scale models that make use of natural sunlight and atmospheric conditions will always achieve similitude of the 30  downward components of long- and shortwave radiation (Kanda, 2006). Surface properties of the scale model such as albedo (α), emissivity (ε), absorptivity (a) and transmissivity (tr) determine the degree of similitude for upwelling radiative fluxes. Matching surface albedo ensures similitude of reflected shortwave radiation and similitude of upwelling longwave radiation requires the matching of surface emissivity and observed surface temperature. Scale models constructed of real building materials can achieve these surface property requirements (McPherson et al., 1989), but because surface temperature is inherently tied to other physical processes such as turbulent transfer and heat conduction, some complications can arise in the matching of observed surface temperature (Kanda, 2006).  2.3.2  Flow  While ensuring similitude in radiative processes is fairly straightforward, similitude of flow or convective processes requires more analysis (Kanda, 2006). Boundary conditions leading to free and forced convection observed at the full scale must be replicated in the scale model. Free convection results from differences in surface-air temperature giving rise to buoyant motion and dominates under conditions of strong radiative heating and little wind. Mechanical mixing of air (i.e., appreciable wind) underlies forced convection (Stull, 1988). A mixture of both processes can also occur. Monteith (1973) and Mills (1997) suggest similitude of free, forced, and mixed convection can be assessed by comparing the ratios of buoyant to inertial forces represented by the non-dimensional Grashof (Gr) and Reynolds (Re) numbers, respectively:  η=  Gr Re 2  (2.1)  where Gr = 158 x d3 x ∆T (where ∆T is the difference between surface and air temperature and d is the characteristic length dimension) and Re2 ≈ 108 u2 (where u is wind speed). The Grashof number is the ratio of a buoyancy force times an inertial force to the square of a viscous force. A 31  large value of Gr implies relatively minor viscous forces (which tend to inhibit circulation) so free convection is strong (Monteith, 1973). The Reynolds number expresses the ratio of inertial forces in a fluid to viscous forces and therefore describes the importance of turbulence in the flow. Beyond a critical value of Re (typically taken to be several thousand in urban configurations, as demonstrated by wind tunnel experiments, e.g., Uehara et al., 2003), flow tends to change from laminar to turbulent. Rules of thumb developed from experimental evidence state that when Gr is greater than 16 x Re2, buoyancy forces dominate over inertial forces and similitude of Gr is dominant. When Gr is less than 0.1 x Re2 buoyancy forces are negligible (i.e., forced convection is the dominant heat transfer mechanism) and emphasis turns to ensuring similitude of Re (Monteith, 1973). The relative importance of free and forced convection in thermally-stratified flows can also be described with the Richardson number Ri, a dimensionless parameter used to characterize atmospheric stability in the lowest layer of the atmosphere (Oke, 1987). For non-turbulent conditions with little flow, ensuring similitude of Re and Ri becomes less critical. Desired flow and stability conditions are easier to achieve in environments where the fluid type, velocity, and temperature can be externally prescribed, such as in wind tunnel, flume or chamber experiments (Richards, 1999).  2.3.3  Thermal inertia  Perhaps the most challenging dynamical feature to scale appropriately, thermal inertia is a function of the material properties, size, and the nature of the fluid surrounding the scale model. Similar to the approach taken to scaling convective processes, it is necessary to strive to achieve agreement between the full and small scales of dimensionless parameters describing thermal response. A material’s thermal response over time can be represented with the dimensionless  32  Fourier number (Fo), which is a dimensionless time parameter that is the ratio of the heat conduction rate to the rate of thermal energy storage:  Fo =  κH t s  2  L  =  kst  ρ scsLs 2  (2.2)  where t is time (s), κHs, ks, ρs and cs are the thermal diffusivity (m2 s-1), conductivity (W m-1 K-1), density (kg m-3), and specific heat (J kg-1 K-1) of the solid, respectively, and LS is the length through which conduction occurs. This dimensionless time parameter characterizes how large objects and objects with low thermal diffusivity respond more slowly than small objects or those with high thermal diffusivity. The Biot number (Bi; Keith and Black, 1980) is a dimensionless heat transfer coefficient defined as the ratio of the convective heat transfer coefficient for the fluid, hcf, and the conductive heat transfer coefficient for the solid, hks (units of W m-2 K-1)  h h L Bi = cf = cf h ks ks  (2.3)  If the thermal resistance of the fluid/solid interface exceeds the thermal resistance of the interior of the solid, Bi will be < 1. When Bi is much less than one, the interior of the solid is assumed to be isothermal, although this temperature may be changing as heat passes into the solid. Values of the Bi < 0.1 imply that heat conduction inside the body is much faster than the heat conduction away from its surface, internal temperature gradients are negligible, and heat can be assumed to be constant throughout the volume of the material. Bi > 0.1 constitutes a thermally thick substance and indicates that more complicated heat transfer equations are required to describe the non-uniform temperature field within the material body (Incropera et al., 2006). The Fourier and Biot numbers together characterize the conductive nature of an object. Similitude of thermal inertia requires that geometrically similar objects with the same Bi  33  (according to time measured as Fo) will also have the same dimensionless temperature response,  φ (Chapman, 1984): ϕ = e -BiFo  (2.4)  Studies involving the scale modeling of urban environments are largely unable to satisfy the requirements for thermal similitude. As a result, little work on the scale modeling of the urban energy balance has been attempted (Kanda, 2006). While using real-world construction materials such as concrete, brick, or wood ensures similarity in the thermal and radiative properties of the individual materials, the integrated thermal inertia of the model will not equal that of a full-scale prototype. Kanda (2006) suggests a method to overcome lack of thermal similitude by first using measured turbulent characteristics and transfer coefficients of the scale model to tune similar parameters in a numerical model. Then, the volumetric heat capacity of the numerical model is scaled to that of the scale model so that the performance of the numerical model can be evaluated against scale model data. Once the numerical model has been shown to perform satisfactorily, the volumetric heat capacity of the numerical model is further scaled to that of a real urban setting.  34  Chapter 3  A SCALE MODEL TO STUDY URBAN RADIATION SOURCE AREAS  Observations of radiative exchanges are carried out with measurements from a physical scale model exposed out-of-doors. This method has distinct advantages over other common observation approaches, such as wind tunnel modeling or full-scale observations. Wind tunnel modeling allows isolation and simplification of climatic processes by controlling the impinging flow and the form of surface structures and some other boundary conditions which can be ideal for turbulence/dispersion studies (Plate, 1999). Full-scale observations have the advantage of using natural radiation forcing and turbulence, albeit specific to that particular site and time (Pearlmutter et al., 2005). On the other hand the sheer size and complexity of cities makes adequate spatial sampling very difficult. Open-air physical scale modeling is a compromise between the two methods: it allows for the flexibility and systematic comparisons associated with physical modeling while still being open to natural environmental forcing (atmospheric turbulence and radiation loading; Mills, 1997). Chapter Two provides a discussion of the practice of scale modeling of the urban environment. Here, a methodology is developed to simulate the radiative exchanges within and above the urban canopy layer (UCL) of a physical scale model. The chapter concludes with a summary of the numerical and analysis methods employed in the study, and an assessment of the experimental set-up.  3.1 Scaling considerations Urban areas and their ability to affect the atmosphere can be described according to four basic features: the urban structure (building dimensions and spacing between buildings), the urban cover (built, paved, bare soil, vegetated, water), the urban fabric (construction and natural 35  materials), and urban metabolism (anthropogenic heat, water, and pollutants; Oke, 2006). These features combine into characteristic urban classes that can span from a densely-packed central business district with relatively tall buildings and very little vegetation to a semi-rural setting with one- or two-story buildings and large swaths of vegetated areas. In the absence of a universal and standardized urban classification scheme, Ellefsen’s (1990/91) Urban Terrain Zones scheme has been used to describe urban structure according to three types of building contiguity and 17 sub-types of function, location in the city, and building height and construction information (Oke, 2006). Oke (2004) proposes a simpler Urban Climate Zones scheme, which uses groups of Ellefsen’s zones but also includes the canyon aspect ratio, λS, which has been shown to relate to flow regime types (Oke, 1987), shading and longwave screening (Oke, 1981), heat island genesis, and the degree of surface permeability. Oke’s (2004) Urban Climate Zones scheme is further advanced by Stewart and Oke (2009) by incorporating sky view factor, thermal admittance and anthropogenic heat flux to generate a series of Built Climate Zones (BCZ; Table 3.1 and Figure 3.1). In this study, the impact of urban structure on measured radiative flux source areas is modeled at two scales (1:60 and 1:30) using three array configurations. Following the built climate zone classifications the model configurations include an old city core (BCZ2), a medium density residential site/detached lowrise (BCZ7) and an open block setting/light industrial (BZ5). The model configurations do not duplicate exactly any particular full-scale location but the surface materials and arrangement of the scaled elements possess similar characteristics to those observed at various urban sites.  3.1.1 Similitude Given that reduced-scale physical models are unable to fully replicate the complex morphology of cities and their meteorological exchange processes, it is difficult for these models to satisfy all 36  - Agricultural series (ACZ1...ACZ4) - Natural series (NCZ1...NCZ5) BCZ1: Compact highrise  BCZ2: Compact midrise  BCZ3: Compact lowrise  BCZ4: Industrial processing  BCZ5: Open-set blocks  BCZ6: Extensive lowrise  BCZ7: Detached lowrise  BCZ8: Lightweight lowrise  BCZ9: Dispersed midrise  BCZ10: Dispersed lowrise  0  100 m  Figure 3.1 Classification of the Built Climate Zones according to their perceived ability to modify local climate. Adapted from Stewart and Oke, 2009.  of the similarity requirements important in scale modeling. In the present study the challenges to achieving similitude are addressed following the approach outlined in Chapter Two. The model design consisted of three uniform configurations, differentiated hereafter by canyon aspect ratio. A summary of the relationship between the scaled elements to  37  corresponding real-world dimensions is given in Table 3.2. The overall dimensions of the model array are large enough to ensure that measured radiation fluxes are largely derived from within  Table 3.1 Typical properties in the Built Climate Zone classes illustrated in Figure 3.1. Adapted from Stewart (pers. comm.)  1 2 3  Built Climate Zone  Canyon aspect ratio λS  Sky view factor Ψs  Terrain roughness 1  Impervious plan fraction 2 (%)  Zone thermal admittance (J m-2 s-½ K-1x 102)  QF (W m-2) 3  BCZ1 BCZ2 BCZ3 BCZ4 BCZ5 BCZ6 BCZ7 BCZ8 BCZ9 BCZ210  >2 1–3 1.5 0.2 - 0.5 0.5 - 2 0.05 – 0.2 0.5 - 1.5 1 - 1.5 0.1 - 0.5 < 0.5  0.4 - 0.6 0.3 - 0.6 0.4 – 0.7 0.7 - 0.9 0.6 - 0.9 0.8 - 0.95 0.6 - 0.9 0.7 - 0.9 0.8 - 0.9 >0.8  8 6-7 6 5-6 6-8 5 5-6 4-5 5-6 5-6  > 90 > 85 > 80 40-70 60-80 > 80 40 - 70 > 70 30 - 40>70 < 30  12 - 17 12 - 20 12 - 15 15 - 30 12 - 17 12 - 15 7 - 19 6 -10 6 - 20 6 - 20  > 100 30 - 40 20 - 30 200 - 800 20 - 35 30 – 50 10 - 15 <5 5 - 10 <5  Effective terrain roughness class in the modified Davenport classification (Davenport et al., 2000). Impervious plan fraction (sum of building and impervious plan fractions) Local not building scale values  the limits of the model and do not contain abnormal sources or sinks from the edges of the array. Values for sky view factor at ground level ΨS from the model are similar to those found at fullscale sites of the relevant BCZ. In the case of the λS = 1.25 model configuration, ΨS = 0.41, which is comparable to European city center sites such as Basel (0.36 – 0.51; Christen, 2005) and Marseille (0.40; Grimmond et al., 2004). Likewise the two more open surface geometries have sky view factors within the range of those observed at residential and light industrial sites in Vancouver (Voogt and Oke, 2003). Ideally, details of building construction and the nature of the ground surface and substrate to be used in the model are determined from surveys of a full-scale urban environment. Several simplifications were made in the present study, however. The use of realistic interiors (i.e.,  38  Table 3.2 Relationship between scaled elements in the scale model to corresponding real-world dimensions. λS = 1.25  λS = 0.63  λS = 0.42  BCZ2  BCZ7  BCZ5  old city center  medium density residential site  low-density residential or light industrial site  Model : full scale Real building height Real building length Real building width Real lot length Real lot width  1:60 15 m 24 m 24 m 36 m 36 m  1:30 7.5 m 12 m 12 m 24 m 24 m  1:30 7.5 m 12 m 12 m 30 m 30 m  Sky view factor ΨS  0.41  0.70  0.79  Built Climate Zone Description  insulation, drywall, windows, flooring, etc.) and roofing materials (i.e., asphalt shingles, clay or slate tiles, fiberglass, metal or wood roofing) was not attempted. The thickness of the scaled building walls relative to the interior cavity is greater than in the real world. The scale model simulates radiative emissions from a non-vegetated urban setting of simple and repeating geometry. Therefore it is necessary to ensure the physical processes governing these radiation exchanges are suitably scaled. The characteristic length scale of radiation (10-7 – 10-4 m) is considered negligible when compared to the linear scale of even a small scale model (Oke, 1981) hence similarity of radiation always exists. Placing the model outdoors and utilizing real urban materials satisfies the requirements for dynamical similarity of radiation, because that ensures the surface albedo and surface emissivity are matched, and the downward components of short- and longwave radiation are those of the real world.  3.1.2 Assumptions Several assumptions are made concerning the construction and nature of the model. It is assumed that:  39  •  Practical considerations regarding the site, overall weight of the model, and its ephemeral nature necessitated the use of a light, expansive, and removable surface cover. The materials used to represent the ground surface have a smaller thermal mass than the materials used to construct the scaled building structures. This means that the ground surfaces are more thermally responsive to solar forcing, compared to the roof and wall surfaces. A consequence to this is that contrary to the thermal behavior commonly observed in most real-world urban settings even under full solar exposure, roof surfaces often remain cooler than street surfaces.  •  No attempt is made to precisely match the thermal properties of the model to those of a particular full-scale location. The hollow concrete building blocks used in the model are similar, and in many cases, identical, to those used in the construction and insulation of full-scale building walls. The material composition is considered thermally similar to local construction.  •  The model is of sufficient size to produce microclimate processes and features similar to those in the real world including: diurnal patterns of surface warming and cooling, reflection and ‘trapping’ of short- and longwave radiation in the canyons and effective thermal anisotropy arising from temperature patterns created by the three-dimensional surface structure.  3.2 The model The model array consists of an urban-like array of scaled ‘buildings’ constructed of hollow concrete masonry blocks with solid capping slabs. It was situated on a rooftop on the campus of Arizona State University in Tempe, Arizona for the period November 2006 through January 2007.  40  3.2.1 Site and operation The arid climate of the Salt River Valley in Arizona’s northern Sonoran Desert (in which the Phoenix metropolitan area is centrally located, Figure 3.2) provides ideal conditions to observe radiatively-driven thermal conditions. Atmospheric humidity and average annual rainfall (210 mm at Phoenix Sky Harbor International Airport) is low, even during the November through  ●  Figure 3.2 Central Arizona landuse classifications from 2000. Phoenix Sky Harbor International Airport is shown by the red star in the middle of the figure. Site location in Tempe is shown by the blue circle. Source: Central Arizona – Phoenix Long-Term Ecological Research (CAP-LTER), Arizona State University.  March rainfall season. Daytime air temperatures during the winter are mild (average daily maximum in December is 19.4°C) while nighttime temperatures frequently drop to below freezing (average daily minimum in December is 6.7°C). Sunshine in the Phoenix area averages 86% of possible, ranging from a minimum monthly average of around 78% in December and January to a maximum of 94% in June (NOAA, 1996). These generally dry and clear atmospheric conditions in the fall and winter seasons allow a robust regime of daytime heating 41  and nighttime cooling of surfaces through interception of insolation over the day and efficient longwave radiative losses to space at night. The rooftop of the six-story Engineering Research Building (ERC) on the campus of Arizona State University (ASU), approximately 10 km southeast of Phoenix Sky Harbor Airport, was chosen as the location for the scale model study. This site has logistical advantages, such as its high level of security, the availability of uninterrupted A/C power, and its central location and proximity to resources on and around the ASU campus. Being the tallest structure in the immediate area, the rooftop of the ERC is free of obstructions (e.g., trees, other buildings) which could potentially cause unwanted microclimatic influences such as horizontal screening, wind channeling or anthropogenic heating or cooling which might impinge on the model array (Figure 3.3). The ERC rooftop was designed for the express purpose of supporting engineering experiments related to solar collectors and is able to sustain heavy loads. The surface itself is comprised of a layer of steel grating (3 cm x 6 cm gaps) mounted on 2-m high support piers creating a deep crawlspace between the building and the grating. The overall roof dimensions are approximately 23 m x 85 m and the building’s long axis is oriented in the north-south direction. The northern-most 23 m x 25 m of the roof is occupied by an elevator shaft, stairwell, enclosed storage area, and an elevated 13 m x 13 m platform tilted 17° from horizontal so as to create a south-facing surface on which to conduct solar panel experiments. The remaining 23 m x 60 m of the southern portion of the ERC roof is largely free of structures (aside from a dormant ventilation stack on the eastern edge of the roof, an active ventilation stack adjacent to the roof on the western edge, and antennae at the southern tip of the roof. The southern area therefore was the optimal area on which to construct the scale model array (Figure 3.3a).  42  a)  b)  Figure 3.3: Engineering Research Center (ERC) on the campus of Arizona State University in Tempe, Arizona, USA. Photograph (a) is approximately oriented with north at the top of the picture. The model itself is visible as the dark grey circle on the light grey patch at the south end of the building with the dark roof. The eastern extension of the light grey area is where the ancillary measurements were conducted. Source: GoogleEarth©. Photograph (b) is a ground-level hemispherical photo from the center of the array, showing the open nature of the site.  3.2.2 Construction The model on the south end of the ERC roof occupied a total area of approximately 20 m x 20 m. Because the existing steel grating was not an ideal surface platform on which to situate the scale 43  model, a removable surface was installed. It consisted of 1.2 m x 1.3 cm x 2.4 m polystyrene sheets overlain with 1.2 m x 1.3 cm x 2.4 m fiberboard sheathing. The combined 1.2 m x 2.6 cm x 2.4 m surface components were arranged contiguously over the 20 m x 20 m area and affixed to the steel grating with cable ties and 13 cm metal bolts. The entire surface was primed and painted with outdoor paint to match the grey tinged with bluish-red color of the concrete blocks used to simulate ‘buildings’. Each model element (i.e., ‘building’) consists of four hollow cubic concrete masonry blocks 20 cm on a side arranged flush with one another and topped with two 20 cm x 3 cm x 40 cm concrete cap blocks. The total dimension of each ‘building’ element in the model is, therefore, 40 cm x 40 cm x 25 cm. The physical and thermal properties of the materials used to construct the model are given in Table 3.3.  Table 3.3 Physical and thermal properties of the individual materials comprising the scale model array. Material Description Sheathing  Fiberboard (asphalt-bonded wood fibers)  Polystyrene  Expanded polystyrene with visqueen coating  Concrete Block  Constructed of cement and sand  Cap Block  Concrete of uniform texture and color  Density (kg m-3) 256.3  25 – 200  1681.9  2002.3  Thermal Conductivity (W m-1 K-1)  Specific Heat (J kg-1 K-1 x 103)  Thermal admittance (J m-2 s-1/2 K-1)  4.17  0.08  .0013  1.6 – 4.6  2.4  0.86  .88  1128  2.2  0.86  .88  1231  R value 1.32  Sources: Oke (1987), manufacturer specifications  Array configurations were defined geometrically by their street canyon aspect ratio, λS = zb /W, where zH is the height of the roughness elements and W the horizontal distance (spacing)  between vertical facets of consecutive elements (see Figure 1.2). Canyon widths were uniform in  44  both ‘street’ orientations, so Wx = Wy. The initial experimental configuration used a street canyon aspect ratio λS = 1.25, as determined by elements of height 25 cm at a horizontal spacing on all sides of 20 cm (Figure 3.4). The total lot area, AT, of each array element was 60 cm x 60 cm. The  Figure 3.4 Schematic representation showing the relative location of sensors within the λS = 1.25 ‘building’ array.  entire array was approximately circular in shape, with nineteen ‘buildings’ and eighteen cross ‘streets’ along the 11.2 m diameter. This array formulation comprised 306 ‘buildings’, giving a total model weight of 15,546 kg or 15.546 tonnes. By doubling the building spacing to 40 cm, the resulting configuration had a street canyon aspect ratio of λS = 0.63 and a lot area AT of 80 cm x 80 cm (Figure 3.5). Unlike the initial configuration, this second design was not symmetrical 45  Figure 3.5 Schematic representation showing the relative location of sensors within the λS = 0.63 ‘building’ array.  about the north-south and east-west axes. It contained fifteen ‘buildings’ along the east-west axis (12.4 m axis) and sixteen ‘buildings’ along the north-south axis (11.6 m axis) for a total of 208 ‘buildings’ (overall weight of 10,567 kg or 10.567 tonnes). The third and final array configuration used an element spacing of 60 cm resulting in a street canyon aspect ratio λS = 0.42 and a lot area AT of 100 cm x 100 cm (Figure 3.6). In this case, thirteen ‘buildings’ and twelve ‘streets’ along the east-west and north-south axes resulted in an array diameter of 12.4 m in both directions. There were 145 ‘buildings’ in this configuration, with a total weight of 7,366 kg (7.366 tonnes). A summary of surface component areas for each array configuration is provided in Table 3.4.  46  Figure 3.6 Schematic representation showing the relative location of sensors within the λS = 0.42 ‘building’ array.  Table 3.4 Surface component areas for each array configuration. All areas have units of cm2 x 102 Area  Symbol  λS = 1.25  % of AC  λS = 0.63  % of AC  λS = 0.42  % of AC  47 21 5 21 53  64 32 16 16 40 104  61 31 15 15 39  100 48 36 16 40 140  71 34 26 11 29  Plan (2D) Street (N-S or E-W) Street intersection Roof Wall (N, S, E, W) Complete  AP AS(N-S, E-W) AI AR AW(N, S, E, W) AC  36 16 4 16 40 76  Total active (3D/2D)  AC/AP  2.1  1.6  1.4  Hemispherical photographs taken at ground level (Figure 3.7) at the canyon midpoint of the three array configurations show their relative view factor of the walls (ΨW) and sky (ΨS) (Table 3.5 and Appendix A).  47  Figure 3.7 Hemispherical photographs taken at ground level at the canyon midpoint of the three model array configurations: λS = 1.25 (top), λS = 0.63 (middle), λS = 0.42 (bottom)  48  Table 3.5 Sky and wall view factors for the three array configurations, as calculated from the floor of the canyon at mid-width and mid-block. See Appendix A for method of calculation. View factor  λS = 1.25  λS = 0.63  λS = 0.42  of walls for floor (ψW)  0.59  0.30  0.21  of sky for floor (ψS)  0.41  0.70  0.79  In addition to sampling the simple case (untreated and flat concrete ‘roofs’) for all three geometrical configurations, some ‘roof’ treatments were applied to the 0.63 and 0.42 arrays. Two surface treatments were applied to the λS = 0.63 array. First the flat concrete ‘roofs’ were painted over with a layer of white outdoor paint. Then, a few days later, a coat of black outdoor paint was applied. In the λS = 0.42 array some of the ‘roofs’ were replaced with solid concrete doublesloped ‘roofs’, some with 17°- and other with 30°-pitch angles. (These triangular capping blocks were made by pouring concrete into moulds. The ‘roofs’ had no overhangs.) The orientation of the ridgelines of these ‘roofs’ alternated between the north-south and east-west directions. Following that set of experiments, all ‘roof’ surfaces, pitched and flat, were painted white (Figure 3.8). A more detailed summary of surface and geometrical treatments is given in Appendix B.  3.2.3 Operational considerations As with any outdoor experiment, weather conditions played a primary role in daily operations and later in the assessment of time periods most suitable for analysis. Maintenance of a continuous data stream from the principle sensor systems is critical in the classification of Intense Observation Periods (IOPs) for analysis. Fair weather (cloudless sky) conditions are ‘ideal’ atmospheric conditions for the study of radiative exchanges and the surface thermal environment. Therefore, clear- to mostly cloud-free sky conditions and a near- to fully operational array of sensors are the primary criteria used to identify IOP days in this study. 49  Figure 3.8 An example of a surface treatment applied to roofs in the λS = 0.42 model configuration. Here, all roofs (flat, and some double-sloped with 17°- and 30°-pitch angles) are painted white.  Twenty-five IOP days are identified for the operational period spanning 22 November 2006 (YD 326) – 12 January 2007 (YD 12). Table B.1 in Appendix B provides a summary of the six-hourly atmospheric conditions and the corresponding availability of data over the experimental period.  3.3 Measurements Two over-arching objectives guided the design of the measurement platforms. Firstly, sustained measurements of complete (i.e., three-dimensional) facet surface temperatures were required. Secondly, vertical profiles of radiation fluxes extending from the canyon ‘floor’ through the ‘building’ layer to well above the ‘roofs’ were measured from two distinct locations within the array.  3.3.1 Surface temperature measurements The surface temperatures of wall, roof, and road facets of the model were continuously monitored by infrared thermocouples. In addition to the value of knowing the thermal response to facets with different solar aspects, this permits estimation of the complete surface temperature  50  of the total array. Supplementary measurements were performed with an infrared camera positioned at varying locations outside the array domain.  3.3.1.1 Measurements using infrared thermocouples Surface temperature measurements were conducted using twelve 28° half angle FOV infrared thermocouples (Apogee Instruments Inc., Model IRTS-P, herein referred to as IRTc) located in the northeast corner of the model array (see Figures 3.4-3.6 for exact locations). These sensors are sensitive in the 6.5 to 14 µm waveband and are capable of measuring surface temperatures between -10°C to +55°C to within 0.3°C. The sensors were positioned to sample east-, west-, south-, and north-facing walls (two sensors per wall), one flat roof, one north-south oriented ‘road’, one east-west oriented ‘road’, and one ‘road’ intersection. Samples were taken every ten seconds and data stored as five-minute averages by a Campbell Scientific Inc. (CSI) Model CR10X datalogger which was interfaced with a CSI Model AM25T multiplexer. Further instrument specifications and post-field calibration methods are given in Appendix C. To position the sensors to measure wall temperature it was necessary to insert the body of the sensor inside a ‘building’ block looking outwards. To accomplish this 2.54 cm diameter holes were drilled through a concrete block face, the sensor placed inside with its FOV cone pointing orthogonally at the opposing wall surface (Figure 3.9a). The IRTc sensors to monitor horizontal surfaces were mounted in the downward-looking position on a tripod (Figure 3.9b). Care was taken to ensure the desired target surface was contained within the sensor FOV.  3.3.1.2 Measurements using the infrared camera Thermal images to supplement the surface temperature measurements from the IRTc array were captured by a FLIR Thermacam™ Model S-60 infrared camera positioned at various locations around the array perimeter throughout the experimental period. The camera detector is a 320 x 51  240 pixels focal plane array, uncooled microbolometer which is sensitive in the 7.5 to 13 µm waveband. It is capable of measuring surface temperatures between -40°C to +120°C with a  a)  b)  Figure 3.9 Installation of the Apogee IRTS-P infrared thermometers to measure surface temperatures of walls (a) and horizontal (roof, roads, and road intersections) surfaces (b). Location of individual sensors is identified with arrows.  sensitivity of 0.08°C at 30°C. The camera contains a 24° FOV lens with a spatial resolution of 1.3 mrad. A built-in detachable 4" color LCD screen displays the digital images captured by the system. The 16-bit thermal JPEG images are stored on a removable memory card and are 52  downloaded onto a PC for processing and analysis. IDRISI image processing software was used to extract individual facet surface temperatures from each image. IDRISI software is used to first draw polygons around the desired areas to be analyzed (see, for example, Figure 3.10). Every pixel is assigned a temperature value, so IDRISI is used to perform statistical analyses (average, standard deviation, maximum/minimum values) for each identified polygon.  Figure 3.10 Example of an infrared image used to assess surface temperatures of individual facet of the physical scale model. Here, the four roof surfaces for which average temperature and standard deviation are calculated with IDRISI image processing software are outlined in black.  The camera was mounted on a tripod at a height of 1.5 m. The system was placed at different positions around the array perimeter and the camera was tilted so as to point towards the ground at off-nadir angles. The viewing angle always allowed for multiple facet surfaces to be viewed in each thermal image. To protect the sensor from overexposure to the sun, the camera was encased in a removable styrofoam jacket (Figure 3.11). The camera was programmed to continuously capture thermal images every five minutes which corresponded to the data  53  averaging interval of the IRTc sensors. The camera was operated for sixteen observation periods (herein referred to as IRIOPs) and generated a total of 6116 images (Table 3.6).  Figure 3.11 FLIR infrared camera (with protective styrofoam cover) mounted on a tripod and positioned so as to include multiple surface facets within its FOV.  3.3.2 Radiation flux measurements Near-continuous observations of radiative fluxes were carried out from two instrument installations within the array. All four components of the net radiation budget (K↑, K↓, L↑, and L↓) were measured by a fixed radiometer located at the center of the array. Vertical profiles of  net radiation Q* and upwelling shortwave radiation K↑ were measured using two sets of sensors mounted orthogonally on an automated traversing system which was located adjacent to the central fixed radiometer.  3.3.2.1 Static radiation flux measurements A Kipp & Zonen Model CNR1 net radiometer was installed on an aluminum tripod mast (Campbell Scientific Inc. Model CM120) sited along the north-south axis of the array (Figures 3.4-3.6 and 3.12). The tripod was securely anchored to the roof grating approximately one meter 54  north of the center point of the array. When mounted on a crossarm, the slightly off-center location of the mast allowed the sensor head of the radiometer to be located directly above the ‘roof’ of the center ‘building’ of the array. The crossarm was mounted on the south face of the  Table 3.6 Duration and description of sampled facets corresponding to each of the sixteen periods for which an infrared camera was in operation (IRIOP).  λS IRIOP1  1.25  IRIOP2  1.25  IRIOP3  1.25  IRIOP4  1.25  IRIOP5  0.63  IRIOP6  0.63  IRIOP7  0.63  IRIOP8  0.42  IRIOP9  0.42  IRIOP10  0.42  IRIOP11  0.42  IRIOP12  0.42  IRIOP13  0.42  IRIOP14  0.42  IRIOP15  0.42  IRIOP16  0.42  Start YD 326; 1430 YD 329; 1525 YD 334; 1420 YD 336; 1140 YD 340; 1604 YD 345; 1530 YD346; 1645 YD 363; 0955 YD 364; 1715 YD 2; 0930 YD 3; 1750 YD 6; 0920 YD 6; 1700 YD 8; 1630 YD 9; 0910 YD 11; 1020  End YD328; 1045 YD331; 0900 YD 336; 1130 YD 337; 1035 YD 341; 0850 YD 346; 1530 YD 348; 1525 YD 364; 1705 YD 2; 0925 YD 3; 1735 YD 5; 0925 YD 6; 1650 YD 8; 1500 YD 9; 0855 YD 10; 1435 YD 12; 0935  Sampled Facets Flat roof, north- and west-facing walls Flat roof, north- and west-facing walls Flat roof Flat roof, north- and west-facing walls North- and east-facing wall, north-south and streets North- and west-facing walls, flat roof, flat white roof North- and west-facing wall, flat roof, flat black roof North- and east-facing wall, flat roof South- and west-facing wall, flat roof South- and west-facing walls, flat roof, east-west road, northand south-facing 30° pitched roofs North- and east-facing walls, flat roof, north-south road, eastand west-facing 17° and 30° pitched roofs North- and east-facing walls, flat roof, north-south road, eastand west-facing 17° and 30° pitched roofs North- and west-facing walls, flat roof, east-west road, northand south-facing 17° and 30° pitched roofs North- and west-facing walls, flat white roof, east-west road, north- and south-facing 17° and 30° pitched white roofs North- and west-facing walls, flat white roof, east-west road, north- and south-facing 17° and 30° pitched white roofs North- and west-facing walls, flat white roof, east-west road, north- and south-facing 17° and 30° pitched white roofs  mast (to avoid the shadow of the mast being cast across the sensor heads at any time). The CNR1 was exposed at a height of 1.61 m (Figure 3.12) and remained in that position for the duration of the experiment, as did the ‘building’ located directly below the sensor head. Given the horizontal 55  dimensions of the model and the sensor height, Equation 1.3 is used to derive view factors for each configuration. For the λS = 1.25 setup, 92% of the upwelling radiative fluxes measured by the CNR1 originate from within the array. For λS = 0.63, the view factor is 0.93 and for λS = 0.42  Figure 3.12 Kipp & Zonen CNR1 net radiometer (identified by the yellow arrow), mounted at a height of 1.61 m from a tripod at the center of the array.  it is 0.94. Details regarding the nature of these source areas are discussed in the following chapters. The CNR1 measures the upward and downward components of both shortwave and longwave radiation with four separate sensors mounted in a single instrument body. Solar radiation is measured by two CM3 pyranometers, one facing upward the other downward, and longwave radiation by two CG3 pyrgeometers similarly oriented (see Table 3.7 for sensor specifications). Measured values are used to compute net radiation Q* and albedo α. The sensor contains a heating resistor to prevent the accumulation of dew or frost on the receiver head but in the arid environment of the present site this feature was deemed unnecessary and not activated. A 56  Table 3.7 Sensor specifications of the radiation sensors used in the study.  Spectral range (µm) Response time (1/e, s) Accuracy (%) Sensitivity (mV W-1 m-2) Field-of-view  Kipp & Zonen NR-Lite 0.2 - 100 20 N/A  Kipp & Zonen CNR1 CM3 0.305 - 2.8 12 10% (daily sum)  Kipp & Zonen CNR1 CG3 5.0 - 50.0 12 10% (daily sum)  LI-COR LI-200X 0.4 - 1.1 .00001 5%  0.1  0.01-0.035  0.005-0.035  0.005  180°  180°  150°  160°  CSI Model 23X datalogger sampled sensor signals every five seconds and 60 s averages were stored in memory.  3.3.2.2 Dynamic radiation flux measurements Vertical profiles of Q* and K↑ extending from near the floor up through the urban canopy layer and into the urban boundary layer of the array were measured near the CNR1 (see Figures 3.43.6 for exact locations). The core of the installation was a custom-built 2.2-m high aluminum mast with a stepping motor at the top that controlled the vertical movement of a track to which the radiometer assembly was attached (Figure 3.13a). The stepping motor was in turn controlled by pulses, the pattern of which was programmed into a datalogger. Two 1-m crossarms oriented orthogonally extended from the mast, each supporting a Kipp & Zonen Model NR Lite net radiometer and a LI-COR Model LI-200X pyranometer (Figure 3.13b), (see Table 3.7 for sensor specifications). A vertical traverse began at a height of 12.5 cm above the ground (corresponding to 0.5zb where zb is the ‘building’ height). During a traverse the sensors measured Q* and K↑ at a sampling frequency of one second and 60-s averages were recorded. Once the reading at a given level was complete, the 23X datalogger sent 1114 pulses to the stepping motor, exciting a gear that moved the track 12.5 cm to the next measurement position. Travel time between positions was roughly 15 s. The instruments paused at the new location for 45 s without taking measurements for 45 s. Given the response time of the sensors (Table 3.7), this allowed the 57  a)  b)  Figure 3.13 The 2.2 m traversing mast (a) which continually moved two arms containing four radiation sensors (denoted by arrows; b) to twelve positions within and above the UCL.  58  radiometers sufficient time to adjust to the new FOV, before taking a measurement and proceeding to the next position. After conducting measurements at twelve positions (every 12.5 cm, up to 1.5 m), the instrument package descended to the starting position at 0.5zb. The entire cycle took approximately 32 minutes to complete.  3.3.3 Ancillary observations An area of 8.5 m (north-south axis) by 6.5 m (east-west axis) located near the eastern edge of the array, containing only the constructed styrofoam and painted sheathing surface cover was used for ancillary observations of net radiation and surface temperature in the absence of the concrete block structures (Figure 3.14a). A camera tripod located near the center of the area supported a Kipp & Zonen NR Lite net radiometer, an Apogee IRTc, and a Vaisala HMP35C temperature/relative humidity probe with radiation shield (Figure 3.14b). The net radiometer was mounted at a height of 0.84 m and 3 m from the nearest change in surface cover. This gave the instrument a view factor of approximately 0.93 (i.e., 93% of the measured upwelling radiative flux signal originated from the applied surface). The IRTc was placed just below the net radiometer, at a height of 0.61 m and 45° off nadir, such that the surface area viewed was an ellipse with a short axis of 0.7 m and a long axis of 1.2 m, centered in the region just beneath the radiometer sensor head.  3.4 Numerical methods Two numerical models are employed in this study. The surface-sensor-sun relations model (SUM) is used to assess the surfaces ‘seen’ in the FOVs of the radiometers and therefore serves as the basis for modeling radiative flux source areas. A parameterized form of a threedimensional backward Lagrangian footprint model (LPDM-B) calculates the peak location of the turbulent flux footprint and its streamwise dimension. 59  a)  b)  Figure 3.14 Area adjacent to the scale model array from which observations of surface temperature, net all-wave radiation and atmospheric temperature/relative humidity were conducted (a). The camera tripod supported a Kipp & Zonen NR Lite net radiometer, an Apogee IRTc, and a Vaisala HMP35C temperature/relative humidity probe with radiation shield (b).  3.4.1 Surface-sensor-sun Urban Model (SUM) The surface-sensor-sun relations model (SUM) of Soux (2000) and Soux et al. (2004) predicts the surface area ‘seen’ by a sensor of known FOV pointing in any direction when placed at any point in space above a specified urban surface structure. Per user-specified surface characteristics, the model first builds a three-dimensional simple surface array (spatial dimensions in an (x, y, and z) coordinate system). A fourth parameter describes each point’s physical nature (e.g. wall, roof, alley, street surface, thermal and radiative properties, etc.). 60  Model resolution (grid size) is determined by the distance between each point in the array and is adjustable. Constructing the array in sub-sections, SUM contains building-street-building-alley combinations in both the x- and y- directions and the pattern is repeated as many times as necessary to complete the specified array size. Once the surface array and sensor location and FOV are properly prescribed, the model uses a simple ray-tracing technique to determine first which surface elements are within in the FOV of the sensor and then, for the points that fit the criteria, whether or not each point is ‘seen’ or ‘unseen’ by the sensor. Solar position is either explicitly provided by the user or calculated by a model sub-routine and determines which cells on the surface are shaded or sunlit. All surface cells (sunlit and shaded) within the sensor FOV that are not blocked by another building contribute to the overall sensor-detected radiance. The contribution of each viewed cell to the overall FOV of the sensor is calculated using a contour integration approach based on Stokes theorem for a differential area (sensor) and a finite area (individual cell facets), such that the view factor from a differential area dEi to a finite patch Ej with n polygon edges is calculated from:  ψ dEi − Ej   1 n = ∑ β k ni • (rk × r(k +1) )  2π  k =1  (3.1)  where βk is the angle between the normalized vectors nk and r(k +1) is defined from dEi to each pair of vertices k and (k+1), and n i is the normal vector of the sensor dEi (Figure 3.15). The view factors are then summed and reported as totals of sunlit and shaded components of each facet of the urban surface (Voogt, 2008). These view factor calculations constitute the model’s primary output. Modeled view factors can be used in combination with known or modeled facet temperatures to calculate the average surface temperature of the system, as well as the anisotropy arising from surface-sensor-sun geometric combinations (Soux et al., 2004; Krayenhoff and Voogt, 2007; Voogt, 2008). 61  Figure 3.15 Geometry used to evaluate the view factor of a surface element. Here, a wall element is illustrated but the same form is extended to all surface elements. Source: Soux et al., 2004.  Soux et al. (2004) validated the model from both a geometric and radiation standpoint. In the theoretically-based geometric validation SUM was run to replicate a simple urban canyon structure with a hemispherical sensor positioned above the center of the canyon at building height. Model-calculated sky view factors were compared to Oke’s (1981) sky view factor calculations from a hypothetical canyon. SUM was found to perform extremely well, achieving sky view factors within 1% of published values. An image-based geometric validation was attempted by comparing photographs taken from a tower-mounted camera with model generated output of surfaces ‘seen’ and the associated view factor calculations. Uncertainties about the exact location of the sensor resulted in differences between model calculated view factors and view factors derived from the images. The authors point to the complexity of the chosen images and the wide margin of error for the modeled sensor location to explain the differences. Even so, the geometric validation demonstrates that SUM is able to model surface facet view factors reasonably well. 62  Soux et al.’s (2004) radiation validation used measured facet surface temperatures combined with modeled view factors to calculate an average temperature of the system, which was then compared to the surface temperature observed by a single narrow-FOV sensor mounted above the surface. This validation was carried out with measurements from a scale model and at the full scale, with varying results. SUM performed well against scale model results over a range of sensor locations and viewing angles. The model also performed well over a three-hour period when the position of the sensor remained fixed. The full scale radiation validation was subject to the same geometric uncertainties regarding sensor location as the image-based geometric validation and also required some adjustments to the model to account for the differences in signal response between the remote sensor and the model. The sensor-specific FOV modification resulted in good agreement between modeled and measured surface temperatures, although there was scatter in the data at the highest temperatures. This scatter was attributed to the greater range in facet temperatures at times when high temperatures exist, which means that errors associated in estimating surface facet view factors are exacerbated under conditions of greater facet temperature variability. Another reason given for the scatter at the highest temperatures is related to plumes of warm air bubbling up from the hot roof surfaces, temporarily cooling those surfaces. Such fluctuations were averaged out of the measured roof temperatures (5-min means) but were captured in the 20-s reading by the tower-mounted sensor. SUM was further tested following modification to the model to include a coupling with the actual building structure of a study area using Geographic Information System (GIS) data (Voogt and Soux, 2003; Voogt, 2008). Using the same methodology of the radiation validation discussed above, model simulations were compared with airborne observations of surface temperature over a light industrial area and downtown area of Vancouver, B.C. The additional surface information such as variable building heights and shapes afforded by the GIS formulation improved the model’s ability to capture the spatial variability related to the thermal 63  anisotropy compared to the use of SUM’s regular internal surface structure. Voogt (2008) cautions that the application of SUM is limited by the need for detailed observations of facet surface temperatures. For the Phoenix scale model study, SUM was run with the GIS modification. Every cell in the GIS input file was assigned a surface parameter identifying it as a roof, street, intersection or wall surface (Figure 3.16) and the distance between each cell is equal to two centimeters in the real world. In this experiment alleys were equivalent to street surfaces. Primary geometric input  Wall N-S Street E-W Street Roof Intersection  Figure 3.16 Example of the GIS input file used to represent the surface geometry of the scale model arrays. The λS = 0.42 array is shown here. Each pixel is assigned a facet type and the dimensions and spacing are prescribed according to values given in Table 3.8.  64  parameters used to construct the GIS files to simulate the scale model surface are given in Table 3.8. View factor calculations were constrained by SUM’s inability to calculate hemispherical FOVs at sensor positions above roof-level, so SUM instead calculated the view factors of surfaces ‘seen’ by the three near-hemispherical down-facing radiation sensors used in the study: the 150° pyrgeometer sensor of the CNR1 located at a fixed height of 161 cm at the center of the scale model array and the two 160° LI-COR pyranometers attached to the traversing system. The twelve radiometer heights for both orthogonal sensors were modeled (see Figure 3.4 – 3.6 for the exact x-y locations of the sensors). Modeled view factors are combined with observed facet surface temperatures for analysis of upwelling longwave radiation from the system.  Table 3.8 Basic surface geometric input parameters used to run SUM for each scale model configuration. Input Parameter  Units  λS = 1.25  λS = 0.63  λS = 0.42  Surface azimuth Surface slope Street orientation Building width Building length Building height Street width Alley width Total array length Total array width  degrees degrees degrees cm cm cm cm cm cm cm  0 0 0 20 20 13 10 10 660 660  0 0 0 20 20 13 20 20 720 720  0 0 0 20 20 13 30 30 720 720  3.4.2 Simple parameterization scheme for turbulent flux footprints Kljun et al. (2002) introduced the Lagrangian Particle Dispersion Model-Backward (LPDM-B) to address some shortcomings in other turbulent flux source area models in use (i.e., inapplicability outside the surface layer, high CPU time, etc.; see Chapter One for an overview). The model is based on the three-dimensional Lagrangian stochastic particle Puff-Particle Model 65  developed by de Haan and Rotach (1998), which itself evolved from a two-dimensional version by Rotach et al. (1996). Unlike most Lagrangian particle dispersion models that fulfill the wellmixed condition for only one given stability regime, the LPDM-B satisfies the well-mixed condition for stable to convective conditions. It is also valid for measurement points within and above the surface layer. The LPDM-B tracks particle trajectories that are initiated at the measurement point to any potential surface source, whereas conventional forward trajectory models release particles at the surface source(s) and track their trajectories until they have passed the measurement location. Although the backward approach is specific to a given measurement location, sources with varying geometries and locations can be considered with a single simulation. The backward modeling approach allows for inhomogeneity of the flow, since all the calculated trajectories contribute to the footprint estimate. Forward trajectory models, on the other hand, resolve spatially inhomogeneous flow by using multiple simulations to model a large number of sources, which consumes a proportional amount of computational time (Flesch et al., 1995). The model requires input of the distribution of turbulence statistics and uses a stochastic differential equation (a generalized Lengevin equation) to describe the diffusion of a Lagrangian particle released from a fixed position and at a given velocity. An ensemble of such particle trajectories is initiated with random velocities from the receptor location. For each particle, the release velocity and touchdown locations and velocities are stored and used in the footprint estimation following Flesch et al. (1995). Footprints have traditionally been estimated by overlaying the upwind area with a grid and summing the particle touchdowns within each grid cell. This method has the disadvantage of relying on the selected grid spacing and the number of particles released in the simulation. Alternatively, LPDM-B uses the density kernel method after de Haan (1999). This statistical treatment treats the values of the touchdowns as data points each with an attached distribution (kernel function). The distributions are then summed for any point 66  in space. This method requires fewer simulated particles than the traditional grid method, thereby reducing CPU time. While suitable experimental data are required to determine if flux footprint models provide correct predictions, the constraints that are given by the model assumptions (e.g., restriction to the surface layer, horizontal homogeneity, and stationary turbulence) imply a lack of reliable full-scale observations with which to evaluate such models. Wind tunnel experiments, however, are able to fulfill the requirements for stationary turbulence and homogenous surfaces. LPDM-B was evaluated using data from SF6 tracer release experiments in a wind tunnel with a sheared convective boundary layer (Kljun et al., 2004) and was found to reproduce the observed peak location and shape of the concentration footprint estimates for various sampling heights. In the absence of additional experimental data, LPDM-B has also been tested against results of other flux and concentration footprints. Kljun et al. (2002) compared footprint functions from LPMD-B with those from Schmid’s (1994, 1997) analytical SAM/FSAM model, which itself has been tested against experimental data of trace gas fluxes by Finn et al. (1996). Theoretical restrictions of SAM/FSAM constrained the comparison to forced convection and neutral stability within the surface layer. In conditions where SAM/FSAM is valid, the comparison between LPDM and SAM/FSAM is satisfactory, although non-negligible differences in the location of the peak flux footprint under neutral conditions were found. These differences are attributed to limitations in the analytical model, which the authors deem as “too restrictive for real situations”. LPDM-B was also compared with flux footprint estimates from a Lagrangian forward footprint model (Rannik et al., 2000) for neutral stratification, with excellent agreement between the two models both in terms of the peak location and shape of the footprint functions. Excellent correspondence was also found in comparing LPDM-B with Kormann and Meixner’s (2001) analytical model for different measurement heights and unstable to neutral conditions within the surface layer (Kljun et al., 2003). 67  To facilitate more accessible flux footprint estimates, Kljun et al. (2004) introduced a simple parameterization based on the original LPDM-B formulation. The advantage to Kljun’s parameterized approach over previous simple parameterizations (e.g., Horst and Weil (1992, 1994); Schmid (1994); Hsieh et al. (2000)) is that it is not limited to a particular turbulence scaling domain or range of stratifications. Kljun et al. (2004) applied a scaling procedure based on a few variables easily derived from turbulence measurements: along wind distance from the receptor (x) standard deviation of vertical velocity fluctuation (σw) surface friction velocity ( u* ) measurement height (zm) roughness length (z0) height of the planetary boundary layer (h) and crosswind integrated flux footprint function ( f y ). These variables are chosen as the basis for the scaling procedure because they explicitly consider the stability regime, surface properties, and advective and thermal/mechanical transport processes on which footprint size and shape depends. Combining these values into four dimensionless combinations, a non-dimensional form of the crosswind integrated footprint function, F* , as a function of a non-dimensional alongwind distance, X * , is derived:  σ X * =  w  u*  α2      α1  x zm  (3.2)  −1  σ   z  F* =  w  1 − m  z m f h   u*    y  (3.3)  where α1 and α2 are optimization parameters. The scaling procedure is tested against footprint estimates derived from the LPDM-B model for a broad range of stabilities and receptor heights from close to the ground to far into the boundary layer. The peak location and extent of the scaled footprints agree with LPDM-B simulations. When plotted in a dimensionless framework ( F* vs. X * ) for a given surface roughness, the footprint estimates collapse into an ensemble of 68  similar curves. Furthermore, a linear relation between dimensionless groups was found when α1 = -α2 = 0.8. A single non-dimensional master footprint function describing the ensemble of scaled footprint estimates within one roughness regime is derived: b  ^    ^   X + d X   *   * + d  F* = a expb1 −  c   c         ^  ^  (3.4)  ^  where F* ( X * ) is the parameterization of F* ( X * ) and a, b, c, and d are fitting parameters that ^  ^  depend on the roughness length. This parameterization is confined by X * ,max = c - d and F* , max = ^  ^  a where X * ,max is the peak location and F* , max is the peak value of the parameterization. A stepwise regression method was used to find the fitting parameters a, b, c, and d. The ^  dependence of X * ,max on roughness length as an analogy to Horst and Weil’s (1992) surface ^  model is derived: X *  ,max  ≈ Ax(B-lnz0). The peak location of the footprint in a dimensional  framework can be found:  x max  σ ≈ Ax (B − ln z 0 )z m  w  u*      −0.8  (3.5)  where Ax, and B are fitted model parameters set to 2.59 and 3.42, respectively (Kljun et al., 2004). When given R (percentage of the footprint included within a certain distance from the measurement point, 0-90%), the streamwise dimension of the footprint estimate, xR, can also be calculated. The applicability of Equation 3.5 is restricted to the following conditions: -200 ≤ zm /L ≤ 1, u* ≥ 0.2 m/s, zm > 1 m, and zm < h. Long- and short-term flux studies are regularly subject to different atmospheric conditions which require a large number of CPU-intensive calculations. The advantage to Kljun et al.’s parameterized scheme is that it allows for a quick but precise assessment of the maximum  69  influence location for the measurement and the streamwise dimension of the footprint (Barcza et al., 2009). It does not, however, generate a two-dimensional rendering of the flux footprint, such as those produced by more traditional footprint modeling methods. However, the ability to ensure that the location of maximum influence and the streamwise dimension of the footprint are contained within the radiative flux footprint is of primary importance in the current context.  3.5 Assessment of experimental set-up Unavoidable in any field study are uncertainties and unintended experimental errors that must be considered when interpreting results. A discussion of such issues is presented here. The ability of the physical scale model to generate replicable results is discussed. Then, two primary causes for uncertainty related to the experimental set-up are identified: those arising from the placement of sensors and those stemming from systematic bias between sensor types.  3.5.1 Replicability of the model Surface temperature measurements of individual facets are limited to the IRTc array and those facets which are fully contained in the instantaneous FOV of the infrared camera. A single facet temperature measurement is assumed to characterize the surface temperature of all such facet types (i.e. the measured surface temperature from a south-facing wall is extended to represent the all south-facing walls in the scale model). To test this assumption, infrared imagery from the site is analyzed to: 1) test the variability within construction materials and 2) assess the overall construction of the site. For the first objective, thermal images from the two most open scale model geometries were selected. Each image contained three or more of the same facet type, for which average facet temperature and standard deviation were calculated using FLIR ThermaCam Researcher software (top portion of Table 3.9). Images captured around solar noon of fully sunlit south walls 70  and flat roofs are used (see, for example, Figure 3.10), as it is assumed that any differences in the material response to solar forcing would be highlighted at the time of greatest insolation. The analysis could not be extended to the street and intersection surfaces, as at no time were multiple examples of these facets contained in the camera FOV. The average temperature and standard deviation of each analyzed facet, along with the small overall range of values amongst a group of facet types, demonstrates the consistency of the scale model materials. The consistency of the material response to solar forcing implies that a single surface facet temperature from a particular facet type can be extended to represent all such facet types across the scale model array.  Table 3.9 Summary of facet temperature analysis to assess the replicability of the scale model. The average temperature of individual facets (with the standard deviation of each measurement in parentheses) selected for analysis, along with the overall range of values demonstrates the consistency of the scale model materials and construction. Time (LAT)  Facet Type  λS  Ts (1)  Ts (2)  Ts (3)  Ts (4)  Ts (5)  Overall Range  1200 1200 1200 1150 1200  Flat roof South wall Flat roof White flat roof Black flat roof  0.42 0.42 0.42 0.63 0.63  20.6(2.1) 37.4(2.1) 24.1(3.1) 18.4(3.2) 30.2(2.0)  19.6(2.1) 36.9(2.0) 23.8(3.5) 17.0(2.4) 30.1(2.0)  20.1(1.8) 36.7(1.9) 24.1(3.1) 18.1(2.1) 29.8(1.5)  19.6(1.2) 36.6(1.8) 23.7(3.6)  36.4(2.0)  30.5(1.5)  30.7(2.0)  1.0 1.0 0.4 1.4 0.9  1500 1445 1010  West wall Flat roof Flat roof  1.25 1.25 1.25  39.9(2.9) 28.0(2.8) 15.1(2.0)  39.4(3.0) 28.7(2.7) 15.5(1.8)  27.4(2.5) 15.6(1.7)  28.2(2.5) 15.5(1.9)  29.0(2.8) 15.6(1.8)  0.5 1.6 0.5  To determine if the scale model was constructed in a reasonably repeated fashion such that each ‘building’ displays similar patterns of irradiance amongst its facets, images in which facets contain non-uniform thermal patterns are selected for analysis (bottom portion of Table 3.9). Images from the morning and afternoon periods, when the selected roof and wall facets show a high degree of temperature variability within each facet, are used. Results indicate that even when each facet is subjected to variable insolation (mixed sunlit and shaded pattern on a single facet), the overall patterns between facet types are similar.  71  3.5.2 Placement of sensors Effort was made to position the IRTc sensors so that a large proportion of the intended facet was within the sensor FOV. Too small a projected FOV would not provide a reasonable estimate of average facet temperature, particularly at times when a single facet is subjected to a mixed sunlit/shaded pattern. A fixed sensor FOV and variable canyon aspect ratio through the experiment means that there is a compromise in terms of the relative size of the instantaneous FOV versus the facet area. An inevitable consequence of this approach is that in some cases, the intended target facet did not solely populate the IRTc FOV. This is especially the case the farther the sensor was sited from the target surface. The dimensions and orientation of the projected FOV are calculable if the sensor FOV and height and angle at which the sensor is mounted relative to the target are known (see Appendix A). Because the exact configuration of each IRTc sensor is not known, examination of the data reveals potential issues. A projected FOV extending beyond the intended target incorporates two possible elements: other surface facets or a portion of the sky. The problem of ‘seeing’ sky is confined to sensors intended to measure wall temperature, as all horizontal facets are measured with downpointing sensors that are incapable of detecting the sky. An IRTc ‘seeing’ a portion of the sky can be identified by examining the time series of wall surface temperatures. In the late evening/early morning hours, all wall surfaces should cool to nearly the same temperature (within 0.2 °C of one another; see results in Chapter Four). A sensor with a FOV that is partially occupied by sky, however, will register a consistently cooler temperature bias (by 2-3 °C) relative to the other wall surfaces at this time. In this case the sensor signal (Lsensor) is assumed to be a linear combination of the signal from the target of interest and the signal from the sky: Lsensor = Fwall Lwall ∗ Fsky Lsky  (3.6)  where L is the radiance/radiation from the wall or sky and F is the fractional component of the wall or sky. Lsensor is the measured problematic value, Fwall is (1-Fsky), Lwall is the average 72  radiance from the three ‘correct’ walls (the target of interest), Fsky is approximated, and Lsky is calculated (see below). Given that Lsky and Lwall are known values, Fsky and Fwall can then be adjusted so as to match the measured Lsensor. Once a match is achieved, that portion of the signal derived from the much cooler sky is eliminated and a signal containing just the intended target can be restored. For this data set, one IRTc sensor in each scale model configuration was determined to be ‘seeing’ sky. The correction first requires an estimate of sky conditions, for which Idso’s (1981) expression relating atmospheric emissivity in the 8-14 µm waveband to the zenith sky is used:  ε 8−14 = 0.24 + 2.98 × 10 −8 eo 2 exp(3000 / To )  (3.7)  where eo is vapor pressure and To is screen-level air temperature. This expression alone is not suitable for use in the present context, as the sensors were not pointed towards zenith. Equation 3.7 is combined with Unsworth and Monteith’s (1975) equation relating the variation of atmospheric emissivity with zenith angle Z:  ε (Z ) = ε 8−14 + b ln(sec Z )  (3.8)  where b is the slope of the ε(Z) vs. ln(secZ) line. Zenith angle Z is estimated to be 57°, based on sensor-building geometry and site photos. The slope b is estimated from the literature to be 0.09. Once emissivity for the portion of the sky the IRTc’s are ‘seeing’ is known, longwave radiation from the sky (Lsky) in the 8-14 µm waveband is calculated using measured air temperature and the Stefan-Boltzmann equation with narrow-band coefficients: Lsky = 1.25 × 10 −9 (To + 273.15)  4.49  (3.9)  To remove the sky portion from the measured signal requires knowledge of the sky view factor (Fsky). This is estimated by determining the combination of Lsky and Lwall (where Lwall is the average temperature of the three walls that are isothermal at night) that matches the time series from the problematic sensor. Once a reasonable Fsky is decided upon (here, Fsky was found to be 73  approximately 0.035), the data are corrected by subtracting 0.035Lsky from the original signal and dividing by Fwall to get the corrected Lwall. A less straightforward consequence of imprecise IRTc siting, which is extremely difficult to fully account for, is the case when a projected FOV includes other, unintended, facets. For example, an IRTc directed at a flat roof may also measure a portion of the ground surfaces, a road-facing sensor could pick up some wall surface. Unlike the case of an IRTc ‘seeing’ the much cooler sky, isolating a sensor that partially views another facet(s) is nearly impossible. The time series of temperature for different components of the surface have complex temporal patterns that are not easily estimated, which complicates the correction procedure relative to that used for the mixed sky and wall case. Comparing IRTc data to average facet temperatures from the infrared camera may provide a first-order estimate for determining problematic sensors. This method is restricted, however, in that the camera can not be positioned so as to fully view all facets at the same time. For all times the camera contained an unobstructed view of a particular facet(s), the data are compared with IRTc readings in Table 3.10. There is generally good agreement between camera and IRTc values but as expected, correlation drops off slightly as spacing between the IRTc sensor and the viewed facet increases. Evidence of this experimental error is also seen when using the IRTc data set to perform a radiation validation of SUM. The model is run for a 150° downward-looking sensor for each scale model configuration to generate view factors of all facet categories. The view factors are then combined with measured facet surface temperatures to calculate an average modeled temperature of the system for a 24-hour period (5-min. average values). Modeled values are compared with the surface temperature detected by the 150° CNRI pyrgeometer (Figure 3.17). It is assumed that any differences in surface emissivity between the thermal infrared waveband (measured by the IRTc) and the longer wavelengths measured by the CNR1 pyrgeometer (see Table 3.7) are negligible, so that all temperatures are reported as brightness temperature. 74  Table 3.10 Comparison of facet surface temperature measured with the IR camera and the IRTc array. Data includes only those facets that are completely viewed by the camera. n is the number of data points used in each comparison. Facet sampled λS = 1.25 IRIOP1 IRIOP2 IRIOP3 IRIOP4 λS = 0.63 IRIOP5 IRIOP6 IRIOP7 λS =0.42 IRIOP8  IRIOP9  IRIOP10  IRIOP11  IRIOP12  IRIOP13  IRIOP14  IRIOP15  IRIOP16  Number of facets  n  Slope  Intercept  R2  0.9672 0.9701 1.0934 1.0229 1.0353 1.1016  -1.0241 0.7206 -1.0322 -1.6959 -2.2901 -0.4393  0.9538 0.9721 0.9937 0.998 0.9979 0.9962  0.9667 1.0617 0.9000 1.0064  0.0829 1.5924 -1.3436 -1.0713  0.9687 0.9895 0.9629 0.9852  1.2049 1.1048 0.9795 1.1044 1.1948 1.3958 0.8560 1.1049 0.9006 1.2054 0.9690 0.9459 1.1048 0.9593 0.9286 1.1048 1.1958 0.7362 0.9579 1.0594 1.1984 0.6976 1.2950 0.9694 0.9485 1.2948 0.9750  0.9238 1.4424 -1.7967 1.8821 0.9703 2.0036 -0.7842 0.9682 -1.1043 1.1795 -0.4689 1.4239 -2.1208 1.1048 -1.1423 0.6895 -0.9578 1.3539 1.7650 0.7890 -1.9674 1.4332 0.5859 0.8694 -1.5743 -0.6968 1.0843  0.9586 0.9622 0.9907 0.9621 0.9900 0.9279 0.9684 0.9888 0.9741 0.9224 0.9806 0.9705 0.8964 0.8011 0.9375 0.9759 0.9498 0.9330 0.9005 0.9836 0.9307 0.9653 0.9490 0.9877 0.9254 0.9697 0.9608  Flat roof West-facing wall West-facing wall Flat roof Flat roof West-facing wall  Two Two One Two Three Two  532  East-facing wall North-facing wall Flat white roof Flat black roof  Two One Six Six  202  East-facing wall North-facing wall Flat roof Flat roof South-facing wall West-facing wall Flat roof South-facing wall East-west road East-facing wall North-south road Flat roof East-facing wall Flat roof North-south road Flat roof North-facing wall East-west road Flat white roof North-facing wall East-west road Flat white roof North-facing wall East-west road Flat white roof North-facing wall East-west road  Six Four Five Four Five Three Three Three One Four One Four Three Six One Two One One Two One One One One One One One One  500 272 276  289 561 375  771  386  476  91  532  198  354  280  75  35  MAE = 0.6 °C RMSE = 0.8 °C R2 = 0.99 D = 0.99  Measured Them (°C)  30 25 20 15 10 5 0  λS = 1.25  -5 -5  0  5  10  15  20  25  30  35  Modeled Them (°C)  35  MAE = 0.8 °C RMSE = 0.9 °C R2 = 0.99 D = 0.99  Measured Them (°C)  30 25 20 15 10 5 0  λS = 0.63  -5 -5  0  5  10  15  20  25  30  35  Modeled Them (°C)  35  MAE = 1.2 °C RMSE = 1.1 °C R2 = 0.99 D = 0.99  Measured Them (°C)  30 25 20 15 10 5 0  λS = 0.42  -5 -5  0  5  10  15  20  25  30  35  Modeled Them (°C)  Figure 3.17 Comparison of modeled (using SUM) and measured near-hemispherical (150° FOV) surface temperature (Them) for each scale model configuration. Statistics of model performance (mean average error (MAE), root mean-square error (RMSE), goodness-of-fit (R2) and Willmott’s index of agreement (D) are included and 1:1 agreement is indicated by the dashed line.  76  The model performance statistics indicate excellent overall agreement between measured and modeled values, with very little scatter in the data. The slight hysteresis pattern in all three configurations suggests a systematic bias in the measured temperatures or error in SUM’s geometric formulation. Unlike the geometric uncertainties contained in the validation exercises carried out by Soux et al. (2004) and Voogt (2008), the current study involves a known and simplified urban surface arrangement that is prescribed with a customized GIS input file, allowing for near certainty in performing a radiation validation. Therefore, issues relating to SUM’s internal formulation are ruled out. Given the aforementioned uncertainties in the IRTc measurements, this is presumed to be the cause of the hysteresis. Insight into the minor hysteresis pattern is perhaps gained by examining the time series of the reported temperature differences (measured minus modeled; Figure 3.18). Each scale model set-up has a unique pattern in the bias. Analysis from adjacent days with similar atmospheric conditions shows the respective patterns are repeated (not shown). Together these observations imply no consistent or systematic source of error spanning the three scale model configurations and a lack of physical basis for the observed biases in Figure 3.18. Attempts to replicate the bias pattern by assuming a radiometer tilt in modeling view factors were unsuccessful (not shown), further supporting the notion that the source of error is a sampling issue embedded in the facet temperature data. Isolating the source of error for each time period was attempted by comparing facet temperatures from IR camera imagery to IRTc temperatures. Because the IR camera could not completely view all facets at one time, the comparison was extremely limited in its power. The fact that no one sensor could be the cause of error further complicates matters. Given that the diurnal temperature time series of individual facets display reasonable patterns of behavior (see Chapter Four) it is assumed that the majority (greater than 80%) of the  77  Them - Tmod (°C)  2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 336  λS = 1.25 336.25  336.5  336.75  337  Them - Tmod (°C)  Time (LAT)  2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 342  λS = 0.63 342.25  342.5  342.75  343  Them - Tmod (°C)  Time (LAT) 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 364  λS = 0.42 364.25  364.5  364.75  365  Time (LAT)  Figure 3.18 Comparison of measured near-hemispherical surface temperature (Them) with modeled values (Tmod). Data are five-minute averages.  projected FOV of each IRTc contained the intended surface. Further, it is relevant to note that interest here lies not in the absolute values of facet surface temperature, but the relative differences between them.  3.5.3 Sensor intercomparisons Section 3.5.1 discusses issues related to facet brightness surface temperature measured with the infrared camera and infrared radiation thermocouples and concludes that while there are some 78  differences in the signals, such differences are most likely attributed to measurement errors related to FOV uncertainty and therefore confined to specific sensors. Instrument biases are assumed to not be a significant error source in the surface temperature data set. Furthermore, Appendix C describes the calibration procedure and subsequent data corrections performed for the IRTc sensors. A brief side-by-side intercomparison involving the radiometers from the experiment was performed at the site, following removal of the concrete elements from the study area. The NRLITE radiometers (with attached LI-200X pyranometer sensors) were mounted alongside the CNRI at a height of 1.3 m, at the center of a 12 m x 14 m area of painted fiberboard surface (Figure 3.19). The surface was not perfectly flat or uniform in color, as the edges of the  Figure 3.19 Side-by-side field intercomparison of the radiometers used in the scale model study.  79  fiberboard panels curled slightly in the absence of the concrete blocks. It is assumed that this surface heterogeneity does not significantly contribute to differences in measured net radiation. The comparison was run for one complete day under cloudless sky conditions at a sampling frequency of five seconds. One-minute averages were recorded for analysis (Figure 3.20). There is generally excellent agreement between the NRLITE sensors, with measured Q* differences of within 2 W m-2 at night and 5 W m-2 during the day (R2 = 0.9985 and slope = 1.0031 for all times). The LI200X pyranometers compare well, measuring within 2 W m-2 of one another at all times during the day (R2 = 0.9996 and slope = 0.9996; not shown). Relative to the LI200X pyranometers, upwelling shortwave radiation measured by the CNR1 is underestimated during the day, from 2% at solar noon to 10% in the mid-afternoon. Q* measured by the CNR1 radiometer, although capturing the same overall features detected by the NRLITE sensors, 300  East-West NRLITE 250  North-South NRLITE  -2  Net Radiation, Q* (W m )  CNR1 200 150 100 50 0 -50 -100 379.6  379.8  380  380.2  380.4  380.6  Time (Local, 60-s)  Figure 3.20 Time series of Q* observed during the radiometer intercomparison study undertaken immediately following the scale model experiment.  contains an offset (not shown). Relative to the NRLITE sensors, the CNR1 overestimates Q* during the day and underestimates Q* at night (Figure 3.20). The nighttime underestimation is fairly consistent throughout that period, at 10 - 15 W m-2. The relative overestimation of Q* 80  around solar noon has a greater range, typically between 20 - 40 W m-2. Both sensors have unique spectral properties (see Table 3.7), and in the absence of shortwave radiation, the observed bias is likely to be related to differences in the longwave radiation sensors. An additional intercomparison study of the NRLITE net radiometers and the down-facing LI200X pyranometers was performed over a two-week period of mixed sky conditions over a flat expansive surface of short grass. The results were consistent with the intercomparison performed at the scale model site. Both sensor types exhibited excellent agreement during clear sky conditions, with the pyranometers consistently within 2 W m-2 (R2 = 0.999 and slope = 0.9995) of one another and the NRLITE sensors measuring within 5 W m-2 during the day and 2 W m-2 at night (R2 = .9998 and slope = 0.9947 for all times) (not shown). The excellent overall agreement of the sensors mounted on the traversing mast is encouraging and necessary, since the profile measurements of radiative fluxes form the bulk of the analysis of the spatial variability of radiative fluxes that is presented in Chapter Four. The 2 W m-2 difference between the pyranometer sensors in the traversing system amounts to less than 1% of the maximum reflected shortwave radiation. The 5 W m-2 difference in daytime Q* measured by the traversing net radiometers amounts to approximately 2.5% of the net all-wave radiation measured by each sensor. It is therefore determined that for the purposes of assessing radiation fluxes from the traversing mast, for which data from the CNR1 are not required, no correction to the sensors’ signals is needed.  81  Chapter 4  SCALE MODEL RESULTS: SURFACE TEMPERATURE SURVEY  This chapter along with Chapter Five addresses the first of the four objectives laid out in the first chapter, that is, to design, construct, and test an outdoor scale model of a simplified urban form to model three-dimensional surface temperature patterns and radiation flux source areas at the local scale. Details of the design, construction, instrumentation approach, data correction techniques, and implications of the experimental set-up are provided in previous chapters and appendices and are referred to where appropriate. This chapter specifically focuses on the objective to physically model three-dimensional surface temperature patterns and includes a discussion on the utility of scale modeling as a viable technique for such a study. Measured facet surface temperatures are used to illustrate the urban surface temperature when using different conceptualizations of the urban surface. Facet temperatures are also combined with modeled surface view factors to demonstrate the directional variation (anisotropy) of urban surface temperature measurements.  4.1 Observed facet surface temperature For each of the three array configurations described earlier in Chapter Three, observations from one diurnal period characterized by cloudless skies, are selected for analysis (Figures 4.1 and 4.2). Each analysis period occurs at least three days following rearrangement of the scale model into each of its progressively larger building spacing versions. This delay ensures that surface components have sufficient time to adjust to the change in radiative and turbulent exposure. The terminology describing individual facet orientation is as follows: walls are referred to by the compass direction in which they face (e.g., “south walls” are located on the south side of a 82  Apparent Temperature (°C)  45 S Wall N Wall E Wall W Wall Air  35 25  λS = 1.25  15 5 -5 0  b)  2  4  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  Apparent Temperature (°C)  45 S Wall N Wall E Wall W Wall Air  35 25  λS = 0.63  15 5 -5 0  c)  2  4  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  Apparent Temperature (°C)  45 S Wall N Wall E Wall W Wall Air  35 25  λS = 0.42  15 5 -5 0  2  4  6  8  10  12 14 Time (LAT)  16  18  20  22  24  Figure 4.1 Diurnal variation of the surface temperature of individual vertical facets for the three scale model configurations. λS = 1.25 is shown in panel (a), λS = 0.63 is shown in panel (b) and λS = 0.42 is shown in panel (c). Data are five-minute averages.  building and are therefore south-facing) and street/canyon surfaces are described by their alongstreet direction (e.g., “north-south streets” run in the north-south direction and therefore along the east/west edges of buildings). In each array configuration, the overall thermal behavior of each facet follows a predictable pattern corresponding to the angle, timing, and duration of solar exposure. The south 83  45 Apparent Temperature (°C)  a)  Roof N-S street E-W street Intersection Air  35 25  λS = 1.25  15 5 -5 0  2  4  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  45 Apparent Temperature (°C)  b)  Roof N-S street E-W street Intersection Air  35 25  λS = 0.63  15 5 -5 0  2  4  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  45 Apparent Temperature (°C)  c)  Roof N-S street E-W street Intersection Air  35  25  λS = 0.42  15 5 -5 0  2  4  6  8  10  12 14 Time (LAT)  16  18  20  22  24  Figure 4.2 Diurnal variation of the surface temperature of individual horizontal facets for the three scale model configurations. λS = 1.25 is shown in panel (a), λS = 0.63 is shown in panel (b) and λS = 0.42 is shown in panel (c). Data are five-minute averages.  and east wall surfaces initiate their morning warming patterns at sunrise and nearly overlap with one another through most of the morning (Figure 4.1). South walls continue to be fully irradiated and warm for two hours after solar noon and achieve the greatest daytime temperature of any wall surface. North walls are the coolest of the four vertical facets, never receiving direct insolation at any time. The temperature of east walls peak earliest in the day, just prior to solar 84  noon, and approximately three hours before the west walls reach their maximum daily temperature. Approximately two hours after sunset all wall surfaces cool to within 0.3 °C of one another and continue to cool throughout the night at the same rate, but not achieving the same absolute temperature, as the air. These patterns are best displayed in the case of the most open configuration (λS = 0.42; Figure 4.1c) where solar access is greatest. North-south streets and intersections follow a warming and cooling pattern similar to each other, quickly achieving their peak values when fully exposed to the sun around solar noon (Figure 4.2). Given the relatively low wintertime solar angle (30° – 36° above the horizon at solar noon), east-west streets remain largely shaded and thus do not demonstrate as large a diurnal temperature range as the other street components. Contrary to the thermal behavior commonly observed in most real-world urban settings, even under full solar exposure, roof surfaces remain cooler than fully-exposed street surfaces. The 2.5 cm solid concrete capping slabs simulating roof surfaces have much larger thermal mass than the same thickness of the combined polystyrene-fiberboard sheeting used to simulate ground surfaces. The ground surface, therefore, has a more robust thermal response to solar heating, causing a relatively sharp rise and fall of its surface temperature near midday. Similarly, at night, whilst small-scale temporal variations in air temperature are reflected by similar fluctuations in the street surface temperature patterns, the greater lag in thermal response of the roof surfaces prevents them from registering any small-scale (less than 15 minute) variations in thermal forcing. Surface thermal patterns corresponding to roof treatments (color and roof angle) are shown in Figures 4.3 – 4.5. Surface temperatures of treated roof facets are compared to those with an untreated flat roof surface. Flat white roof surfaces in the λS = 0.63 case remain cooler than their untreated counterpart through the daytime (Figure 4.3a). At peak insolation the absolute difference in temperature between the roof types is nearly 10°C. This is directly due to the increase in the overall albedo of the array from 0.19 with untreated roofs, to 0.29 with the 85  45  35 30  40 Apparent Temperature (°C)  Apparent Temperature (°C)  45  White roof N-S street E-W street Intersection Air Untreated roof  40  25 20 15 10 5  a)  0 -5 345.5  45  346 346.25 Time (LAT)  346.5  30  15 10 5  40  20 15 10 5  c)  0 345.75  20  45  25  -5 345.5  25  -5 347  Apparent Temperature (°C)  35  30  346 346.25 Time (LAT)  346.5  346.75  b)  0  346.75  S Wall N Wall E Wall W Wall Air  40 Apparent Temperature (°C)  345.75  35  Black roof N-S street E-W street Intersection Air Untreated roof  35 30  347.25  347.5 Time (LAT)  347.75  348  S Wall N Wall E Wall W Wall Air  25 20 15 10 5  d)  0 -5 347  347.25  347.5 Time (LAT)  347.75  348  Figure 4.3 Diurnal variation of the surface temperature of individual horizontal surfaces with white roof (a) and black roof (b) treatments and with their corresponding vertical surfaces (c) and (d) for the λS = 0.63 scale model configuration. Data are five-minute averages.  white roof treatment. At night both the white and untreated roof types cool to within 0.1 degrees of one another. Black flat roofs in the λS = 0.63 configuration decrease the overall albedo of the array, from 0.19 to 0.15. At their peak temperature, the black roofs are approximately 4°C warmer than the untreated case (Figure 4.3b). As is the case with white roofs, the black roofs cool throughout the late afternoon and evening to approximately the same temperature as the untreated roof. The thermal patterns of unpainted, solid concrete, double-sloped roofs with 17°- and 30°pitch angles in the λS = 0.42 configuration show predictable patterns of diurnal warming and cooling (Figures 4.4 and 4.5). The east-facing roof facets closely resemble the warming pattern of the east-facing walls, with their morning temperature ascent initializing before the west-facing 86  a)  40  Flat roof N-S street E-W street Intersection Air  Apparent Temperature (°C)  35 30 25 20 15 10 5 0 -5 -10 0  2  40  b)  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  S Wall N Wall E Wall W Wall Air  35 Apparent Temperature (°C)  4  30 25 20 15 10 5 0 -5 -10 0  c)  40  4  6  8  10 12 14 Time (h, LAT)  16  18  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  17 E Roof 17 W Roof 30 E Roof 30 W Roof Air  35 Apparent Temperature (°C)  2  30 25 20 15 10 5 0 -5 -10 0  2  4  20  22  24  Figure 4.4 Diurnal variation of the surface temperature of individual horizontal surfaces (a), vertical surfaces (b), and east-west oriented 17° and 30° pitched roof surfaces (c) for the λS = 0.42 scale model configuration. Data are five-minute averages.  roofs and walls. The east-facing roof facets (Figure 4.4c) achieve their peak temperature just after solar noon, while the west-facing roof facets, similar to the west-facing walls, become 87  a)  40  Flat roof N-S street E-W street Intersection Air  Apparent Temperature (°C)  35 30 25 20 15 10 5 0 -5 -10 0  2  40  b)  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  S Wall N Wall E Wall W Wall Air  35 Apparent Temperature (°C)  4  30 25 20 15 10 5 0 -5 -10 0  c)  40  4  17 N Roof 17 S Roof 30 N Roof 30 S Roof Air  35 Apparent Temperature (°C)  2  30 25 20 15 10 5 0 -5 -10 0  2  4  Figure 4.5 Diurnal variation of the surface temperature of individual horizontal surfaces (a), vertical surfaces (b), and north-south oriented 17° and 30° pitched roof surfaces (c) for the λS = 0.63 scale model configuration. Data are five-minute averages.  warmest in mid-afternoon. A more stark contrast in sloped roof temperatures occurs when the spine of the roof runs east-west (Figure 4.5c). The maximum temperatures of south-facing roof 88  facets are nearly 10°C warmer than north-facing roofs that receive little direct solar radiation. In all cases, no matter the roof orientation, the 30° roofs are exposed more to the sun than the 17° ones and therefore become warmest.  4.1.1 Comparison with full-scale observations To provide some context for the scale model observations of facet surface temperature, results are compared with full-scale measurements from a light industrial (LI) site in Vancouver, British Columbia, Canada (49°N 123°W). This site is characterized by a very simple building structure consisting of one- and two-storey flat roof warehouses (Voogt and Oke, 1998) and little vegetation (AV < 5%; Masson et al., 2002). The average building height is 7.3 m and the proportion of complete surface area to plan area (Ac/Ap) is 1.4. Streets are primarily oriented in the cardinal directions. In terms of the Built Climate Zone classification scheme (see Table 3.1), the LI site is characterized as BCZ5, which corresponds to the λS = 0.42 scale model configuration (Table 3.2). Truck-mounted infrared remote sensors measured temperatures of walls and streets at the LI study area (Voogt and Oke, 1998). These traverses were conducted only during the daytime on August 15, 1992, so comparisons with Phoenix observations are restricted to daytime hours. Differences in absolute surface temperatures between the study sites (Figure 4.6) are due primarily to differences in background climate conditions. Greater insolation and warmer overall atmospheric conditions at the LI site contribute to the consistently warmer facet surface temperatures recorded there. Sunrise at the LI site occurred at 0500 local time (versus 0730 in Phoenix) and sunset was at 1930 local time (versus 1730 in Phoenix). In addition, the range in air temperature recorded at the LI site was approximately 15°C - 22°C (Voogt, 1995) while the air temperature range from the Phoenix scale model study was 3°C - 16°C. Although matching absolute surface temperatures between the two study sites is impossible, the relative timing and 89  a)  45 LI Nwall  40  LI Swall PHX Nwall  Observed T s (°C)  35  PHX Swall  30 25 20 15 10 5 0 -5 0  b)  4  6  8  10 12 14 Time (LAT)  16  18  20  22  24  6  8  10 12 14 Time (LAT)  16  18  20  22  24  6  8  10 12 14 Time (LAT)  16  18  20  22  24  45 LI Ewall  40  LI Wwall PHX Ewall  35 Observed T s (°C)  2  PHX Wwall  30 25 20 15 10 5 0 -5 0  c)  2  4  45 LI E-W road  40  LI N-S road  35  PHX E-W road  Observed T s (°C)  PHX N-S road  30 25 20 15 10 5 0 -5 0  2  4  Figure 4.6 Measured surface temperatures for both the λS = 0.42 scale model configuration (PHX) and the apparent surface temperatures from the Vancouver LI study site. North- and south-facing walls are shown in (a), east- and west-facing walls in (b) and east-west and north-south roads in (c). Sunrise/sunset times from Vancouver LI are represented by the solid vertical lines; Phoenix sunrise/sunset times are represented by the vertical dashed lines.  90  behavior of the temperature curves helps to demonstrate the utility of the scale modeling technique employed here. In the case of the north- and south-facing walls (Figure 4.6a), a few items stand out. First, the temperature difference between the two wall facets is greater in the Phoenix case than at the LI study site. This is because the LI north-facing walls intercept insolation not only in the morning but also later in the day and therefore continue a more pronounced warming pattern. In other words the north-facing walls in the summertime LI case are able to intercept solar radiation early and late in the day due to the large solar zenith angles when the azimuth angle is less than 90°. In Phoenix, however, the north-facing walls are never directly exposed to sunlight (solar azimuth angles greater than 90° relative to the north-facing walls) and therefore remain considerably cooler than their south-facing counterparts. At both sites, south-facing walls peak in temperature about 90 minutes after solar noon. The north-facing walls peak later in the afternoon (at approximately 1530 LAT at the LI site and 1430 LAT at the Phoenix site). The observed lags in the daily maximum temperature of east- and west-facing walls (Figure 4.6b) also indicate similar thermal behavior between the full- and reduced-scale sites. The east-facing walls at both sites peak in temperature about 4.5 – 5 hours after sunrise while the west-facing walls peak much later in the day, between 2 – 3 hours before sunset. The west-facing walls also warm to slightly higher temperatures than the east-facing walls at both sites. The absolute surface temperature of the road surfaces is comparable between the sites, a result of the anomalous thermal properties of the materials used to construct the surface of the scale model. Even so, both north-south road surfaces peak in temperature about 60 – 90 minutes after solar noon. The east-west roads at both sites register their maximum temperature at approximately the same time (1330 LAT). Data from both sites are normalized to 1.0 following the approach proposed by Oke (1998). The x-axis is the fraction of day since sunrise (where 0.0 corresponds to sunrise and 1.0 91  corresponds to the time of sunset) and the y-axis (surface temperature) is plotted according to the minimum and maximum recorded temperature from each facet (where 0.0 corresponds to the minimum temperature and 1.0 corresponds to the maximum temperature of the dataset). Some similar thermal patterns between the sites are more apparent in this non-dimensional framework (Figure 4.7). The temperature patterns of the roads, north- and south-facing walls (Figures 4.7a and 4.7b) are driven by solar exposure that is approximately symmetric about solar noon. As a result these surfaces warm and cool at approximately the same rate. The east- and west-facing walls (Figure 4.7c) are subject to non-symmetrical contributions of direct and diffuse radiation, however. The times of sunrise and sunset with respect to each of these facets is set not in the traditional framework (i.e., with respect to level ground with an unobstructed horizon) but in a more local sense, dictated by the shading from buildings in the solar direction. For example, the local sunrise for a west-facing wall occurs well after solar noon, when the wall receives direct solar radiation (in contrast to the entirely diffuse radiation from the morning hours). This results in an offset which is especially discernible in the LI case. In addition to the more complex, nonuniform shading pattern at the LI site, the thermal patterns in the LI case are likely further complicated by sea breeze-induced advection (Voogt, 1995). LI data are, therefore, in some respect not as ‘ideal’ as the scale model case but even so, the overall thermal patterns between the sites are comparable.  4.1.2 Comparison with numerical simulations Additional context as to the facet surface temperature features observed at the scale model site can be gained by comparison with numerical simulations. Krayenhoff and Voogt’s (2007a) Temperatures of Urban Facets in 3-D (TUF-3D) microscale urban energy balance numerical model can be used to simulate urban surface temperatures for a variety of surface geometries and properties, weather conditions, and solar angles. Similar to the surface structure of the scale 92  Normalized temperature (0=T min , 1=Tmax )  LI E-W road LI N-S road  1  PHX E-W road PHX N-S road  0.5  0 0  0.5  a)  1  Normalized temperature (0=T min , 1=Tmax )  Fraction of day (0=sunrise, 1=sunset)  LI Nwall LI Swall  1  PHX Nwall PHX Swall  0.5  0 0  b)  0.5  1  Normalized temperature (0=T min , 1=Tmax )  Fraction of day (0=sunrise, 1=sunset)  LI Ewall LI Wwall  1  PHX Ewall PHX Wwall  0.5  0  c)  0  0.5  1  Fraction of day (0=sunrise, 1=sunset)  Figure 4.7 Normalized course of facet temperatures from the Vancouver light industrial (LI) and scale model (PHX) sites for road surfaces (a), north- and south-facing walls (b), and east- and west-facing walls (c).  93  model study, the TUF-3D model domain is composed of non-vegetated, dry urban units which consist of plane-parallel roofs, walls, and streets that are then repeated across the domain to create a ‘neighborhood’. Radiation, conduction, and convection sub-models calculate the full surface energy balance, from which facet surface temperatures are extracted. TUF-3D has been tested against full-scale urban surface temperature measurements from a densely built-up site in Basel, Switzerland and from the Vancouver light industrial site, and been found to perform well at both the facet-average and sub-facet scales (Krayenhoff and Voogt, 2007a). Here, TUF-3D is run for the λS = 1.25 scale model configuration. Parameters are fixed and based on the geometric structure of the site and tabulated thermal and radiative parameters (Table 4.1). Measured K↓, L↓, wind speed and direction, air temperature, water vapor pressure, and air pressure provide the forcing data to the model. Because TUF-3D was originally formulated with parameters developed and tested at the full-scale, some modifications to the model coding were required to account for the unique nature of the scale model site. Wall and roof thicknesses represented in TUF-3D were greater than the actual scale model dimensions, as the volume of concrete contained in the interior of each scaled ‘building’ (i.e., the two sides of each of the four individual blocks comprising a ‘building’ that were not exterior walls) was evenly distributed amongst the exterior surfaces. The constant deep sub-surface temperature in TUF-3D was set sufficiently low (to 8.5°C), to mimic the loss of heat down through the ground and building floor surfaces. Individual facet-average wall, roof, and ground temperatures modeled with TUF-3D are compared to corresponding measured data in Figure 4.8. To correspond with the surface formulation in TUF-3D, the observed ground temperature is an areaweighted value of intersections, north-south, and east-west roads. Mean bias error (MBE), rootmean-square error (RMSE) and coefficient of determination (r2) are used to quantify bias, absolute error and covariance between the model and observations, respectively (Table 4.2).  94  Table 4.1TUF-3D model input parameters used in the scale model simulations. Parameter Geometric λS zb zb/Lb  Unit  Value  m  1.25 0.25 0.625  Radiative αRoof αWall αRoad εRoof  0.21 0.21 0.21 0.94  εWall εRoad  0.94 0.94  Initial Temperatures Troof Troad Twall Tintw (building interior air temperature)  °C °C °C  4.2 5.2 5.9  °C  8.5  Tints (constant deep-ground temperature of roads)  °C  8.5  Tfloor (constant deep-ground temperature of floors)  °C  8.5  Thermal Roofs ∆x  m  Layer 1 0.005  Layer 2 0.01  Layer 3 0.015  Layer 4 0.017  k  W m-1 K-1  0.86  0.86  0.86  C Streets ∆x  MJ m-3 K-1  1.50x106  1.50x106  1.50x106  0.86 1.50 x106  m  0.05  0.08  0.006  0.007  k C Walls ∆x k C  -1  -1  -3  -1  Wm K  MJ m K m  1.20x10  1.5 6  0.005  -1  -1  -3  -1  Wm K  1.5  MJ m K  0.01  0.86 1.50x10  1.20x10  0.86 6  0.01  0.86 6  1.50x10  2.00x10  0.86 4  0.015  0.86 6  1.50x10  2.00x104  0.86 6  1.50x106  Overall, the agreement is good, with high r2 values and MBE and RMSE values comparable to Krayenhoff and Voogt’s (2007a) model validation at the Vancouver light industrial site (TUF-3D performance statistics from the Krayenhoff and Voogt (2007a) 95  a) Apparent Surface Temperature (°C)  45 S Wall (obs) N Wall (obs) S Wall (TUF-3D) N Wall (TUF-3D)  40 35 30 25 20 15 10 5 0 -5 0  b)  2  4  6  8  10 12 14 Time (h, LAT)  16  18  20  22  24  10 12 14 Time (h, LAT)  16  18  20  22  24  10 12 14 Time (h, LAT)  16  18  20  22  24  Apparent Surface Temperature (°C)  40 E Wall (obs) W Wall (obs) E Wall (TUF-3D) W Wall (TUF-3D)  35 30 25 20 15 10 5 0 -5 0  c)  2  4  6  8  Apparent Surface Temperature (°C)  40 Flat Roof (obs) Ground (obs) Flat roof (TUF-3D) Ground (TUF-3D)  35 30 25 20 15 10 5 0 -5 0  2  4  6  8  Figure 4.8 Scale model measured surface temperatures (obs) plotted with corresponding TUF-3D apparent surface temperatures for the λS = 1.25 scale model configuration. North- and south-facing walls are shown in (a), east- and west-facing walls in (b) and the flat roof and area-weighted ground surfaces in (c). 96  Vancouver LI study included r2 values greater than 0.91, MBE values within 2.1°C and RMSE values less than 2.9°C). Moreover, TUF-3D is able to replicate the general thermal patterns observed for each surface facet in the scale model. The TUF-3D surface temperatures of all four wall facets (Figures 4.8a and 4.8b) and the ground (Figure 4.8c) are too warm at night by 2-3 Celsius degrees. The nocturnal roof temperatures (Figure 4.8c) match well during the night, which suggests insufficient canyon venting by the numerical model may play a role in the warmer wall and road temperatures. A similar constraint was pointed out by Krayenhoff and Voogt (2007a) in their model validation exercise at the full-scale LI site. At the morning onset of solar forcing there are no substantial lags (rendering high r2 values) between the numerical model and the observed data. The largest bias is observed with the surfaces receiving the greatest amount of insolation (roof and south-facing wall) while the least amount of bias is seen in the primarily shaded surfaces (north-facing walls and the ground).  Table 4.2 Comparison of modeled (TUF-3D) and measured facet-average apparent surface temperatures (°C) for the λS = 1.25 scale model configuration. n = 280. S wall  N wall  E wall  W wall  Ground  Roof  MBE RMSE  2.0 2.3  1.4 1.7  1.6 2.1  1.9 2.8  0.6 2.0  3.0 3.0  r2  0.98  0.95  0.94  0.94  0.95  0.99  4.2 Surface temperature of the system The ability of the scale model to effectively reproduce the essential thermal features of a comparable full-scale site is evidence of the model’s similitude and versatility. The dataset of facet-scale surface temperature can therefore be utilized to better examine the relationship between the surface structure (defined here by canyon aspect ratio) and a larger, more local-scale consideration of observed surface temperature. Individual ‘building’ facet temperatures are used  97  to estimate the ‘complete’ surface temperature of each scale model configuration (Section 4.2.1). This measure then forms the base case against which results from other urban surface conceptualizations are compared (Section 4.2.2). These data are also used to compare the directional variation of surface temperature (effective thermal anisotropy) observed at the scale model to that of full-scale study sites (Section 4.2.3).  4.2.1 The complete (three-dimensional) surface temperature The repeating pattern of scaled ‘buildings’ and absence of vegetation of the scale model simplifies the potentially tedious task of characterizing the complete urban surface, i.e. the boundary between the air and every element comprising the surface system. Here, the complete active surface area AC of each array configuration is estimated by adding the areas of walls (AW), roofs (AR), streets (AS), and street intersections (AI): AC = AW + AR + AS + AI  (4.1)  In accordance with Voogt and Oke (1997) individual facet surface temperatures are combined in proportion to their area fraction in order to estimate the area-weighted complete surface temperature (TC) of a unit building lot (see Figure 1.2 for a description): n  TC = ∑ f i Ti  (4.2)  i =1  n  where  ∑f  i  = 1 , fi is the fractional area of the ith surface facet and n is the number of facets  i =1  (e.g., flat roof, two street surfaces, one street intersection, and four walls) each with a surface temperature Ti. Ti is obtained from the dataset of observed facet temperatures described in Section 4.1 above. Refer to Table 4.3 for a listing of surface component areas for each array configuration. The complete surface temperature is a brightness temperature that is not corrected for surface emissivity (Norman and Becker, 1995). It is assumed that the simple repeating pattern 98  Table 4.3 Surface component areas for each array configuration. All areas have units of cm2 x 102 Area  Symbol  Plan (2D) Street (N-S or E-W) Street intersection Roof Wall (N, S, E, W) Complete  AP AS(N-S, E-W) AI AR AW(N, S, E, W) AC  λS = 1.25  % of AC  λS = 0.63  % of AC  λS = 0.42  % of AC  36 16 4 16 40 76  47 21 5 21 53  64 32 16 16 40 104  61 31 15 15 39  100 48 36 16 40 140  71 34 26 11 29  of the array, and the homogenous nature of the materials of which it is constructed, allow the complete surface temperature of the array to be represented by that of a unit building lot. The validity of the assumption of uniformity is demonstrated in Chapter 3 with an analysis of thermal imagery of individual facets. The diurnal patterns of TC from each array configuration are plotted together (along with the air temperature observed adjacent to the scale model) in Figure 4.9. The proportion of roof surfaces comprising the complete surface area in each model configuration ranges from 11% to 21% (Table 4.3). It is never the dominant facet type, so any differences in the pattern of TC  T C (°C)  35  λS=1.25  30  λS=0.63  25  λS=0.42  20 15 10 5 0 -5 0  2  4  6  8  10  12  14  16  18  20  22  24  Time (h, LAT)  Figure 4.9 Diurnal variation of the complete (three-dimensional) surface temperature for the three scale model configurations. Data are five-minute averages and corresponding air temperature for each day is shown by the thin lines.  99  between configurations is not likely attributable to varying amount of roofs in the calculation of AC. In the two most open geometries, street and intersection surfaces are the greatest contributors  to AC, so their thermal pattern has the greatest influence on the overall thermal pattern of TC. For example, when λS = 0.63, the timing and behavior of TC closely mirrors the temperature patterns of north-south streets and intersections (Figure 4.2b). When λS = 1.25, the thermal pattern of wall surfaces have the most influence on AC. Evidence of this is seen in the longer duration of the peak value of TC, which is caused by the continuous and progressive warming of the three walls exposed to direct insolation: the east-facing walls in morning, followed by the south-facing walls around solar noon and then the west-facing walls in the afternoon. The daily maximum air temperature lags the maximum value of TC in all three cases, but the relative timing of that lag is not constant (ranging from 1.5 – 3 hours) amongst the scale model configurations. At night in all three configurations the overall surface temperature of the system cools at the same rate as the air temperature, so that the absolute difference between TC and Ta remains fairly constant. In the λS = 1.25 configuration this difference is approximately 4°C while in the λS = 0.63 and λS = 0.42 configurations the differences are 6°C and 7°C, respectively. The complete surface temperature remains cooler than the air temperature until about 0930 LAT, and then drops below air temperature again in the late afternoon (approximately 1600 LAT for the λS = 0.63 and λS = 0.42 configurations and 1700 LAT for the λS = 1.25 configuration).  4.2.2 Comparison of urban surface definitions Different definitions of the urban surface yield different results concerning the overall surface temperature of the system. Figure 4.10 shows the difference in surface temperature between TC and that of a bird’s-eye view, ground-level, and roof-top definitions of the urban surface, for each untreated array configuration (see Section 1.2.1 and Figure 1.1 for a summary of definitions). The bird’s-eye surface definition is typically not applicable in tower-based 100  Temperature Difference (°C)  6.0  λS = 1.25 3.0 0.0 Tc - Bird's eye -3.0  Tc - Rooftop Tc - Ground level  -6.0 0  2  4  6  8  a)  10  12  14  16  18  20  22  24  Time (h, LAT)  Temperature Difference (°C)  6.0  λS = 0.63 3.0 0.0 Tc - Bird's eye -3.0  Tc - Rooftop Tc - Ground level  -6.0 0  2  4  6  8  b)  10  12  14  16  18  20  22  24  Time (h, LAT)  Temperature Difference (°C)  6.0  λS = 0.42 3.0 0.0 Tc - Bird's eye -3.0  Tc - Rooftop Tc - Ground level  -6.0 0  c)  2  4  6  8  10  12  14  16  18  20  22  24  Time (h, LAT)  Figure 4.10 Difference between TC and three alternative definitions of the urban surface temperature for the three scale model configurations (λS = 1.25 in (a), λS = 0.63 in (b) and λS = 0.42 in (c). Data are five-minute averages.  measurement programs of surface-atmosphere fluxes, because a down-facing wide-FOV pyrgeometer is close enough to the surface to ‘see’ vertical (wall) surfaces. This surface formulation is, however, commonly adopted by researchers using aircraft- or satellite-based measurement systems using down-facing narrow FOV sensors much further from the surface. 101  The surface ‘seen’ from such a vantage point is such that vertical facets have a negligible view factor. Likewise, the ground-level surface definition is most commonly applied in the case that surface temperature measurements are conducted from the ground (well within the urban canyon), so that roofs and much of the wall facets are not included in the measurement. Although the very nature of a particular measurement position inherently influences the surface definition most appropriate for that application, the only actual, or true, comprehensive definition of the surface is the complete surface, AC. The complete surface temperature TC therefore serves as the basis for comparison here. With this in mind, some common patterns in surface temperature formulations are seen between the three array configurations. The smallest difference between TC and other surface temperature measures occurs at night, when thermal gradients between and amongst surfaces is least. The ground-level temperature remains warmer than TC (negative bias) throughout much of the morning and into the mid-afternoon, at which time TC becomes warmer. The bird’s-eye formulation follows a similar pattern. This is expected, since both include ground surfaces in their formulation. Less overall difference is observed in the bird’s-eye formulation in all three scale model configurations because the temperature pattern of roof surfaces acts to temper the robust thermal response of the ground surface. The λS = 1.25 scale model configuration contains the largest differences between TC and the other three definitions of surface temperature (Figure 4.10a). At approximately solar noon, the ground level surface temperature is 5°C warmer (negative difference) than TC. The bird’s-eye formulation is about 2.5°C warmer than TC while the rooftop temperature is within 1°C of TC at solar noon. Appreciable biases are also evident in the mid-afternoon, but at this time TC is warmer (positive difference) than the ground surface by nearly 5°C and warmer than the bird’seye formulation by approximately 1.5°C. The roof surfaces remain warmer than TC at this time, by about 2°C. The magnitude of these differences generally decreases as canyon aspect ratio 102  decreases (Figures 4.10b and 4.10c). Similar to the λS = 1.25 case, the greatest overall difference with TC in the λS = 0.63 scale model configuration (Figure 4.10b) occurs with the ground-level formulation. Ground surfaces are approximately 4°C warmer than TC at solar noon and then cooler than TC in the mid-afternoon by about 2°C. These differences are smaller in the λS = 0.42 scale model configuration (-3°C at solar noon and 1.6°C in the mid-afternoon; Figure 4.10c). Differences between TC and the ground level and bird’s-eye formulations are least in the λS = 0.42 case because this scale model configuration contains the largest relative proportion of ground surface in its complete surface temperature formulation. These simplified, twodimensional conceptualizations are often used to characterize the thermal environment of the urban surface. Results from the scale model study show, however, that in the higher density built climate zone scenarios, such simplifications that exclude vertical (wall) surfaces may result in large surface temperature differences when compared to the complete, three dimensional surface temperature of the system.  4.2.3 Surface temperature dependence on sensor viewing geometry Remote sensing of urban surface temperature is complicated by the directional variation (anisotropy) of the surface temperature and hence the upwelling thermal emissions. Anisotropy results from combination of the three-dimensional urban surface structure, the sensor viewing direction and its field of view, and the patterns of sunlit and shaded surfaces that are responsible for microscale surface temperature contrasts (Voogt, 2008). Because of this anisotropy, remotely sensed surface temperatures are biased as functions of both viewing direction and time, in comparison with the representative complete surface temperature. Such patterns are welldocumented over natural or agricultural surfaces (e.g., Kimes et al., 1980; Balick and Hutchison, 1986; Paw U et al., 1989; Lipton, 1992; Lagouarde et al., 2000) but similar studies from urban areas are not as prevalent in the literature (Lagouarde et al., 2004). 103  Motivated by the assertion of Roth et al. (1989) that urban areas are prone to similar anisotropic variations as those observed in non-urban settings, Voogt and Oke (1997) used airborne thermal scanner and vehicle traverse observations from three land-use areas (residential, light industrial, and downtown) in Vancouver, B.C. to demonstrate the under-sampling of the complete (three-dimensional) surface. The observed differences of up to 9°C with viewing direction and anisotropy was greatest in the high-rise downtown district. Lagouarde et al. (2004) identified ‘hot spot’ effects and -5 to +7 °C differences in surface temperature between nadir and off-nadir measurements from two districts in Marseille, France. In a wintertime study in Toulouse, France, Lagouarde and Irvine (2008) confirmed the hot spot feature while also observing significant daytime anisotropy between -4 and +10 °C between oblique and nadir viewing positions. The simple scale model here allows the study of effective thermal anisotropy in the absence of extraneous influences on surface temperatures, such as mixed surface materials (glass, metal, wood, etc.; Voogt, 2008), moisture sources, and anthropogenic fluxes (Ichinose et al., 1999). Isolation of the impact of surface geometry with respect to differential solar loading  on the viewed surface temperature can be explored with this dataset. The SUM model provides the ability to extend the analysis to other viewing angles and azimuths (Soux et al., 2004) in order to assess the degree of effective thermal anisotropy arising from off-nadir viewing directions. Model simulations are performed for each scale model configuration at 0900, 1200, and 1500 LAT using a 36° sensor FOV at 5° increments in the off-nadir angle, and 10° increments in the azimuth angle. The sensor height was 19zH. This was chosen to provide maximum coverage of the scale model domain for the largest off-nadir angle and to minimize the dependence of the results on the exact sensor position relative to the scale model surface. Interpolated results are summarized as polar plots (Figure 4.11).  104  λS = 1.25  λS = 0.63  λS = 0.42  105  Figure 4.11 Modeled directional radiometric surface temperature (°C) over the three scale model configurations for 0900 LAT (left column), 1200 LAT (middle column) and 1500 LAT (right column) for each viewing direction (5° increments in off-nadir angle and 10° increments in azimuth angle) using a 36° FOV sensor at 19zH. S indicates the position of the sun.  The plots demonstrate the influence of solar forcing as it affects the microscale surface temperature distribution. A hot spot is located in the direction opposite to that of the solar azimuth, and therefore migrates in response to the daily solar path. This means it occurs from northwesterly viewing directions in the morning to northerly view directions near solar noon, and northeasterly view directions in the afternoon. The warmest temperatures are observed at large off-nadir viewing angles towards the north, when the most directly-sunlit south walls and northsouth oriented streets dominate the sensor FOV. Temperatures drop off gradually as azimuths increase or decrease from either side of the hot spot region. Large off-nadir viewing angles in the direction of solar azimuth that view the predominantly shaded surfaces (north walls, west walls in the morning, east walls in the afternoon, east-west oriented streets) contain the coolest temperatures. Anisotropy at solar noon decreases with wider canyon geometry, as expected according to coupled model simulations (Krayenhoff and Voogt, 2007b). For all three model configurations nadir view directions are relatively warm, a function of maximum roof and street temperatures at this time of day. The overall pattern of anisotropy near solar noon for λS = 0.42 is very similar to the combined simulations for many points over the Vancouver light industrial district with the same canyon aspect ratio (Figure 14a from Voogt, 2008). The absolute value of anisotropy for the scale model is slightly smaller (2.5°C compared to 3.5°C) than that in the Vancouver study. The temporal variation of anisotropy, shown in Figure 4.11, is also similar to that shown in Krayenhoff and Voogt’s (2007b) coupled model simulations. These results suggest that the anisotropy generated by the scale model is reasonable, despite the anomalous thermal properties of the roof surfaces in the scale model.  106  4.3 Summary of results The complex structure of cities makes the comprehensive measurement of surface temperature difficult. The microscale variations of surface temperature that arise due to variations in surface thermal and radiative properties and solar exposure create yet other levels of complexity. Even remote sensing techniques are sometimes hampered by the inherent three-dimensional structure of cities that makes the simultaneous temperature measurement of all facets comprising the complete urban surface difficult. This research demonstrates that the challenge of measuring the true, complete urban surface temperature can be reduced by physically downscaling the urban setting, so long as care is taken in achieving similitude between the full-scale environment and its reduced-scale equivalent. The surface temperature survey conducted at the Phoenix scale model study points to outdoor scale modeling as a powerful tool for directly assessing urban surface temperature patterns at the facet scale, as well as the variation in surface temperature according to different conceptualizations of the urban surface. Results from the scale modeling experiment are shown effective for demonstrating: •  Average facet temperatures from scaled-down facets and diurnal temperature patterns of facets relative to one another are comparable to those observed in real-world settings.  •  That while the comparison of observed facet surface temperatures with TUF-3D numerical model output is not intended to be a rigorous numerical model validation exercise, it does draw attention to the power of scale modeling in providing valuable test data for numerical models.  •  Patterns of effective thermal anisotropy, which are most commonly observed at the full scale from aircraft and/or a combination of measurement platforms near the ground (e.g., vehicle traverses, foot surveys, using an array of stationary sensors) can be successfully reproduced by a scale model. Although observed anisotropy is primarily a concern from 107  the perspective of the remote sensing of urban surface temperature and not the physical processes responsible for those temperatures, Lagouarde and Irvine (2008) point out that most studies of urban thermal anisotropy are performed at the scale of the entire city and questions remain about the variability in anisotropy over smaller urban samples. For example, the impact of smaller-scale urban features such as large individual buildings or open city squares to the observed anisotropy is not well understood. In the absence of observations from such a site, a scale model could be constructed to assess these impacts. This, in turn, can improve the interpretation and correction of satellite-based observations of surface temperature from such sites and in the development of highresolution thermal infrared sensors. •  Also related to the remote sensing of the urban thermal environment, the twodimensional urban surface conceptualizations that are often adopted by researchers can result in large temperature differences when compared to the complete, three dimensional surface temperature of the system. This is especially the case in the higher density built climate zone scenarios, where excluded vertical (wall) surface can comprise a significant proportion of the complete surface area.  Surface temperature data from an outdoor scale model such as the one presented here have the potential to be used in various applications, especially those related to urban design: •  To complement numerical and full-scale studies commonly used by urban planners to assess general strategies in urban development and the impact of urban form on the local climate.  •  To test and refine methods that use bulk heat transfer approaches for modeling sensible heat fluxes from the complete urban surface (e.g., Voogt and Grimmond, 2000).  108  •  To better understand pedestrian-level outdoor thermal comfort in urban canyons by using measured data to calculate an index of thermal stress based upon the energy exchanged between a person and the built environment (Pearlmutter et al, 2007).  •  To test shading structures to be used as cooling implements as well as the effectiveness of building materials designed to mitigate urban-enhanced warming (especially in extreme hot-arid climates, e.g., Pearlmutter and Rosenfeld, 2008).  109  Chapter 5  SCALE MODEL RESULTS: RADIATION FLUXES  In this chapter, analyses of the spatial variation in radiation fluxes are conducted with measured and modeled vertical profiles of reflected shortwave, upwelling longwave emittance, and net allwave radiation. This is done using observations from sensors mounted on the traversing mast to conduct profile measurements at two locations in the scale model array. The close proximity of the sensors permits the assumption that downward short- and longwave radiation from above roof level is uniform across the scale model array. Therefore, only measured upward radiative fluxes need be considered. Presented here are reflected shortwave radiation measured with the LI-COR LI200X pyranometers, emitted upwelling longwave radiation derived from average facet temperature measurements combined with modeled surface view factors, and net allwave radiation measured with the Kipp & Zonen NRLITE net radiometers.  5.1 Uniformity of radiation fluxes An assessment of the spatial variability of upwelling radiative fluxes first requires an understanding of the scale model’s overall response to radiative forcing. Chapter Three included a discussion regarding the uniformity of the scale model materials and construction as it relates to characterizing representative facet surface temperatures at the individual facet scale. Since radiation flux measurements are performed at a scale larger than the individual facet, a more local-scale assessment of uniformity is required. Individual components of the measured radiation budget during ideal atmospheric conditions (no reported cloud cover, daytime maximum temperature between 13°C and 18°C, nighttime minimum temperature between 0°C and 2°C, and overall relative humidity during the period between 10% - 50%) display a repeating 110  pattern from day to day (Figure 5.1). The coherent K↑ and L↑ patterns over the three-day period point to the ability of the scale model to replicate reflected solar radiation and emitted longwave radiation under identical radiative forcing. Therefore, the experimental control afforded by the simple scale model design, combined with the atmospheric conditions of the location, indicate analysis limited to one cloudless diurnal period for each trial is appropriate. L-down  700  L-up  K-down  K-up  Q*  Energy Flux Density (W m -2)  600 500 400 300 200 100 0 -100 -200 334  334.5  335  335.5  336  336.5  337  Time (YD, LAT)  Figure 5.1 Time series of individual radiation flux densities measured by the CNR1 net radiometer. Fluxes are 60-s averages.  5.2 Modeled view factors SUM-calculated view factors of surfaces ‘seen’ by the down-facing 160°-FOV pyranometers, in each array configuration, are presented in Figure 5.2. The left-hand side of Figure 5.2 (panels ac) gives the view factors of roofs, walls, intersections, and streets corresponding to sensors approximately positioned in and above a north-south canyon (dashed line) and an east-west canyon (solid line). Figure 5.2d – 5.2f gives a further breakdown of surface view factors, illustrating each wall component that is ‘seen’ by the sensors. Due to operational constraints, only in the λS = 1.25 configuration are the sensors positioned at the midpoint of the east-west and north-south canyons (see Figure 3.4). In the λS = 0.63 configuration the sensors are 111  a)  d)  6  6  5.5  Roof (E-W)  5.5  North Wall (E-W)  5  Wall (E-W)  5  South Wall (E-W)  Intersection (E-W)  4.5 4  zm /zb  zm /zb  Intersection (N-S)  2.5  West Wall (N-S)  2.5  Street (N-S)  2  1.5  1.5  1  1  East Wall (N-S)  0.5  0.5 0.0  0.2  0.4  0.6  0.8  0.0  1.0  e) Wall (E-W)  5  5.5  North Wall (E-W)  5  South Wall (E-W)  Intersection (E-W)  4.5  Roof (N-S)  4  3.5  Wall (N-S)  3.5  zm /zb  4  Intersection (N-S)  2.5  Street (N-S)  1.5  1.5  1  1  0.5  0.5 0.6  0.8  North Wall (N-S) South Wall (N-S) West Wall (N-S)  2.5 2  0.4  East Wall (E-W)  3  2  0.2  West Wall (E-W)  4.5  Street (E-W)  3  1.0  East Wall (N-S)  0.0  0.1  View factor  f)  6 Roof (E-W)  5.5  Wall (E-W)  5  5.5  North Wall (E-W)  5  South Wall (E-W)  4  3.5  Wall (N-S)  3.5  zm /zb  Roof (N-S)  zm /zb  4  Intersection (N-S)  2.5  2  1.5  1.5  1  1  0.5  0.5  0.2  0.4  0.6  View factor  0.8  North Wall (N-S) South Wall (N-S)  3  2  0.0  East Wall (E-W)  West Wall (N-S)  2.5  Street (N-S)  λS = 0.42  West Wall (E-W)  4.5  Street (E-W)  3  0.3  6  Intersection (E-W)  4.5  0.2 View factor  λS = 0.63 c)  0.3  6  Roof (E-W)  5.5  0.2 View factor  6  0.0  0.1  View factor  λS = 1.25  zm /zb  South Wall (N-S)  3  2  b)  North Wall (N-S)  3.5  Wall (N-S)  3  East Wall (E-W)  4  Roof (N-S)  3.5  West Wall (E-W)  4.5  Street (E-W)  1.0  East Wall (N-S)  0.0  0.1  0.2  0.3  View factor  Figure 5.2 Surface view factors ‘seen’ by the 160°-FOV down-facing radiometer located approximately in/above a north-south (N-S) canyon (dashed lines) and an east-west (E-W) canyon (solid lines) at heights 0.5zb to 6zb for the λS = 1.25 (top row), λS = 0.63 (middle row) and λS = 0.42 (bottom row) scale model configurations. Left-hand panels (a-c) show total view factors of the primary facet types (walls, roofs, streets, intersections). The right-hand panels (d-f) show view factors of each wall component.  112  positioned at the canyon endpoints (see Figure 3.5) whilst in the λS = 0.42 configuration the sensors are positioned between the canyon endpoints and the intersection (see Figure 3.6). The exact x-y locations of the sensors are outlined in Figures 3.4 - 3.6. In each scale model configuration, the greatest variability with height of surfaces ‘seen’ by the pyranometers occurs at the lowest levels. Above four times the building height, component view factors of all surfaces remain largely constant. At 4zb wall view factors collapse to within 0.01 of one another (Figure 5.2d – 5.2f). This sensor height also corresponds to the uppermost measurement position at which the FOV of the pyranometer is entirely located within the bounds of the scale model array. At measurement locations located at or below roof level (1.0zb or 0.5 zb, respectively) since no roofs are ‘seen’ by the sensor, all upwelling radiation fluxes originate from street, intersection, and wall components. When the sensors are positioned at the canyon midpoint in the λS = 1.25 configuration (Figure 5.2a), street and wall surfaces dominate their FOVs at the lowest measurement heights, but as they are raised through the UCL, roofs are the dominant surface facet ‘seen’ by both sensors. The greater building density of the λS = 1.25 configuration (relative to the two more open surface geometries; Table 4.2) means that wall surfaces constitute an appreciable proportion of the sensor FOV at all heights, even above roof level. When the sensors are positioned at the canyon endpoint in the λS = 0.63 configuration (Figure 5.2b), street and intersections dominate their FOVs at the lowest measurement heights, but as they are raised above roof level, roofs and walls are increasingly ‘seen’ by the sensors. At heights above 2.5-3zb the relative proportion of roofs, walls, and intersections ‘seen’ by both sensors are each approximately 22% (+/- 5%) of the sensors’ FOVs. Street surfaces comprise a larger proportion of the sensors’ FOV at the highest levels (around 32%). In the most open geometry, when the sensors are positioned between the canyon endpoint and the intersection (Figure 5.22c), street and intersection surfaces remain the dominant facets 113  ‘seen’ by the sensors, at all heights. Above 3zb, streets and intersections account for 32% and 36% (respectively) of the sensors’ FOV. Building surfaces (walls and roofs) play a lesser role in this configuration, particularly at the greater measurement heights where both surface facet types account for 16% of the sensors’ FOV. The SUM model is also used to determine the proportion of sunlit and shaded facet surfaces contained within each sensor’s FOV. This information is particularly valuable in interpreting the spatial variability of measured reflected shortwave radiation. Three approximate times during the day – 0900 LAT, 1200 LAT, and 1500 LAT – are considered for analysis. The model is run with solar position (azimuth and zenith) from these three times as inputs. Given the repeated block layout of the scale model arrays, the patterns of sunlit and shaded facets that emerge over the course of the IOP days are straightforward and are discussed, in the context of measured surface temperature, in the previous chapter. A more complicated pattern emerges, however, when surface-sun geometry is considered in the context of sensor position, particularly at the lowest measurement heights. These patterns are not thoroughly presented here but are referred to when appropriate. Profile plots detailing surface view factor calculations for the model are provided in Appendix D.  5.3 Reflected shortwave radiation The variability of measured reflected shortwave radiation, K↑, in the vertical direction for the three scale model configurations is summarized in Figure 5.3. Although the traversing mast was continuously operational, Figure 5.3 focuses on vertical profiles measured at three times of day (approximately 0900 LAT, 1200 LAT, and 1500 LAT). These are the times when surface view factors were calculated using SUM. The left-hand column shows profile measurements for the λS = 1.25 scale model configuration, the middle column gives results for λS = 0.63, and the right-  114  λS = 1.25 a)  λS = 0.63 d)  E-W canyon  5.5  g)  E-W canyon  5.5  N-S canyon  4.5  3.5  3.5  3.5  zm /zb  4.5 zm /zb  4.5  2.5  2.5  2.5  1.5  1.5  1.5  0.5  0.5  0  25  0900 LAT  50  75  100  125  150  -2  K ↑ (W m )  0.5 0  e) E-W canyon  50  75  100  125 150  3.5  25  50  75  2.5  2.5  1.5  1.5  0  K ↑ (W m )  25  50  75  100  125  25  N-S canyon  50  75  100  N-S canyon  4.5 zm /zb  zm /zb  1.5  150  E-W canyon  5.5  4.5  2.5  125  K ↑ (W m )  N-S canyon  3.5  150  i) E-W canyon  5.5  4.5  125  -2  1200 LAT  K ↑ (W m )  f) E-W canyon  5.5  0  150  -2  1200 LAT  c)  100 -2  0.5  0.5  100 125 150 -2  1200 LAT  zm /zb  3.5  zm /zb  3.5  0  75  K ↑ (W m )  N-S canyon  4.5  0.5  50  E-W canyon  5.5  N-S canyon  4.5  1.5  25  h)  4.5  2.5  zm /zb  0  0900 LAT  -2  K ↑ (W m )  E-W canyon  5.5  N-S canyon  zm /zb  25  0900 LAT  b) 5.5  E-W canyon  5.5  N-S canyon  N-S canyon  zm /zb  λS = 0.42  3.5  3.5  2.5  2.5  1.5  1.5  0.5 0  25  50  75  0  K ↑ (W m )  1500 LAT  0.5  0.5  100 125 150 -2  25  50  75  100  125  150  0  1500 LAT  25  50  75  100  125  150  -2  -2  K ↑ (W m )  1500 LAT  K ↑ (W m )  Figure 5.3 Vertical profiles of measured reflected shortwave radiation (K↑) at approximately 0900 LAT (top row), 1200 LAT (middle row) and 1500 LAT (bottom row) from the λS = 1.25 (left column), λS = 0.63 (middle column), and λS = 0.42 (right column) scale model configurations.  hand column shows results for the λS = 0.42 case. Observations from both the east-west and north-south sensors are included. In all scale model configurations K↑ shows a slight increasing trend with height in the morning, very little change with height around solar noon, and a slight decreasing trend with height in the afternoon. The slopes of these trends are constant, both between sensors and 115  amongst scale model configurations, at heights above 3zb. At sensor heights above this level, the view factors of sunlit and shaded surfaces contained within the FOV of a down-facing pyranometer do not vary, so the consistent trends in measured K↑ at these levels are not a function of changing radiation source areas but of changes in the radiation forcing (K↓) impinging on the system. The top half of the profile measurements occur over a period of roughly fifteen minutes, which, in the morning and afternoon corresponds to an overall increase or decrease of insolation of 50-60 W m-2. Assuming the measured surface albedo of the scale model is constant at heights well above roof level, it is expected that the proportion of reflected solar radiation also increases or decreases over the course of fifteen minutes. In fact, the slopes of the K↑ vs. height profile from the top portions of Figure 5.3a- 5.3i match the slope of the corresponding signal of dK↑/dt from the fixed (CNR1) measurements (not shown). It is therefore reasonable to assume that the trends observed at the upper levels are not the result of varying source areas. The greatest overall difference in measured K↑ between the sensors occurs around solar noon, from below roof level (zm/zb = 0.5; Figures 5.3b, 5.3e, and 5.3h). The wall and street surfaces comprising the north-south canyons are fully illuminated at this time and therefore subject to multiple shortwave reflection. The sensors located in the east-west canyons are subject to a varying combination of shaded and sunlit surfaces and don’t ‘see’ as much reflected shortwave radiation. The sensor in the east-west canyon of the λS = 1.25 array (Figure 5.3b) ‘sees’ primarily shaded surfaces (north- and south-facing walls and east-west street floor), except for a small portion (about 15% of the overall FOV) of the sunlit intersection. The degree of shading detected by the east-west sensor at zm/zb = 0.5 decreases with increasing building spacing, so differences in measured K↑ also begin to lessen. In the λS = 1.25 configuration, the difference in reflected shortwave radiation observed by the sensors at zm/zb = 0.5 at solar noon is  116  89 W m-2. In the λS = 0.63 configuration this difference is 15 W m-2 while in the λS = 0.42 configuration, the difference is barely discernible at just 5 W m-2. Diurnal time series plots of reflected shortwave radiation from four sensor heights (zm/zb = 0.5, 1.5, 2.5, and 3.5) for each scale model configuration are given in Figures 5.4 – 5.6. In all three scale model configurations, measurement positions from above roof level do not produce any significant differences in measured K↑ between the N-S and E-W sensors. When the pyranometers are positioned below roof level in the λS = 1.25 array (Figure 5.4a) a distinct daytime pattern emerges. K↑ measured by the north-south sensor quickly peaks at solar noon,  a)  b)  140  E-W canyon  zm/zb = 0.5  120  N-S canyon  -2  K ↑ (W m )  -2  80 60  80 60  40  40  20  20 0 0  6  12  18  24  0  6  Time (LAT)  E-W canyon  zm/zb = 2.5  N-S canyon  140  18  24  E-W canyon  zm/zb = 3.5  120  100  N-S canyon  100 -2  K ↑ (W m )  -2  12 Time (LAT)  d)  140 120  K ↑ (W m )  N-S canyon  100  0  c)  E-W canyon  zm/zb = 1.5  120  100 K ↑ (W m )  140  80 60  80 60  40  40  20  20  0  0 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.4 Time series of measured reflected shortwave radiation (K↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 1.25 scale model configuration. 117  when that canyon is fully sunlit. The east-west canyon in this dense surface configuration never experiences full illumination, so the sensor measures far less reflected shortwave radiation over the course of the day from below roof level. In this scenario, K↑ peaks about two hours after solar noon, when a portion of the east-west sensor FOV includes a sunlit intersection. Another distinct pattern is observed below roof level in the λS = 0.63 array (Figure 5.5a). Although in this case neither sensor is sited in an entirely shaded canyon throughout the day, a phase shift is evident. The north-south sensor peaks, as expected, at solar noon, when that a)  b) E-W canyon  zm/zb = 0.5  140 120  100  100 K ↑ (W m )  120  N-S canyon  -2  80 60  80 60  40  40  20  20  0  0 0  6  12  18  24  0  6  Time (LAT)  12  18  24  Time (LAT)  c)  d) E-W canyon  140  zm/zb = 2.5  E-W canyon  140  zm/zb = 3.5  N-S canyon  120  100  100 K ↑ (W m )  120  N-S canyon  -2  -2  K ↑ (W m )  E-W canyon  zm/zb = 1.5  N-S canyon  -2  K ↑ (W m )  140  80 60  80 60  40  40  20  20  0  0 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.5 Time series of measured reflected shortwave radiation (K↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.63 scale model configuration.  118  a)  b) zm/zb = 0.5  140  N-S canyon  120  100  100 K ↑ (W m )  120  E-W canyon  zm/zb = 1.5  N-S canyon  -2  -2  K ↑ (W m )  140  E-W canyon  80 60  80 60  40  40  20  20  0  0 0  6  12  18  24  0  6  Time (LAT)  12  18  24  Time (LAT)  d)  c) zm/zb = 2.5  140  120  100  100 K ↑ (W m )  120  E-W canyon  zm/zb = 3.5  140  N-S canyon  N-S canyon  -2  -2  K ↑ (W m )  E-W canyon  80 60  80 60  40  40  20  20  0  0  0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.6 Time series of measured reflected shortwave radiation (K↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.42 scale model configuration.  canyon is fully illuminated. The east-west sensor, on the other hand, reaches its maximum value of K↑ about one hour earlier. Because this sensor is positioned at the eastern endpoint of the eastwest canyon (see Figure 3.5), it is open to insolation through most of the morning hours but is then in partial shade through the afternoon. In all three scale model configurations, K↑ measured by the north-south sensor from zm/zb = 0.5 displays a more abrupt pattern in the morning increase and afternoon decrease of K↑ relative to sensor heights above roof level. When the sensor is contained in a canyon, radiation exchanges occurring within the FOV are very much dictated by conditions at the street/intersection surface. When the surface becomes mostly- to fully sunlit, 119  the sensor is quick to respond to the onset of reflected shortwave radiation. Once the sensor ‘sees’ a myriad of sunlit and shaded surfaces from higher measurement positions, the response is tempered and the morning increase and afternoon decrease in observed reflected shortwave radiation is more gradual from above roof level.  5.4 Emitted upwelling longwave radiation As with the measured profile of reflected shortwave radiation, the variability of emitted upwelling longwave radiation from each scale model configuration is presented both as vertical profiles at three times over the course of the day (Figure 5.7) and as time series plots from four sensor heights (Figures 5.8 – 5.10). These are not directly measured fluxes but are derived by combining modeled view factors (Figure 5.2) with measured facet temperature. The resultant apparent surface temperature is then converted with the Stefan-Boltzmann relationship into emitted longwave radiation. As observed in the K↑ profiles, L↑ shows a slight increasing trend with height in the morning, very little change with height around solar noon, and a slight decreasing trend with height in the afternoon (Figure 5.7). These trends are apparent in all three scale model configurations. Again, this is the result not of changing radiation source areas, but of overall warming and cooling patterns of the entire system. At all times in each configuration, differences in L↑ are indiscernible at heights above 3zb. Similar to the K↑ case, the greatest overall difference in emitted upwelling longwave radiation between the sensors occurs at around solar noon and from below roof level (zm/zb = 0.5; Figures 5.7b, 5.7e, and 5.7h). The absolute magnitude of the L↑ flux differences is comparable to differences in observed K↑. In the λS = 1.25 configuration, the difference in emitted longwave radiation observed by the sensors at zm/zb = 0.5 at solar noon is 45 W m-2 (versus 89 m-2 difference in K↑). In the λS = 0.63 configuration the difference is 38 W m-2 (versus 15 W m-2 120  λS = 1.25  λS = 0.63  a)  E-W canyon  5.5  λS = 0.42  d)  g) E-W canyon  5.5  N-S canyon  4.5  4.5  3.5  3.5  3.5  zm /zb  4.5  2.5  2.5  2.5  1.5  1.5  1.5  0.5  0.5  0.5 325  375  425  475  525  325  375  -2  e)  E-W canyon  425  475  zm /zb  3.5  375  2.5  2.5  1.5  1.5  0.5  525  0.5  325  -2  375  L ↑ (W m )  475  525  325  375  f)  N-S canyon  475  i)  E-W canyon  5.5  N-S canyon  N-S canyon  4.5  3.5  3.5  3.5  1.5  zm /zb  4.5 zm /zb  4.5  2.5  525  L ↑ (W m )  1200 LAT  E-W canyon  5.5  425  -2  L ↑ (W m )  1200 LAT E-W canyon  5.5  425  -2  1200 LAT  525  N-S canyon  3.5  0.5  475  E-W canyon  5.5  3.5  zm /zb  zm /zb  h)  N-S canyon  4.5  1.5  425  L↑ (W m )  0900 LAT  4.5  325  375  -2  4.5  2.5  zm /zb  325  525  E-W canyon  5.5  N-S canyon  c)  475  L ↑ (W m )  0900 LAT  0900 LAT 5.5  425  -2  L ↑ (W m )  b)  E-W canyon  5.5  N-S canyon  zm /zb  zm /zb  N-S canyon  2.5  2.5  1.5  1.5  0.5 325  375  425  475 -2  L ↑ (W m )  1500 LAT  525  0.5 325  375  425  475  525  0.5 325  1500 LAT  375  425  475  525  -2  -2  L ↑ (W m )  1500 LAT  L ↑ (W m )  Figure 5.7 Vertical profiles of emitted upwelling longwave radiation (L↑) as derived from measured facet surface temperature and modeled view factors at approximately 0900 LAT (top row), 1200 LAT (middle row) and 1500 LAT (bottom row) from the λS = 1.25 (left column), λS = 0.63 (middle column), and λS = 0.42 (right column) scale model configurations.  difference in K↑) and in the λS = 0.42 configuration, the difference is 3 Wm-2 (versus 5 Wm-2 difference in K↑). Of the three scale model configurations, the λS = 1.25 array contains the greatest overall variability of L↑ at the lowest measurement heights (Figure 5.8a), a function of the distinct combinations of facets contained in each sensor’s modeled FOV. The east-west sensor records slightly more L↑ than the north-south sensor in the morning and afternoon 121  a)  b) E-W canyon  zm/zb = 0.5  550  N-S canyon  L ↑ (W m )  500 -2  -2  L ↑ (W m )  500  E-W canyon  zm/zb = 1.5  550  N-S canyon  450 400 350  450 400 350  300  300 0  6  12  18  24  0  6  Time (LAT)  12  c)  24  d) E-W canyon  E-W canyon  550  zm/zb = 2.5  550  N-S canyon  500  zm/zb = 3.5  N-S canyon  -2  L ↑ (W m )  500  -2  L ↑ (W m )  18  Time (LAT)  450 400 350  450 400 350  300  300 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.8 Time series of modeled emitted upwelling longwave radiation (L↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 1.25 scale model configuration.  traverses (Figures 5.7a and 5.7c). This is because the sunlit south-facing walls in the east-sensor FOV are approximately 3° - 4°C warmer than the dominant sunlit east-facing walls ‘seen’ by the north-south sensor at 0900 LAT and the sunlit west-facing walls ‘seen’ in the afternoon (see Figure 4.1a). At solar noon in the λS = 1.25 configuration (Figure 5.7b), the north-south sensor primarily ‘sees’ the sunlit north-south streets and intersections, which, due to the thermal nature of the surface, have a rapid response to solar forcing and peak in temperature at around solar noon (Figure 5.8a).  122  Spatial variability of emitted upwelling longwave radiation is not as evident in the λS = 0.63 and λS = 0.42 scale model arrays (Figures 5.9 and 5.10). The greatest difference in modeled L↑ between the two sensors occurs at solar noon in the λS = 0.63 configuration (Figure 5.7e and  5.9a), when the sensor located at the end-point of a north-south canyon ‘sees’ a large proportion of sunlit north-street and intersection (over 92% of the total FOV from below roof level and 61% of the total FOV at roof level; not shown). The afternoon traverse (Figure 5.7f) displays easily detectable differences only from measurement positions at and below roof level, when the eastwest street ‘seen’ by the sensor is approximately 5°C warmer than the intersection and northsouth street facets. a)  b) E-W canyon  zm/zb = 0.5  550  N-S canyon  L ↑ (W m )  500 -2  -2  L ↑ (W m )  500  E-W canyon  zm/zb = 1.5  550  N-S canyon  450  400  350  450  400  350  300  300 0  6  12  18  0  24  6  12  24  Time (LAT)  Time (LAT)  c)  d) E-W canyon  550  zm/zb = 2.5  E-W canyon  550  N-S canyon  500  zm/zb = 3.5  N-S canyon  L ↑ (W m )  500 -2  -2  L ↑ (W m )  18  450  400  350  450  400  350  300  300 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.9 Time series of modeled emitted upwelling longwave radiation (L↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.63 scale model configuration. 123  a)  b) E-W canyon  zm/zb = 0.5  550  N-S canyon  L ↑ (W m )  500 -2  -2  L ↑ (W m )  500  E-W canyon  zm/zb = 1.5  550  N-S canyon  450 400  350  450  400  350  300  300 0  6  12  18  24  0  6  Time (LAT)  12  24  Time (LAT)  c)  d) E-W canyon  E-W canyon  550  zm/zb = 2.5  550  N-S canyon  500  zm/zb = 3.5  N-S canyon  L↑ (W m )  500 -2  -2  L ↑ (W m )  18  450  400 350  450  400  350  300  300 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.10 Time series of modeled emitted upwelling longwave radiation (L↑) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.42 scale model configuration.  5.5 Net allwave radiation The variability of measured net allwave radiation Q* from each scale model configuration is presented both as vertical profiles at three times over the course of the day (Figure 5.11) and as time series plots from four sensor heights (Figures 5.12 – 5.14). The slight increasing trend of Q* with height in the morning (Figures 5.11a, 5.11d, and 5.11g), very little change in Q* with height around solar noon (Figures 5.11b, 5.11e, and 5.11h), and a slight decreasing trend of Q* with height in the afternoon (Figures 5.11c, 5.11f, and 5.11i) is apparent in all three scale model 124  λS = 1.25  λS = 0.63  a)  5.5  N-S canyon  g)  E-W canyon  N-S canyon  4.5  3.5  3.5  3.5  zm /zb  4.5  2.5  2.5  2.5  1.5  1.5  1.5  0.5 -100  0  100  200  300  -2  Q* (W m )  0900 LAT  0.5 -100  400  0  200  300  -2  E-W canyon  5.5  4.5  4.5  3.5  3.5  3.5  0  100  200  300  1200 LAT  2.5  2.5  1.5  1.5  0.5 -100  400  -2  zm /zb  4.5  0.5 -100  0  1200 LAT  Q* (W m )  c)  100  200  300  E-W canyon  3.5  200 -2  300  400  2.5  2.5  1.5  1.5  0.5 -100  Q* (W m )  1500 LAT  zm /zb  3.5  zm /zb  3.5  100  200  300  400  -2  E-W canyon N-S canyon  4.5  0  100  Q * (W m )  5.5  4.5  0.5 -100  0  i) E-W canyon  5.5  4.5  1.5  400  E-W canyon  N-S canyon  2.5  300  -2  1200 LAT  -2  Q * (W m )  N-S canyon  zm /zb  0.5 -100  400  f) 5.5  200  N-S canyon  N-S canyon  zm /zb  zm /zb  N-S canyon  1.5  100  Q* (W m )  h) 5.5  2.5  0  0900 LAT  e) E-W canyon  5.5  0.5 -100  400  Q* (W m )  0900 LAT  b)  100  E-W canyon  5.5  N-S canyon  4.5 zm /zb  zm /zb  d)  E-W canyon  5.5  λS = 0.42  0  100  200  300  400  0.5 -100  -2  1500 LAT  Q * (W m )  0  100  200  300  400  -2  1500 LAT  Q* (W m )  Figure 5.11 Vertical profiles of measured net all-wave radiation (Q*) at approximately 0900 LAT (top row), 1200 LAT (middle row) and 1500 LAT (bottom row) from the λS = 1.25 (left column), λS = 0.63 (middle column), and λS = 0.42 (right column) scale model configurations.  configurations. As with the previously discussed upward short- and longwave fluxes, these patterns result not from changing radiation source areas, but from ambient variations in surfaceatmosphere fluxes. In the λS = 1.25 array configuration (Figure 5.11a – 5.11c), the north-south sensor measures a much higher Q* value throughout the day from below roof level than does the east125  west sensor. For the morning traverse, the absolute difference in observed Q* is 240 W m-2. At solar noon this difference is 355 W m-2 and for the afternoon traverse, the Q* difference at zm/zb = 0.5 is 179 W m-2. The east-west sensor in fact measures a negative Q* value in the morning and solar noon traverses, implying that the upwelling long- and shortwave radiation fluxes overwhelm the incoming radiation fluxes at those times. As the corresponding time series plot (Figure 5.12a) shows, this pattern with negative daytime Q* below roof-level persists through the morning until approximately 1500 LAT, when the sensor is briefly (for less than one hour) exposed to direct insolation. a)  b)  400  E-W canyon  400 300  200  200  100  100  0  0  -100  -100 -200 0  6  12  18  24  0  6  Time (LAT)  E-W canyon  zm/zb = 2.5  12  18  24  Time (LAT)  d)  400  400  E-W canyon  zm/zb = 3.5  N-S canyon  300  200  200  N-S canyon  -2  Q* (W m )  300  -2  Q* (W m )  N-S canyon  -2  Q* (W m )  300  -200  c)  E-W canyon  zm/zb = 1.5  N-S canyon  -2  Q* (W m )  zm/zb = 0.5  100  100  0  0  -100  -100  -200  -200 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.12 Time series of net all-wave radiation (Q*) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 1.25 scale model configuration.  126  A similar below roof-level Q* pattern is evident for the 0900 and 1200 LAT traverses in the λS = 0.63 array configuration (Figure 5.11d), but in this case, the east-west sensor measures a greater Q* than the north-south sensor. The absolute difference in Q* between the sensors in the  λS = 0.63 array configuration at 0900 LAT is 207 W m-2 (Figure 5.11d). At solar noon (Figure 5.11e), the difference in observed Q* is 94 W m-2, although as Figure 5.13a illustrates, this difference between sensors at zm/zb = 0.5 in the λS = 0.63 array configuration grows larger just after solar noon (up to 140 W m-2 at 1245 LAT).  a)  b)  400  E-W canyon  zm/zb = 1.5  N-S canyon  300  N-S canyon  300 200 -2  -2  Q* (W m )  200 Q* (W m )  400  E-W canyon  zm/zb = 0.5  100  100  0  0  -100  -100  -200  -200 0  6  12  18  24  0  6  Time (LAT)  12  18  24  Time (LAT)  d)  c) 400  zm/zb = 2.5  E-W canyon  zm/zb = 3.5  N-S canyon  300  200  200 Q* (W m )  300  N-S canyon  -2  -2  Q* (W m )  400  E-W canyon  100  100  0  0  -100  -100  -200  -200 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.13 Time series of net all-wave radiation (Q*) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.63 scale model configuration.  127  This pattern also occurs during the morning traverse in the λS = 0.42 array configuration (Figure 5.11g), although the absolute difference in flux density measured by the two sensors from below roof level is not as great as in the more densely arranged scale model configurations (61 W m-2 versus 207 W m-2 in the λS = 0.63 array configuration and 240 W m-2 in the λS = 1.25 array configuration). At 1200 LAT the north-south sensor below roof level in the λS = 0.42 array configuration observes greater (by 20 W m-2) Q* than its east-west canyon counterpart (Figures 5.11h and 5.14a). The north-south sensor is exposed to more direct insolation at this time, given its position closer to the center of the intersection. a)  b)  350  zm/zb = 0.5  300  350  250  200  200 Q ↑ (W m )  250  E-W canyon  zm/zb = 1.5  300  N-S canyon  N-S canyon  -2  -2  Q* (W m )  E-W canyon  150 100  150 100  50  50  0  0  -50  -50  -100  -100 0  6  12  18  24  0  6  Time (LAT)  12  18  24  Time (LAT)  d)  c) 350  zm/zb = 2.5  250  200  200 Q* (W m )  250  E-W canyon  zm/zb = 3.5  300  N-S canyon  N-S canyon  -2  -2  Q* (W m )  300  350  E-W canyon  150 100  150 100  50  50  0  0  -50  -50  -100  -100 0  6  12 Time (LAT)  18  24  0  6  12  18  24  Time (LAT)  Figure 5.14 Time series of net all-wave radiation (Q*) at four sensor heights: zm/zb = 0.5 (a), zm/zb = 1.5 (b) zm/zb = 2.5 (c) and zm/zb = 3.5 (d) from the λS = 0.42 scale model configuration.  128  The absolute difference in observed Q* below roof level at around solar noon decreases with increasing building spacing and is related to the magnitude of direct insolation received by the sensors. The most open surface geometry allows for the greatest amount of incoming solar radiation to penetrate into the canyons. Results presented in the previous two sections suggest that variability between sensors in the upwelling long- and shortwave terms are not attributable to the upwelling radiation terms. For example, combining both upwelling radiation terms, the north-south sensor in the λS = 1.25 scale array configuration measures 134 W m-2 more than the east-west sensor (at solar noon and from below roof level). However, the corresponding difference in Q* at that time and location is 390 W m-2. This implies that the majority of the variability between the two sensors is attributable to differences in incoming shortwave radiation (i.e., solar exposure). In fact for all three scale model configurations, at no time can the difference in observed Q* from zm/zb = 0.5 be attributed primarily to the upwelling radiation fluxes. Within the context of field campaigns involving the observed urban surface energy budget, however, this is a largely irrelevant point as such studies usually do not conduct radiation flux measurements from within the urban canopy.  5.6 Summary of results Results from this scale model study measuring the spatial variability of upwelling short- and longwave radiation and net radiation from within and above two urban canyons suggest that: •  Radiation flux measurements conducted from above approximately 2.5 times the mean building height generate uniform flux density patterns that do not exhibit any appreciable variability in either the vertical or horizontal directions (assuming uniform fetch within the local scale of the study area) throughout the day.  129  •  At measurement heights below 2.5zb, variable solar exposure results in sunlit and shaded patterns amongst surface facets that produce inconsistent radiation flux source areas. The sensitivity to sensor placement grows more acute at and below roof level.  •  The 2.5zb measurement height threshold also corresponds to the level at and above which the relative proportion of surfaces ‘seen’ by a near-hemispherical FOV down-facing radiometer stabilizes and becomes constant with height (assuming uniform fetch such as the case of the three scale model configurations).  •  Although not explicitly undertaken here, outdoor scale models coupled with traditional radiation instrumentation could be used to complement and validate numerical modeling studies dealing with the measurement and interpretation of urban radiation budgets (e.g., Arnfield, 1982; Mills, 1993; Masson, 2000; Krayenhoff and Voogt, 2007a), in much the same way as Aida (1982) and Aida and Gotoh (1982) for shortwave radiation and Voogt and Oke (1991) for longwave radiation.  Given that differences in measured radiation fluxes are imperceptible from heights above 2.5zb, the challenge with respect to the measured radiation and energy balances then becomes ensuring that 1) the combination of surfaces contained in a radiation source area are representative of the complete, three dimensional surface of the site, and 2) the furthermost extent of the turbulence flux footprints lies within the confines of the radiative footprint. These conditions form the basis of the following chapter which pursues the final three objectives of this thesis.  130  Chapter 6  PROTOCOL TO GUIDE EXPOSURE OF RADIATION AND TURBULENT TRANSFER SENSORS  This chapter addresses the final three objectives listed in Chapter One: 1. Develop a protocol to guide the measurement of three-dimensional radiation flux source areas in urban environments. Drawing upon an established sensor-view model, the aim is to devise a technique to assess which surfaces are contained within the upwelling source area viewed by radiation sensors exposed at a given location. Further, to assess the suitability of that mix to represent the radiation budget for a local area. 2. Combine the radiation flux source area analyses with an established turbulent flux source area model to enable direct comparison of the spatial extent of the two flux source area types. 3. Suggest a protocol to guide the placement of radiation and turbulent flux sensors in a field array that is sensitive both to the properties of the instruments and the surface structure of the local site. Achieving these objectives requires the use of two numerical models. The analysis of threedimensional radiation flux source areas utilizes the Surface-sensor-sun Urban Model (SUM) of Soux et al. (2004), run for the Phoenix scale model. The SUM-derived analyses are combined with output from the simple parameterized turbulent flux source area scheme of Kljun et al. (2004) to consider radiation flux footprint dimensions in the context of turbulent flux footprint estimates.  131  6.1 Measurement protocol for radiant fluxes To develop a measurement protocol for radiation fluxes a set of criteria governing essential requirements of such observations is first established. In the case of stationary observations of the radiation budget with a single tower-mounted radiometer, two criteria are identified: 1. The desired radiometer field-of-view should contain the proportion of roof, wall, and road surfaces contained in the complete (three-dimensional) urban surface as closely as possible. 2. The desired radiometer field-of-view should contain those facets that are primarily responsible for driving the radiation budget of the system. For example, in the Northern Hemisphere, the facets should include those most exposed to insolation during the day, e.g., flat roofs, south-facing walls, east-facing walls in the morning, west-facing walls in the afternoon, and so on. The first criterion is strictly set by surface-sensor geometrical relations that do not need to take into account the varying solar position. The aim here is a comparison of the relative surface areas of individual facets contributing to a modeled FOV with the desired proportion of facets (which here comprises the three-dimensional or ‘complete’ surface area AC, as defined in Chapter One). The three broad surface facet categories – roof, wall, and road – are considered first. Following this simple case, individual facet orientation is considered, whereby the proportion of north-, south-, east-, and west-facing walls, street intersections, and north-south and east-west oriented streets is taken into account. The second criterion is more complex than the first in that it is an explicit consideration of surface-sensor-sun relations driving the measured radiation budget and is therefore temporally dynamic. The analysis is similar to that in the first criterion, in that it focuses on matching modeled sunlit and shaded surface areas for various sensor locations with the “actual” proportion of these facets over the complete surface area, AC. Whereas the first criterion considers just the 132  three broad facet categories and their relative orientations, this approach contains even more categories in that it considers the proportion of each facet that is either sunlit or shaded. Based on the Chi-square statistical test, an agreement index which quantifies the difference between the surface components actually included in a sensor’s FOV according to numerical simulations, and those ideally sought is defined: n  2  AI = [0.1 − ∑ ( Ai − Ai ,mod ) ] × 10  (6.1)  i =1  where i is an individual facet type which may be sunlit, shaded, or the sum of sunlit and shaded components, Ai is the desired proportion of that facet contained in the sensor FOV (the proportion of AC occupied by facet i), and Ai,mod is the proportion of i facet type within the modeled sensor FOV. The scaling constants in Eq. 6.1 allow for a range of AI values between 0 and 1.0 and minimizes clustering of values. Values approaching 1.0 indicate better overall agreement with the proportion of the FOV occupied by the facets sought. Ai is obtained by site survey or a three-dimensional surface database. For the sunlit facet case, Ai is obtained numerically (see section 6.2) and verified by visual inspection of infrared imagery.  6.2 SUM modeling approach For both criteria presented above, the SUM model is run for the three scale model configurations (λS = 1.25, 0.63 and 0.42, respectively), over a logistically feasible range of measurement heights (zm = 1.5 – 4.0zb), at the sixteen distinct sensor locations indicated by the black dots in Figure 6.1. There are nine measurement points above the roof surface (four roof corners, four roof edge midpoints, and the roof center), and because the ‘building’ size is constant in the three scale model configurations, these sensor locations are also unchanged. The remaining sensor locations are uniformly distributed along the street/canyon midpoint and intersection and are therefore positioned further from the ‘building’ as building spacing increases. The chosen sensor locations 133  Figure 6.1 Plan view schematic showing the 16 radiometer locations for which the SUM model is run. While the sensor locations along the roof remain static for each of the three scale model configurations, the relative locations of the street/canyon midpoint sensor locations change with increasing building spacing.  represent one complete building lot of the surface and are focused on the same central ‘building’ over which the CNR1 radiometer was positioned in the scale model experiment. The model is run for a 150° sensor FOV, which is equivalent to the field-of-view of the CNR1 pyrgeometer. Focusing the sixteen sensor positions on the center ‘building’ of the scale model configurations ensures that even from the highest measurement level, at four times the building height, the sensor FOV is entirely contained within the perimeter of the scale model array. Although the SUM model calculates the view factors of the urban surface components for a given sensor, those outputs are not used in the analysis here. Because view factors are, by definition, the proportion of all the radiation output from one surface that is intercepted by another (Oke, 1987), comparing modeled view factors with relative surface areas (Ai in Equation 6.1) is not appropriate. Instead, the total number of sunlit and shaded surface pixels for each facet type (e.g., north-facing walls, roof, east-west road, etc.) contained within the modeled  134  sensor FOV is used to calculate the relative proportion of sunlit, shaded, and total facet types ‘seen’ by the sensor at each location. In the case of the first criterion (matching the proportion of facet types, independent of solar exposure), the sunlit and shaded pixels ‘seen’ for a particular facet are combined to give a total facet contribution of all roofs, roads, and walls to the sensor FOV. Distinguishing between the relative surface areas of shaded and sunlit facets is only considered in the second criterion and to do so, the model is prescribed with solar azimuth and zenith angles at 0900, 1200, and 1500 LAT on the three identified IOP days.  6.3 SUM model results Results herein focus on the agreement index (Equation 6.1) calculated for a range of modeled sensor positions and under varying solar regimes. For a more detailed account of the results of individual SUM model runs, the reader is directed to Appendix D, which contains a series of stacked bar plots comparing model output with the actual proportion of surface components (sunlit and shaded and total) comprising the surface.  6.3.1 Matching facet types Achieving the first measurement criterion – that the desired radiometer field-of-view contains as close as possible the proportion of roof, wall, and road surfaces as is contained in the complete urban surface representation (AC) – requires that the proportion of roof, wall, and road surfaces contained within the modeled sensor FOV be compared to the actual occurrence of those facets in each configuration of the scale model. For the λS = 1.25 configuration, roofs comprise 21% of the complete surface area, while walls and roads comprise 53% and 26%, respectively (see Table 3.4). These morphometric proportions are static, for they do not depend on solar or sensor position, and are shown by the right-most stacked bar plots in Figures 6.2a-c. The sixteen sensor locations for which SUM is run are also plotted for zm /zb = 1.5 (Figure 6.2a), zm /zb = 2.5 (Figure 135  z m /z b = 1.5  a) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5  6  7  8  ROOFS  9  10  11  12  WALLS  13  14  15  16  Actual  ROADS  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  11  12  13 14 ROADS  15  16  Actual  11  12  13 14 ROADS  15  16  Actual  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  Figure 6.2 Stacked bar plots of the contribution of roof, wall, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 1.25 scale model configuration. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 136  6.2b) and zm/zb = 3.5 (Figure 6.2c). Not surprisingly, the variability of surfaces ‘seen’ from each location diminishes with increasing sensor height. The same is true for the two more open scale model configurations (not shown; refer to Appendix D). From zm/zb = 3.0 and above, the radiometer ‘sees’ a fairly uniform, but biased, proportion of facets regardless of sensor position. The fraction of road surface viewed by the sensor above 3.0zb in the λS = 1.25 configuration is less than the actual amount (20% vs. 26%). The radiometer also ‘sees’ more roofs (35% vs. 21%) and fewer walls (45% vs. 53%) than are represented in AC. Similar patterns arise to varying degrees for the other two scale model configurations. From zm /zb = 3.0 and above in the λS = 0.63 configuration, the radiometer ‘sees’ more roofs than those represented in AC (20% vs. 15%), fewer walls (31% vs. 39%) and similar amounts of road surfaces (49% vs. 46%) (not shown; refer to Appendix D). At the upper-most heights in the λS = 0.42 configuration, the proportion of roof surfaces viewed by the radiometer matches that within AC, while the walls are under-estimated (19% vs. 29%), and the roads over-estimated (70% vs.  60%) in the radiometer FOV (see Appendix D). The degree to which the facets contained in the modeled sensor FOV agree with AC is demonstrated in Tables 6.1a – 6.1c. These tables show the agreement indices corresponding to the sixteen sensor locations and from six above roof-level measurement heights. For each sensor height, the location with the highest level of agreement is shown in bold typeface; the poorest agreement at each height is denoted by the highlighted cells. For the λS = 1.25 configuration (Table 6.1a) the greatest average agreement amongst all sensor locations occurs from zm /zb = 2.0 to zm /zb = 3.0. For heights above twice the building height, placing the sensor above or close to the street intersection produces the best agreement with AC. At the lowest sensor height (zm /zb = 1.5), the best correspondence with AC occurs when the sensor is located above the canyon midpoint, be it directly or partially over a road. Figure 6.3 combines these results in a series of contour plots, one for each measurement height, where the red box indicates the building 137  Table 6.1a Summary of agreement indices (AI) for the simple case of matching the proportion of three broad facet categories -- roof, wall, and road -- at sixteen radiometer positions (lefthand column) and at six above roof-level measurement heights (zm/zb) in the λS = 1.25 scale model configuration. Values in bold indicate the best agreement at each sensor height and highlighted cells indicate the poorest overall agreement for each sensor height.  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.13 0.82 0.48 0.52 0.81 0.53 0.92 0.92 0.29 0.92 0.60 0.63 0.51 0.92 0.67 0.68  0.75 0.92 0.89 0.93 0.92 0.86 0.96 0.97 0.78 0.92 0.91 0.94 0.92 0.97 0.98 0.99  0.79 0.76 0.87 0.89 0.76 0.70 0.84 0.86 0.79 0.74 0.86 0.88 0.89 0.86 0.92 0.92  0.75 0.92 0.89 0.93 0.92 0.86 0.96 0.97 0.78 0.92 0.91 0.94 0.92 0.97 0.98 0.99  0.56 0.56 0.63 0.63 0.56 0.55 0.63 0.63 0.56 0.56 0.63 0.63 0.63 0.63 0.68 0.68  0.48 0.48 0.54 0.55 0.48 0.49 0.55 0.54 0.48 0.49 0.55 0.55 0.55 0.54 0.60 0.60  Table 6.1b Same as for Table 6.1a, except that λS = 0.63.  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.01 0.09 0.10 0.15 0.10 0.27 0.46 0.53 0.01 0.10 0.14 0.22 0.22 0.53 0.42 0.43  0.52 0.55 0.69 0.69 0.56 0.61 0.71 0.73 0.53 0.56 0.70 0.70 0.70 0.73 0.82 0.83  0.71 0.70 0.81 0.87 0.70 0.70 0.82 0.87 0.71 0.70 0.82 0.87 0.87 0.87 0.93 0.97  0.83 0.83 0.90 0.91 0.84 0.83 0.90 0.91 0.84 0.84 0.90 0.91 0.91 0.91 0.95 0.95  0.86 0.87 0.91 0.92 0.88 0.88 0.92 0.93 0.87 0.88 0.92 0.92 0.92 0.93 0.95 0.95  0.88 0.88 0.92 0.93 0.88 0.88 0.92 0.93 0.88 0.88 0.92 0.93 0.93 0.93 0.95 0.95  footprint and the edges of each figure correspond to the street/canyon midpoint. Darker contours indicate the poorest agreement with AC, with lighter colors pointing to more ideal locations for siting radiation instrumentation 138  zm/zb =1.5  zm/zb =2.0  zm/zb =2.5  zm/zb =3.0  zm/zb =3.5  zm/zb =4.0  Figure 6.3 Contour plots of the agreement index for 16 radiometer locations (see Figure 6.1) at six heights above roof level for the λS = 1.25 scale model configuration. The red square represents the building footprint and the streets are along the bottom and right perimeters (the right and bottom edges of the figures correspond to the street midpoints). North is at the top of each figure. Lighter tones indicate strongest agreement with AC (the proportion of surfaces sought to be contained in the sensor FOV). Contour lines are drawn every 0.05.  139  As in the λS = 1.25 configuration, the greatest average agreement over all sensor locations in the λS = 0.63 configuration (Table 6.1b) occurs at greater than two times the building height, and that at every height, positioning the sensor close to the street intersection results in the highest level of agreement with AC. The poorest agreement occurs when the sensor head is positioned directly above the roof center or at the building edges. The contour plots (Figure 6.4) further highlight that the farther the sensor is from the surface, the better the agreement with AC.  Table 6.1c Same as for Table 6.1a except that λS = 0.42.  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.01 0.01 0.21 0.15 0.01 0.01 0.26 0.25 0.01 0.01 0.21 0.15 0.15 0.25 0.39 0.27  0.22 0.20 0.43 0.54 0.20 0.20 0.42 0.51 0.22 0.20 0.43 0.54 0.54 0.51 0.69 0.77  0.54 0.56 0.67 0.65 0.56 0.57 0.68 0.65 0.54 0.56 0.67 0.65 0.65 0.65 0.75 0.74  0.65 0.64 0.74 0.76 0.64 0.63 0.73 0.77 0.65 0.64 0.74 0.76 0.76 0.77 0.83 0.84  0.73 0.73 0.79 0.80 0.73 0.73 0.80 0.80 0.73 0.73 0.79 0.80 0.80 0.80 0.86 0.86  0.86 0.77 0.78 0.83 0.83 0.78 0.78 0.83 0.83 0.77 0.78 0.83 0.83 0.83 0.83 0.88  Similar conclusions are reached in the λS = 0.42 configuration (Table 6.1c), although the overall strength of agreement from all measurement locations and heights is less than in the previous two cases. This suggests that as building spacing increases, the ability to match what is contained within the radiometer FOV to actual three-dimensional surface structure of the site decreases. The contour plots from this surface configuration (Figure 6.5) show that for every measurement level, the sensor achieves the greatest agreement with AC when positioned near the intersection.  140  zm/zb =1.5  zm/zb =2.0  zm/zb =2.5  zm/zb =3.0  zm/zb =3.5  zm/zb =4.0  Figure 6.4 Same as 6.3 except for λS = 0.63 scale model configuration.  141  zm/zb =1.5  zm/zb =2.0  zm/zb =2.5  zm/zb =3.0  zm/zb =3.5  zm/zb =4.0  Figure 6.5 Same as 6.3 except for λS = 0.42 scale model configuration.  The added complexity of matching individual facets with different orientations (Table 6.2a – 6.2c) produces results generally similar to those in the simple case above. In the λS = 1.25 142  Table 6.2a Summary of agreement indices (AI) for matching the proportion of all individual roof, wall, and road surface facets at sixteen radiometer positions (lefthand column) and at six above roof-level measurement heights (zm/zb) in the λS = 1.25 scale model configuration. Values in bold indicate the best agreement at each sensor height and highlighted cells indicate the poorest overall agreement for each sensor height.  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.50 0.57 0.68 0.68 0.57 0.86 0.69 0.65 0.55 0.67 0.71 0.71 0.68 0.65 0.81 0.82  0.83 0.85 0.90 0.91 0.85 0.90 0.92 0.92 0.84 0.87 0.91 0.92 0.91 0.92 0.97 0.98  0.83 0.80 0.88 0.88 0.80 0.76 0.85 0.87 0.82 0.79 0.87 0.88 0.88 0.87 0.93 0.93  0.73 0.71 0.78 0.79 0.71 0.69 0.76 0.77 0.72 0.70 0.77 0.78 0.79 0.77 0.83 0.84  0.64 0.65 0.69 0.70 0.65 0.64 0.70 0.69 0.64 0.64 0.69 0.69 0.70 0.69 0.74 0.74  0.58 0.59 0.63 0.63 0.59 0.59 0.63 0.63 0.58 0.59 0.63 0.63 0.63 0.63 0.67 0.68  configuration the overall average agreement amongst all sensor heights and positions is nearly identical (AI = 0.74 in the simple case; AI = 0.75 when facet orientation is taken into account). In both cases, the best agreement occurs when the sensor is mounted between two to three times the building height, at a position close to the intersection (Table 6.2a). The largest departure between the simple and most complex case with regards to optimal sensor placement occurs at the lowest measurement height. In the more complex case, a sensor mounted above the center of the roof is able to capture more of the desired facets from 1.5zb, as it equally ‘sees’ all four wall facets and both street orientations. The only other position from which this is possible is above the intersection. The roof center location in the simple case, on the other hand, does not produce a strong agreement at this measurement height (Table 6.1a). A slightly different scenario arises when the building spacing increases to λS = 0.63. The value of AI amongst all sensor heights and positions in the simple, three-facet category case is 0.74. In the more complex case (Table 6.2b), it is notably higher, at 0.87. The overall pattern of 143  Table 6.2b Same as for Table 6.2a, except that λS = 0.63.  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.45 0.49 0.57 0.61 0.52 0.71 0.62 0.70 0.46 0.52 0.59 0.64 0.64 0.70 0.71 0.71  0.82 0.84 0.86 0.85 0.85 0.88 0.88 0.88 0.83 0.85 0.86 0.86 0.86 0.88 0.90 0.89  0.88 0.88 0.91 0.94 0.88 0.88 0.91 0.94 0.89 0.88 0.92 0.94 0.94 0.94 0.96 0.99  0.93 0.93 0.95 0.95 0.93 0.93 0.95 0.96 0.93 0.93 0.95 0.95 0.95 0.96 0.97 0.98  0.94 0.94 0.95 0.95 0.95 0.95 0.96 0.96 0.94 0.95 0.95 0.95 0.95 0.96 0.96 0.96  0.93 0.93 0.95 0.95 0.93 0.92 0.94 0.95 0.93 0.93 0.95 0.95 0.95 0.95 0.96 0.97  optimal agreement is the same in both the simple and more complex cases, in that the sensor should be mounted above the road or street intersection at a height greater than 2.5zb. Similar to the λS = 1.25 configuration, the largest differences between the two cases occurs at the lowest measurement height. Although in both cases the poorest agreement occurs when the sensor is mounted along the roof edge or corner, a sensor is able to ‘see’ more of the sought-after individual surfaces when facet orientation is taken into account. The overall average agreement amongst all sensor heights and locations in the λS = 0.42 scale model configuration (Figure 6.2c) varies considerably between the simple and more complex case (0.59 vs. 0.83, respectively). In both cases, the average correlation between what is ‘seen’ by the sensor and what is sought after grows with increasing measurement height. Not surprisingly, the worst agreement occurs at the measurement level closest to the surface (1.5zb). The progressively larger difference in AI for the two cases as building spacing increases indicates that in order to maximize the proportion of the true, ‘complete’ urban surface ‘seen’ by  144  Table 6.2c Same as for Table 6.2a, except that λS = 0.42. AI (zm/zb = 1.5)  AI (zm/zb = 2.0)  AI (zm/zb = 2.5)  AI (zm/zb = 3.0)  AI (zm/zb = 3.5)  AI (zm/zb = 4.0)  0.61 0.63 0.69 0.62 0.63 0.64 0.72 0.67 0.61 0.63 0.69 0.62 0.62 0.67 0.69 0.61  0.67 0.65 0.74 0.81 0.65 0.62 0.73 0.79 0.67 0.65 0.74 0.81 0.81 0.79 0.87 0.92  0.85 0.86 0.88 0.86 0.86 0.86 0.89 0.87 0.85 0.86 0.88 0.86 0.86 0.87 0.89 0.86  0.87 0.86 0.90 0.91 0.86 0.85 0.89 0.91 0.87 0.86 0.90 0.91 0.91 0.91 0.94 0.95  0.91 0.91 0.93 0.92 0.91 0.91 0.93 0.93 0.91 0.91 0.93 0.92 0.92 0.93 0.94 0.94  0.92 0.91 0.93 0.94 0.91 0.91 0.93 0.94 0.92 0.91 0.93 0.94 0.94 0.94 0.96 0.97  NW roof corner N roof midpoint NE roof corner N-S road N endpoint W roof midpoint Roof center E roof midpoint N-S road midpoint SW roof corner S roof midpoint SE roof corner N-S road S endpoint E-W road W endpoint E-W road midpoint E-W road E endpoint Intersection  a down-facing radiometer, an explicit consideration of facet orientation, not just simply broad facet type, should be attempted. Regardless of building spacing, some general features can be extracted from these considerations. The following recommendations can be made: •  Matching the relative proportions of the three primary facet types (roofs, roads, walls) ‘seen’ by a radiometer with those which describe the actual surface morphology (AC) is best achieved when the sensor is positioned over a street intersection and mounted at a height of at least two times the building height.  •  Mounting the sensor directly over a roof, as is often done for logistical ease or safety in contemporary urban surface-atmosphere flux measurement campaigns, results in the poorest correspondence with AC (at measurement heights at least two times the average building height).  145  •  Moving the sensor away from the center of the center of the roof and closer to a canyon midpoint or intersection implies the radiometer will derive its signal from a more representative sample of the three-dimensional surface.  •  Although the explicit consideration of the orientation of the individual facets comprising the three facet categories is slightly more difficult to characterize than the simple three facet-type case, this added complexity produces better overall correspondence with AC.  6.3.2 Matching sunlit surfaces The objective of maximizing the fraction of radiatively active (sunlit) roof, wall, and road surfaces in the radiometer FOV produces results similar to those found in the previous two cases (Tables 6.3a – 6.3c). The measurement height that results in the best agreement with the actual breakdown of sunlit surfaces in the λS = 1.25 scale model configuration is found at around 2.02.5zb (Table 6.3a). Agreement decreases with increasing measurement height. At all times of the day, sunlit surfaces are better ‘seen’ from measurement locations near the intersection/canyon endpoints. The roof center is the least ideal location, for the radiometer FOV is dominated by roof surfaces and the sensor is unable to ‘see’ the sunlit east-, south- and west-facing wall components comprising the relatively tight canyons. The proportion of sunlit surfaces ‘seen’ by a radiometer in the λS = 0.63 scale model case (Table 6.3b) is maximized at three times the building height, from measurement locations above the roof center or the southern portion of the roof. In this surface arrangement, siting the radiometer along the roads and intersection is generally the least preferred. These results are contrary to the more closely spaced together λS = 1.25 scale model configuration. Compared with the λS = 1.25 scale model configuration, the λS = 0.63 case also produces stronger overall correlation between the actual proportion of sunlit surfaces and those ‘seen’ by a radiometer.  146  Table 6.3a For all sunlit surfaces in the λS = 1.25 scale model configuration, a summary of the radiometer locations at which the best and poorest agreement occurs at every height. Average agreement for all 16 sensor locations at each height is on the far right column. N/A refers to those cases where the agreement index amongst the 16 sensor locations is within 0.02.  0900 LAT  Best Agreement  Poorest Agreement  Value  Value  z/zb = 1.5  0.79  z/zb = 2.0  0.98  z/zb = 2.5  0.99  z/zb = 3.0  0.98  z/zb = 3.5 z/zb = 4.0  Location Roof center  0.58  Location Intersection  0.69  Roof center, S roof midpoint S roof midpoint Intersection, N-S road S endpoint  0.96  0.96  Intersection, E-W road E endpoint  0.93  Roof center, NW roof corner, N/W roof midpoint  0.95  0.94  Intersection, E-W road E endpoint  0.91  NW/SW roof corner, N/W roof midpoint  0.92  z/zb = 1.5  0.68  Roof center  0.45  E-W road W endpoint  0.59  z/zb = 2.0  0.96  0.80  E-W road midpoint  0.89  z/zb = 2.5  0.95  0.90  E-W road  0.93  z/zb = 3.0  0.91  E roof midpoint SE roof corner, E roof midpoint, N-S road N/A  0.89  N/A  0.90  z/zb = 3.5  0.89  SE roof corner, E-W road E endpoint  0.86  Roof center, NW/SW roof corner, N/W roof midpoint  0.87  0.86  Intersection, SE roof corner, E roof midpoint, N-S road S endpoint, E-W road E endpoint  0.82  NW roof corner  0.84  z/zb = 1.5  0.98  Roof center  0.88  E-W road W endpoint  0.93  z/zb = 2.0  0.99  0.93  Roof center  0.97  z/zb = 2.5  0.95  0.80  Roof center  0.89  z/zb = 3.0  0.88  0.74  0.81  z/zb = 3.5  0.79  Intersection, E-W road E endpoint  0.70  z/zb = 4.0  0.74  Intersection  0.65  Roof center Roof center, NW, SW roof corner, N, S roof midpoint Roof center, NW, SW roof corner, N, S roof midpoint  0.91  0.95  Intersection, E-W road E endpoint E-W road E endpoint Roof center, W roof midpoint  Overall Average  0.95 0.98 0.97  1200 LAT  z/zb = 4.0  1500 LAT Intersection, E-W road E endpoint Intersection, E-W road E endpoint Intersection  0.74  0.68  147  Table 6.3b Same as for Table 6.3a, except that λS = 0..63.  0900 LAT z/zb = 1.5  Best Agreement  Poorest Agreement  Value 0.80  Value 0.69  Location Intersection  Overall Average 0.77  0.85  Intersection  0.90  0.93  NE roof corner, E roof midpoint, E-W road E endpoint  0.94  z/zb = 2.0  0.94  z/zb = 2.5  0.96  z/zb = 3.0  0.98  z/zb = 3.5 z/zb = 4.0  Location Roof center Roof center, S roof midpoint SW roof corner, S roof midpoint  0.94  E-W road E endpoint  0.96  0.98 0.98  Roof center, S roof midpoint, SW roof corner N/A N/A  0.96 0.96  N/A N/A  0.97 0.97  1200 LAT z/zb = 1.5  0.78  Roof center  0.64  0.70  z/zb = 2.0  0.94  Roof center  0.84  NW roof corner Intersection, E-W road E endpoint  z/zb = 2.5  0.94  SW roof corner, S roof midpoint, N-S road S endpoint, E-W road W midpoint and W endpoint  0.91  E roof midpoint  0.93  z/zb = 3.0  0.97  Roof center, SW roof corner, S roof midpoint  0.93  Intersection, E-W road E endpoint  0.95  z/zb = 3.5  0.97  0.94  Intersection, E-W road midpoint and E endpoint  0.95  z/zb = 4.0  0.96  0.94  N/A  0.95  1500 LAT z/zb = 1.5  0.81  0.70  Intersection  0.77  z/zb = 2.0  0.94  0.87  Intersection  0.91  z/zb = 2.5  0.97  0.94  E-W road midpoint  0.96  z/zb = 3.0  0.99  0.96  E-W road  0.98  z/zb = 3.5 z/zb = 4.0  0.99 0.99  0.97 0.98  N/A N/A  0.98 0.98  Roof center, SW roof corner, S/W roof midpoint N/A  N-S road midpoint Roof center, S roof midpoint N-S road S endpoint Roof center, SW/SE roof corner, S roof midpoint N/A N/A  0.89  In the λS = 0.42 scale model configuration radiometer heights of approximately 3.5zb results in the best outcome (Table 6.3c). From measurement levels above 3.0zb, the sensitivity to sensor placement with respect to the roof or street surfaces is not significant (i.e., the difference 148  Table 6.3a Same as for Table 6.3a, except that λS = 0.42.  0900 LAT  Best Agreement  Poorest Agreement  Value  Value  Location  Location  Overall Average  z/zb = 1.5  0.89  Roof center, NW/SW roof corner, N/W/S roof midpoint  0.80  Intersection  0.87  z/zb = 2.0  0.94  Intersection  0.90  E roof midpoint, road midpoint  0.92  z/zb = 2.5  0.97  z/zb = 3.0  0.91  Intersection  0.95  0.97  Roof center, N/W/S roof midpoint, SW roof corner N/A  0.95  0.96  z/zb = 3.5  0.99  S roof midpoint  0.96  0.97  z/zb = 4.0  0.98  N/A  0.97  N/A Intersection, E-W road E endpoint N/A  1200 LAT z/zb = 1.5 z/zb = 2.0  0.88 0.94  0.72 0.81  Intersection Roof center  0.82 0.87  z/zb = 2.5  0.96  0.90  Intersection  0.95  z/zb = 3.0  0.97  0.94  E roof midpoint  0.96  z/zb = 3.5  0.99  0.96  Intersection  0.97  z/zb = 4.0  0.98  N/S roof midpoint Intersection Roof center, N/W/S roof midpoint, NW/SW roof corner Roads, intersection Roof center, S roof midpoint N/A  0.96  N/A  0.97  0.98  1500 LAT z/zb = 1.5  0.88  SE/NE roof corner, E roof midpoint  0.80  Intersection  0.85  z/zb = 2.0  0.95  Intersection  0.90  E-W road midpoint and W endpoint  0.92  z/zb = 2.5  0.97  N/S/E roof midpoint, roof center, SE roof corner, N-S road midpoint  0.92  Intersection  0.96  z/zb = 3.0 z/zb = 3.5 z/zb = 4.0  0.98 0.99 0.99  N/A N/A N/A  0.97 0.97 0.98  N/A N/A N/A  0.97 0.98 0.98  in agreement between the best and worst locations at heights above 3.0zb is very small). Combined with simulations from the λS = 1.25 and λS = 0.63 scale model configurations, it is apparent that the ease with which a radiometer is able to ‘see’ the pertinent sunlit surfaces  149  improves with increased building spacing. The sunlit and shaded patterns associated with a wider canyon formulation are less complex and more sunlit surfaces are present to be viewed.  6.4 Comparison of radiant with turbulent flux source areas Urban radiation observation measurements from towers are often conducted as part of an energy balance study. The sensors used in such studies usually comprise a net pyrradiometer (or several radiometers capable of being combined to give the net radiation) and one or more fast-response sensors capable of giving the turbulent fluxes of sensible and latent heat via the eddy covariance technique. If the resulting surface energy balance is to have internal integrity the sensor source areas for both the radiant and turbulent fluxes whilst not identical should at least be similar. Such similarity should be representative of the scale of the contributing sources and sinks and ideally the source areas should physically overlap to a significant extent. Evidence of the correspondence between the two types of source areas is rarely if ever given in field experimental studies. .  In order to provide the information necessary to properly underpin the design of an  observation protocol to obtain internally consistent surface energy balances at urban sites the following potential criteria are investigated: 1. The height at which a 150° FOV radiometer must be exposed so that the radiation source area fully encompasses the longitudinal dimension (fetch) of a desired turbulent flux cumulative footprint isopleth level (e.g., 70%, 90%). 2. The height at which a 150° FOV radiometer must be exposed so that the radiation source area fully encompasses the location of peak source strength of the turbulent flux footprint. The correspondence between radiant and turbulent flux source areas is investigated in the following way. The representiveness of the radiation source area is assessed using the radiation 150  relations derived from the Phoenix scale model experiments. No measurements of atmospheric turbulent fluxes or their footprints were conducted at the site of the scale model, so the ability to assess turbulence source areas is constrained.  In lieu of such measurements, the simple  parameterized turbulent flux source area scheme of Kljun et al. (2004) is run for a set of idealized atmospheric and surface conditions. The scheme is used to generate estimates of the streamwise dimension of the cumulative footprint estimate (xR) and the distance of the maximum source weight location (xmax) of the footprint function from an idealized tower location (Figure 6.6). This makes it possible to formulate a set of equations relating the measurement height for the radiation fluxes to that of the turbulent flux measurements, as a function of surface roughness and atmospheric stability.  Figure 6.6 Schematic of relative locations and furthest upwind distance from an idealized measurement tower of the 50%, 70% and 90% turbulent flux footprint isopleths. The distance from the tower of the maximum source weight location (xmax) of the footprint function is approximated by the black dot.  151  Model inputs used to define stable, neutral, and convective atmospheric conditions for all model runs are provided in Table 6.4. Four values of roughness length, z0, corresponding to urban terrain, are considered: 0.5 m (low-density suburban), 1.0 m (medium-density suburban), 3.0 m (high-density urban) and 5.0 m (high-density urban/multi-storey blocks) (Oke, 1987). The scheme is run to generate xR at the furthest 50%, 70%, and 90% footprint levels and for turbulent flux measurement heights from 1.25 to 4.0 (run for every 0.25zb) times the building height. The reference building height is taken to be 7.5 m and 15 m, corresponding to the full-scale dimensions of the Phoenix scale model arrays (see Table 3.2).  Table 6.4 Model input parameters defining atmospheric stability for the Kljun et al. (2004) turbulence flux footprint scheme. Stability Class  Standard deviation of vertical velocity σw, m s-1  Convective 1.0 Neutral 0.6 Stable 0.3 Source: Oke (1987), Stull (2000)  Surface friction velocity u*, m s-1  Planetary boundary layer depth, m  0.2 0.8 0.5  2000 1000 200  6.4.1 Matching radiation source areas to turbulent flux footprint estimates (xR) For each surface roughness value within each atmospheric stability class, the distance from the tower at which the furthest 50%, 70%, and 90% cumulative turbulent flux footprint isopleths occur (xR) is calculated and used as the basis for back-calculating the measurement height required for a 150° FOV down-facing radiometer to ‘see’ out to the appropriate xR isopleth level. Under convective atmospheric conditions (Figure 6.7), when turbulent flux footprints originate closer to the tower, the radiometer can be positioned at or below the turbulent flux sensor in order to ‘see’ the 50% isopleth. To encompass the 70% and 90% turbulent flux isopleths, the radiometer must be raised to about two times the height of the turbulent flux sensor. As atmospheric stability turns to neutral (Figure 6.8) and stable (Figure 6.9) conditions, the upwind  152  a)  50% turbulent flux isopleth  10  zm /zb (Radiation)  Low-density Medium-density  8  High-density High-density (2)  6 4 2 0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  3.5  4.0  3.5  4.0  z m /z b (Turbulent)  b)  70% turbulent flux isopleth  10  zm /zb (Radiation)  Low-density Medium-density  8  High-density High-density (2)  6 4 2 0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  c)  90% turbulent flux isopleth  10  zm /zb (Radiation)  Low-density Medium-density  8  High-density High-density (2)  6 4 2 0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  Figure 6.7 Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50% (a), the 70% (b) and the 90% turbulent flux footprint isopleth (c), scaled in terms of building height, for convective atmospheric conditions.  153  a)  50% turbulent isopleth  40 Low-density  zm /zb (Radiation)  Medium-density  30  High-density High-density (2)  20  10  0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  3.5  4.0  3.5  4.0  z m /z b (Turbulent)  b)  70% turbulent flux isopleth  40  Low-density  zm /zb (Radiation)  Medium-density  30  High-density High-density (2)  20  10  0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  c)  90% turbulent flux isopleth  40  Low-density  zm /zb (Radiation)  Medium-density  30  High-density High-density (2)  20  10  0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  Figure 6. 8 Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50% (a), the 70% (b) and the 90% turbulent flux footprint isopleth (c), scaled in terms of building height, for neutral atmospheric conditions.  154  a)  50% turbulent flux isopleth  50  zm /zb (Radiation)  Low-density Medium-density  40  High-density High-density (2)  30 20 10 0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  3.5  4.0  3.5  4.0  z m /z b (Turbulent)  b)  70% turbulent flux isopleth  50  zm /zb (Radiation)  Low-density Medium-density  40  High-density High-density (2)  30 20 10 0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  c)  90% turbulent flux isopleth  50  zm /zb (Radiation)  Low-density Medium-density  40  High-density High-density (2)  30 20 10 0 1.0  1.5  2.0  2.5  3.0  z m /z b (Turbulent)  Figure 6.9 Measurement height of a 150° FOV radiation sensor versus the height of the turbulent flux measurement required to encompass the 50% (a), the 70% (b) and the 90% turbulent flux footprint isopleth (c), scaled in terms of building height, for stable atmospheric conditions.  155  extent of the turbulent flux footprints grow, and so too do the necessary radiometer heights to maintain correspondence. The proportional relationships between the two sensor heights generate a single multiplier relating the necessary radiometer height as a function of the measurement height of the turbulent flux for each atmospheric stability class and surface roughness category (Table 6.5). For example, under neutral atmospheric conditions (commonly observed in urban areas) and the greatest surface roughness (z0 = 5.0 m), the radiometer must be positioned approximately two times the height of the turbulent flux sensor in order to include the 50% isopleth. The height requirement grows to nearly three times to achieve the 70% isopleth, and to over four times the height of the turbulence sensor to ‘see’ out to the 90% turbulent flux isopleth.  Table 6.5 Measurement height (multiplier times the height of the turbulent flux measurement level) to site a 150° FOV radiometer so as to ‘see’ out to 50%, 70%, and 90% turbulent flux footprint isopleths, for each atmospheric stability class and four surface roughness categories. Atmospheric Stability Stable  Neutral  Convective  Surface Roughness  Multiplier for 50% Multiplier for 70% Multiplier for 90% isopleth agreement isopleth agreement isopleth agreement  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0) Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0) Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0)  5.60 4.66 3.16 2.46 4.69 3.90 2.64 2.06 1.03 0.85 0.58  7.86 6.53 4.43 3.46 6.57 5.46 3.71 2.89 1.44 1.20 0.81  11.69 9.78 6.64 5.18 9.85 8.19 5.55 4.33 2.16 1.79 1.22  High-density (z0 = 5.0)  0.45  0.63  0.95  Plotting the ratio of radiometer height to turbulent sensor height, y, versus R (percentage of the turbulent flux footprint included within a certain distance from the measurement point) results in a curvilinear relation in the form: zm(Rad)/zm(Turb) = aR2 + bR + c, and R is in %  156  (Figure 6.10). The fitted coefficients a, b, and c for each roughness category and atmospheric stability class are provided at the right of each plot in Figure 6.10. These relationships are of particular use when the measurement objective is to achieve a known value of R. Conversely, when the axes are reversed, a curvilinear relation expressing R as a function of the adequate radiometer measurement height results (Figure 6.11).  6.4.2 Matching radiation source areas to the maximum turbulence flux source weight location (xmax) In many cases, the necessary measurement height for a radiometer to include the streamwise extent of the turbulent flux footprint fully is impractically large, particularly for large values of R in neutral or stable atmospheric conditions. One alternative is to consider the radiometer measurement height which encompasses the maximum source weight function location xmax. This value is independent of R and is generally located closer to the tower, at a distance that approximately corresponds to the 36% turbulent flux isopleth (Figure 6.6). Since xmax is the longitudinal distance from which the strongest turbulent flux contribution originates, it can be thought of as the absolute minimum along-wind distance away from the tower which must be included in the measured signal. Figure 6.12 summarizes the relationship between the heights at which a radiometer must be positioned in order to ‘see’ to the xmax isopleth level for a range of turbulent flux sensor heights (normalized by building height). As in the previous analyses, stable, neutral, and convective atmospheric conditions are considered, as are four classes of surface roughness. Again, a straightforward linear relationship exists between the two sensor heights. The slope of each line represents the value by which the turbulent flux sensor height must be multiplied in order for the 150° FOV radiometer to include the xmax isopleth level (Table 6.6). In general, the necessary radiometer heights for xmax are more logistically feasible than for the larger isopleth 157  a)  14 Low-density  Convective Conditions  Medium-density  12  Surface Roughness  zm (Rad)/zm (Turb)  High-density High-density  10  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  8 6 4 2  a  b  c  0.0004  -0.026  1.362  0.0003  -0.019  1.025  0.0002  -0.155  0.793  0.0002  -0.012  0.613  a  b  c  0.0018  -0.116  6.115  0.0015  -0.098  5.116  0.0010  -0.062  3.334  0.0008  -0.050  2.654  a  b  c  0.0020  -0.123  6.819  0.0017  -0.114  6.023  0.0012  -0.078  4.096  0.0009  -0.058  3.110  0 40  50  60  70  80  90  100  R (% )  b)  14 Neutral Conditions  Low-density Medium-density  12  zm (Rad)/zm (Turb)  High-density  Surface Roughness  High-density  10  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  8 6 4 2 0 40  50  60  70  80  90  100  R (% ) 14  c)  Stable Conditions  Low-density Medium-density  12  Surface Roughness  zm (Rad)/zm (Turb)  High-density High-density  10  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  8 6 4 2 0 40  50  60  70  80  90  100  R (% )  Figure 6.10 Measurement height of a 150° FOV radiation sensor (expressed in terms of the height of the turbulent sensor) versus R for four surface roughness categories under convective (a), neutral (b), and stable (c) atmospheric conditions (left). The resulting curvilinear relationships take the form zm(Rad)/zm(Turb) = aR2 + bR + c and are fitted with coefficients given in the tables to the right of each graph. 158  a) 100 Surface Roughness  80  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  R (%)  60  40 Low-density Medium-density  20  a  b  c  -18.586  94.689  -27.811  -24.728  107.840  -23.794  -59.650  169.870  -28.458  -97.222  216.110  -27.562  a  b  c  -0.880  20.547  -27.009  -1.281  24.809  -27.273  -2.688  35.760  -25.673  -4.497  46.355  -26.409  a  b  c  -0.596  16.867  -25.776  -0.887  20.621  -26.830  -1.925  30.357  -26.708  -3.078  38.222  -25.398  High-density High-density (2)  Convective Conditions  0 0  2  4  6  8  10  12  14  z m (Rad)/z m (Turb) 100  b)  Surface Roughness  80  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  R (%)  60  40 Low-density Medium-density  20  High-density High-density (2)  Neutral Conditions  0 0  2  4  6  8  10  12  14  z m (Rad)/z m (Turb)  c) 100 Surface Roughness  80  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0)  R (%)  60  40 Low-density Medium-density  20  High-density High-density (2)  Stable Conditions  0 0  2  4  6  8  10  12  14  z m (Rad)/z m (Turb)  Figure 6.11 R (%) versus measurement height of a 150° FOV radiation sensor (expressed in terms of the height of the turbulent sensor) for four surface roughness categories under convective (a), neutral (b), and stable (c) atmospheric conditions (left). The resulting curvilinear relationships take the form R = a(zm(Rad)/zm(Turb))2 + b(zm(Rad)/zm(Turb)) + c and are fitted with coefficients given in the tables to the right of each graph. 159  a)  20 Low-density  Convective Conditions  Medium-density  z m /z b (Rad)  16  High-density High-density (2)  12 8 4 0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  z m /z b (Turb; x max )  b)  20 Low-density  Neutral Conditions  Medium-density  16  High-density  z m /z b (Rad)  High-density (2)  12 8 4 0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  z m /z b (Turb; xmax)  c)  20 Low-density  Stable Conditions  Medium-density  16  High-density  zm /zb (Rad)  High-density (2)  12 8 4 0 1.0  1.5  2.0  2.5  3.0  3.5  4.0  z m /z b (Turb; x max )  Figure 6.12 Measurement height of a 150° FOV radiation sensor versus the turbulent flux measurement height required to encompass the maximum source weight function (xmax) under convective (a), neutral (b) and stable (c) atmospheric conditions, scaled in terms of building height.  160  Table 6.6 Measurement height (multiplier times the height of the turbulent flux measurement level) to site a 150° FOV radiometer so as to ‘see’ out to the maximum source weight function (xmax), for four surface roughness categories within each atmospheric stability class. Atmospheric Stability Stable  Neutral  Convective  Surface Roughness  Multiplier (x turbulence measurement height)  Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0) Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0) High-density (z0 = 5.0) Low-density (z0 = 0.5) Medium-density (z0 = 1.0) High-density (z0 = 3.0)  4.30 3.57 2.42 1.89 3.59 2.99 2.03 1.58 0.79 0.66 0.44  High-density (z0 = 5.0)  0.35  cases. In fact, under convective conditions, the radiometer can be sited below the turbulent flux sensor and will still ‘see’ the xmax level. For neutral conditions that are common in urban atmospheres, a radiometer must be sited between approximately 1.5 and 3.5 times higher than the turbulent flux sensor (depending on the value of the surface roughness). If the surface roughness and atmospheric stability regime of a site are known, the necessary radiometer height can be calculated from a simple logarithmic expression zm(Rad)/zm(Turb) = aln(z0) + b; Figure 6.13).  6.5 Application of the protocol scheme to Urban Flux Network sites The Urban Flux Network is an international database that gathers and distributes information on micrometeorological field campaigns – both past and current – in urban environments. It is maintained by the International Association for Urban Climate. There are currently 35 studies included in the database, with the majority of the sites located in Europe and the United States.  161  5.0 Stable Neutral  zm (Rad)/zm (Turb)  4.0  Convective  Atmospheric Stability  3.0  Stable Neutral Convective  2.0  a  b  -1.0450 -0.8742 -0.1919  3.5722 2.9882 0.6550  1.0 0.0 0.0  1.0  2.0  3.0  4.0  5.0  6.0  Roughness length z 0 (m)  Figure 6.13 Measurement height of a 150° FOV radiation sensor versus roughness length that is required to encompass the maximum turbulent source weight function (xmax) under stable, neutral and convective atmospheric conditions, scaled in terms of the height of the turbulent sensor (left). The resulting logarithmic relationships take the Most of the studies have been conducted using tower-based energy balance measurement arrays, form zm(Rad)/zm(Turb) = aln(z0) + b and are fitted with coefficients given in the table to the right of the graph. r2 in all cases is 1.0.  in addition they also often observe fluxes of carbon dioxide, aerosols, and other trace gases.  Ten sites from the database are selected for analysis in light of the results and recommendations put forward earlier in this chapter. Table 6.7 summarizes some basic information regarding the site characteristics (λS) and location of the radiometer at each study site. In nearly all cases, the primary turbulent flux sensor is located within 2 m of the radiometer and close to the top of the tower. Both of the cited Basel studies, however, conducted profile measurements of turbulent fluxes extending from within the urban canopy layer to above the roughness sublayer. The Basel-Sperrstrasse tower contained sonic anemometers positioned between 0.25zb and 2.17zb; a similar profile ranging from 0.37zb to 2.49zb was observed at the Basel-Spalenring site (Rotach et al., 2005). For the simple case of exposing a radiometer so as to ‘see’ a sample of the surface that is representative of the overall three-dimensional structure, only a handful of the selected sites appear to accomplish their objective. The modeling results in section 6.3.1 suggest a radiometer is best placed over an intersection and mounted at a height of at least two times the building height. All of the selected sites achieve the height requirement, but conformity with the 162  Table 6.7 Basic site descriptions of a sampling of sites in the Urban Flux Network at which tower-based surface energy balance observations have been conducted. Land use descriptions are as follows: RES = residential, COM = commercial, IND = industrial, INS = institutional.  Author  Location/Land Use  Rotach et al. (2005) Rotach et al. (2005) Grimmond et al. (2004) Coutts et al. (2007) Walsh et al. (2004) Masson et al. (2002)  Basel (Sperrstrasse)/RES, COM Basel (Spalenring)/RES, COM Marseille/RES, COM Melbourne (Preston)/RES Vancouver (Sunset)/RES, COM Vancouver (light industrial)/IND  λS  Radiometer zm/zb  1.29  2.17  0.84  2.19  2.23 0.42  2.22 - 2.81 3.33  0.90  4.24  0.39  4.83  Radiometer Location Mid-block; SW-NE street NE building corner, over backyard Roof center Roof corner Open; over lawn and paved surface Roof center  Crawford et al. (2009)  Vancouver (Oakridge)/RES  ~0.50  4.14  Masson et al. (2008) Lemonsu et al. (2008) Moriwaki and Kanda (2004)  Toulouse/RES, COM, INS Montreal/RES  1.67 0.35  2.37 2.21  Lawn between building and street Roof center N roof edge (in backyard)  Tokyo (Kugahara)/RES  2.00  3.42  Backyard  longitudinal placement requirement of the sensor studies differ considerably. The ‘ideal’ intersection standard is close to being achieved in the Basel, Melbourne, and Montreal studies, while the least favorable siting of the radiometer (i.e., over the center of a roof) applies to the Marseille, Toulouse, and Vancouver light industrial studies. The radiometer locations at the Vancouver Sunset and Oakridge sites are also not ideal; in both cases, the tower is set apart from the type of neighborhood (residential/commercial) meant to be characterized by the measurements. The flat open grass and concrete surfaces immediately surrounding the tower at those sites introduce bias into the surfaces ‘seen’ by the radiation sensor. This kind of distortion is similar to that incurred when a radiometer is situated over the center of a building so that the radiometer FOV becomes dominated by the roof surface directly below (see Section 6.3.2). The fact that nearly all the studies in Table 6.7 co-locate the turbulent flux and radiation sensors is contrary to many of the conclusions stemming from the analyses of results conducted here using the Kljun et al. (2004) parameterization scheme and the scale model relations. The ten  163  sites selected are predominantly described as medium- to high-density districts, which places their roughness length values in the range of 1.0 – 3.0 m (Grimmond and Oke, 1999). Assuming a neutral urban atmosphere, Table 6.12 suggests that in order for a 150° FOV radiometer to ‘see’ the location of the maximum source weight function xmax, it must be exposed two to three times higher than the height of the turbulent flux sensor(s). The profile measurements of the turbulent fluxes at both Basel sites have the potential to comply with the aforementioned findings. In both cases, the radiometers were located at a height over twice the building height. According to Table 6.12, this necessitates the turbulent flux sensors be located at around roof level. The problem with this scenario is that of the turbulent flux sensors to measure accurately from within the roughness sublayer (see Figure 1.3c), where flow is influenced by single roughness elements. It seems reasonable, then, to advocate a measurement approach whereby the turbulent flux sensors are located at the lowest height in the inertial sublayer (i.e., just above the roughness sublayer), so that the objective of siting a radiometer two- to three times the turbulent flux measurement level can be more easily achieved. Although several methods to estimate the height of the roughness sublayer exist (e.g., Raupach et al., 1991), Rotach (1999) suggests a value in the range of 2-3 times the mean height of the roughness elements. This implies that radiation sensors should be located at heights of at least four times that of the buildings, in order to include the xmax isopleth level within the sensor FOV. This conclusion is of considerable significance to the conduct of urban surface energy balance measurement campaigns. It suggests that almost all previous studies were conducted with less than ideal experimental arrangements and therefore include various degrees of uncertainty. It gives design guidance for future field studies but places potentially onerous requirements on the height and lateral placement of towers for radiation sensors.  164  Chapter 7  CONCLUSIONS  The overall objectives of this thesis were to use physical scale modeling techniques and numerical analyses to investigate three-dimensional urban surface temperature patterns and radiation fluxes and to develop a protocol to guide the measurement of radiation fluxes in the urban environment. These goals were realized by constructing an outdoor physical model array of scaled “buildings” made of hollow concrete masonry blocks with solid capping slabs on a rooftop in Tempe, Arizona. Three surface configurations (canyon aspect ratios of 1.25, 0.64, and 0.42) of the ‘urban’ array were produced. Observations were made of complete (i.e., threedimensional) facet surface temperatures together with observations of radiation fluxes extending from within, to above, the urban canopy layer at two locations within the array so as to monitor the effect of surface-sensor-sun geometry on the measured radiation flux source area. Field measurements from the scale model were complemented by analyses generated by two numerical models. Their combined results were used to develop a protocol to guide the optimum siting and exposure of radiation sensors in measurement studies of the urban surface energy balance. The siting protocol considered both the influence of surface structure and orientation on the radiation source area and the streamwise dimensions of the turbulent flux source area ‘seen’ by typical radiation and turbulent flux sensors. The main findings of the thesis are summarized in Section 7.1 and Section 7.2 contains suggestions for future work.  7.1 Summary of conclusions Individual chapters provide detailed summaries of conclusions derived from scale model observations and the numerical modeling. The main conclusions of this thesis are as follows: 165  •  The spatial complexity of urban areas that complicates the direct measurement of heterogeneous surface temperature patterns and surface-atmosphere radiation exchanges can be simulated effectively by use of an outdoor physical scale model.  •  Observations of facet temperatures from the scale model constructed here were comparable to those at full-scale urban sites with an approximately similar configuration. In particular, observed spatial and temporal patterns of individual facet temperatures and the effective thermal anisotropy were successfully reproduced by the scale model.  •  Observations of the spatial variation in reflected shortwave, upwelling longwave, and net allwave radiation reveal that measurement heights above approximately 2.5 times the mean building height generate uniform flux density patterns with no appreciable variability in either the vertical or horizontal directions. Below this measurement height, however, the radiation flux source areas are sensitive to the exact sensor placement. This is because the sensor field-of-view is populated by a combination of sunlit and shaded surface facets that are not representative of the local-scale surface composition.  •  An agreement index used to quantify the strength of correspondence between what a sensor ‘sees’ at various points above the urban surface and the actual surface morphology demonstrated that measurement locations near a street intersection give results closest to those sought at the local scale, while positioning a radiometer directly over a single rooftop results in the poorest correspondence. These findings run contrary to the methods employed by many contemporary researchers.  •  A set of simple relations describing the measurement height at which a radiation sensor’s flux source area encompasses the turbulent flux source area (as a function of surface roughness and atmospheric stability) of a turbulent flux sensor revealed that the common practice of co-locating tower-based radiation and turbulence flux sensors at the same  166  height is generally not sufficient to ensure overlap (particularly in stable- to neutral atmospheric conditions). •  To ensure matching of radiation flux source areas to the streamwise extent of turbulence flux source areas, it is recommended that at a minimum, radiation flux sensors be sited so as to contain the location of the maximum turbulent flux source weight. For a neutral atmosphere (commonly observed in urban areas) in an area with medium- to highbuilding densities, this implies radiation sensors should be mounted at two- to three times the measurement height of the turbulence sensor.  7.2 Suggestions for future work The results of this thesis point to the potential for further research in a number of areas. Firstly, the simple, repeating pattern of the scale model array, while proven helpful in achieving the current research objectives, does limit our ability to parlay results to the complicated full-scale urban setting. This technique could be expanded to include more intricate surface geometries (e.g., varying building heights, the inclusion of open or vegetated spaces) and a more diverse sampling of building materials. An obvious extension of the present work stems from the need to further understand and investigate the potential bias in the measured surface energy balance, in terms of the measured energy flux densities, resulting from using mismatched radiation and turbulence flux source areas. Quantitative understanding of this could be achieved in several ways, including numerical and scale model studies and full-scale studies in real cities. Observations of the vertical profile of radiation fluxes similar to those conducted in the scale model study here should be replicated at the full scale and expanded to include the possible effects of seasonality, surface configuration and surface materials. Such profile measurements should be supplemented with similar observations of turbulent flux profiles. 167  The inherent logistical challenges and expensive nature of most urban climate observational studies, however, ultimately limit how comprehensive such field studies are likely to be. As the ability to resolve the complex urban surface in numerical models continues to grow, so too can our understanding of how small-scale urban surface-atmosphere interactions impact the integration of sources from which flux sensors derive their measured signal. Computational fluid dynamics (CFD) modeling used in conjunction with fine-scale urban land cover databases hold great promise in this regard, because the technique allows examination of flow within the urban canopy layer (in and around buildings). For example, a CFD model that includes a solar geometry/shading routine could investigate the impact that thermal emissions from a strongly sunlit wall or roof surface have on measured radiation fluxes, and on the overall surface energy balance. Numerical modeling allows such a seemingly simple scenario be run for various forcing parameters (e.g., varying flow regimes, surface thermal parameters, etc.). Such numerical studies could both help in the interpretation of field and other results, and also prove useful prior to embarking on a field campaign, by guiding the optimal location of sensors relative to the surface area of interest. Building on the recent growth of three-dimensional urban surface databases, backward trajectory models, used to calculated flux footprint estimates (e.g., Kljun et al., 2002), could be developed specifically for urban surface energy balance studies. From this, a more accurate picture of the surfaces “seen” by a turbulence sensor could be achieved, and agreement with radiation flux source areas better accomplished.  168  References  Aida, M., 1982: Urban albedo as a function of urban structure (Part I). Bound.-Layer Meteor., 23, 405-413. Aida, M. and K. Gotoh, 1982: Urban albedo as a function of urban structure – A twodimensional numerical simulation. Bound.-Layer Meteor., 23, 415-424. 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Bound-Layer Meteor., 111, 363-415.  179  Appendix A  VIEW FACTOR CALCULATIONS  Derived from Steyn and Lyons (1985) and Steyn (pers. comm.), the wall view factor ΨW of a vertical wall of height zh and length Lb at an arbitrary point P (as shown in Figure A.1) on the ground as a function of (x,y) is given by:   −1  Lb / 2 − x   L /2+ x  + tan −1  b  − tan  y y      1  ψ W ( x, y ) =      2π  y  tan −1  Lb / 2 − x  + tan −1  Lb / 2 + x  2   2  2  2 2 2  y + z h   y + zh  y + zh               (A.1)  Figure A.1 Coordinate system used in calculating the view factor of a wall for a given point P on the ground.  180  For this study, wall view factors of all three surface configurations were taken from the midpoint of the canyon. Because Equation A.1 corresponds to the view factor of a single wall, the computed value for ΨW using the above expression is doubled in order to account for both walls constituting the canyon. As there are no other surface structures such as vegetation or open spaces in the array that must be accounted for, the difference in 2ΨW from unity gives the sky canyon view factor ΨS.  181  Appendix B  SUMMARY OF WEATHER AND OPERATIONAL CONDITIONS  B.1 Weather conditions Monthly surface meteograms (Figures B.1 – B.3) spanning the three months of the scale modeling experiment show air temperature, dew point temperature, barometric pressure, wind speed, and wind direction recorded by the United States National Weather Service at nearby Phoenix Sky Harbor Airport (see Figure 3.2 for the relative locations of the airport and study site). These plots demonstrate a general shift in background climate occurred during the study period. General weather conditions evolved from warm, fair-weather conditions in November to cooler, wetter conditions in the December/January. The patterns of barometric pressure indicate more persistent anticyclonic conditions in November giving way to more frequent cyclonic or frontal systems in the early winter months.  B.2 Operational summary Although the results presented in previous chapters center on Intense Observational Periods selected from each scale model array, data were gathered nearly continuously over the course of almost two months. Breaks occurred due to power outages and time taken to modify the scale model (i.e., rearranging the blocks or painting roof surfaces) caused breaks in the measurement period. Table B.1 is a summary of the timing of surface treatments (white, black, and pitched roofs), and the associated sky conditions (amount of cloud cover), and the operational status of the various sensor configurations (CNR1 radiometer, vertical profile of radiation fluxes, IRTc sensors measuring vertical (wall) and horizontal (roof and road) surfaces, FLIR infrared camera,  182  and ancillary data from the flat surface adjacent to the scale model) used in the study. The daily operational summary is further sub-divided into six-hour intervals.  Figure B.1 General weather conditions for November 2006 observed at Phoenix Sky Harbor International Airport. Data source: United States National Weather Service  183  Figure B.2 General weather conditions for December 2006 observed at Phoenix Sky Harbor International Airport. Data source: United States National Weather Service  184  Figure B.3 General weather conditions for January 2007 observed at Phoenix Sky Harbor International Airport. Data source: United States National Weather Service  185  Table B.1 Summary of operational status, including roof treatments (see footnote) and operational instrument arrays for the three scale model configurations (λS), divided into six-hourly intervals. ‘X’ indicates an operational instrument platform over the corresponding six-hour period. Day (YD)  Time (hr)  λS  326  0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24  1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25  327  328  329  330  331  332  333  334  335  336  Treatment1  Sky2  CNR1  Radiation Profile  Wall IRTc  Roof+Road IRTc  CLR BKN BKN BKN FEW SCT BKN BKN BKN BKN BKN BKN FEW FEW FEW SCT FEW SCT SCT FEW BKN SCT SCT SCT BKN BKN BKN BKN FEW FEW FEW CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X  FLIR  X X X X X X X X  X X X X X X X X  X X X X X X X X X X  Anc. Tripod X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X  186  Day (YD) 337  338  339  340  341  342  343  344  345  346  347  348  Time (hr) 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24  λS 1.25 1.25 Prep Prep Prep Prep Prep Prep Prep Prep Prep Prep Prep Prep 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625 0.625  X X  Radiation Profile X X  Wall IRTc X X  Roof+Road IRTc X X  X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X  X X X X X X X  X X X X X X X  X X X X X X X X X  X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  Treatment1  Sky2  CNR1  WR WR WR WR WR WR WR WR BR BR BR BR BR BR BR BR BR  CLR CLR CLR CLR CLR SCT SCT SCT CLR CLR CLR CLR CLR FEW CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR CLR FEW FEW FEW SCT SCT SCT FEW CLR FEW FEW FEW SCT BKN SCT FEW FEW BKN BKN FEW BKN BKN BKN  FLIR X X  X X X X  X X X X X X X X X X X X X  Anc. Tripod X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  187  Day (YD) 349  350  351  352  353  354  355  356  357  358  359  360  Time (hr) 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24  X X  Radiation Profile X X  Wall IRTc X X X X X X  Roof+Road IRTc X X X X X X  X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  λS  Treatment1  Sky2  CNR1  0.625 0.625 0.625 0.625 0.625 0.625 Prep Prep Prep Prep Prep Prep Prep 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417  BR BR BR BR BR BR  BKN OVC BKN BKN OVC OVC OVC OVC OVC BKN BKN BKN OVC BKN BKN BKN FEW SCT BKN SCT CLR FEW FEW CLR CLR CLR FEW BKN BKN BKN OVC OVC BKN BKN BKN FEW FEW SCT FEW FEW CLR FEW FEW FEW SCT SCT BKN SCT  FLIR  Anc. Tripod X X X X X X  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  188  Day (YD) 361  362  363  364  365  366  367  368  369  370  371  372  Time (hr) 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24  λS 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417  Treatment1  Sky2  CNR1  30° roofs 30° roofs 30° roofs 30° roofs 30° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° roofs  BKN OVC BKN OVC OVC OVC OVC OVC OVC BKN BKN BKN CLR CLR FEW CLR CLR FEW FEW BKN BKN SCT FEW SCT SCT SCT SCT SCT SCT SCT SCT FEW CLR CLR CLR CLR CLR BKN SCT BKN CLR CLR CLR CLR CLR CLR CLR CLR  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  Radiation Profile X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  Wall IRTc X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  Roof+Road IRTc X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  FLIR  X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  X X X X X X X  Anc. Tripod X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X  189  Day (YD) 373  374  375  376  377  Time (hr) 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24 0-6 6-12 12-18 18-24  λS  Treatment1  Sky2  CNR1  0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417 0.417  30°+17° roofs 30°+17° roofs 30°+17° roofs 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR 30°+17° WR  CLR CLR FEW CLR FEW SCT BKN FEW FEW BKN OVC BKN BKN SCT SCT SCT SCT BKN BKN OVC  X X X X X X X X X X X X X X X X X X X X  Radiation Profile X X X X X X X X X X X X X X X X X X X X  Wall IRTc X X X X X X X X X X X X X X X X X X X  Roof+Road IRTc  X X X X X X X X X X X X X X X X X  FLIR X X X X X X X X X X X X X X X X X X  Anc. Tripod  X X X X X X X X X X X X X X X X X  1  Treaments include: white flat roofs (WR), black flat roofs (BR) and roofs pitched 30° or 17°. The cloud cover is given as CLR (clear, cloudless), FEW (1/8-2/8 cloud coverage), SCT (scattered, 3/8-4/8 cloud coverage, BKN (5/8-7/8 coverage), and OVC (overcast, 8/8 coverage).  2  190  Appendix C  APOGEE INFRARED THERMOCOUPLE (IRTc) IRTS-P  C.1 Instrument Description The Apogee Instruments Inc. IRTc IRTS-P is a small, aluminum-bodied, self-powered infrared radiometer that measures surface temperature by continuously measuring the infrared radiation given off by the target. Its construction includes a thermopile to measure a millivolt output which depends on the temperature difference between the target and the body of the sensor. A Type K thermocouple measures the temperature of the sensor body, which is then used to reference the target surface temperature. Output from both the target temperature and the sensor body temperature are Type K thermocouple signals. Instrument specifications are provided in Table C.1. Table C.1 Apogee infrared thermocouple model IRTS-P specifications. Field-of-view: Mass:  28° half angle 320 g  Dimensions:  6 cm long by 2.3 cm diameter  Scale range:  -10 °C to 55°C  Accuracy: Output:  ± 0.3°C Target temp.: 40 µv per °C difference from sensor body Sensor body temp.: 40 µv per °C difference from datalogger panel  Optics: Spectral response: Response time:  Silicon lens 6.5 - 14 µm < 1 s to changes in target temperature  C.2 Instrument Calibration The Apogee IRTc sensors undergo factory calibrations prior to delivery to generate a series of nine sensor-specific coefficients that are incorporated into the datalogger execution program. Even so, instrument calibrations were assessed following the scale model experiment with the 191  use of a black-body (emissivity = 1.0) chamber. The chamber consists of a hollowed-out cylindrical concrete slab totally enveloped by a bath of well-mixed water. The temperature of the water acts to control the internal surface temperature of the concrete volume. Five fine-wire (0.003”) welded chromel-constantan thermocouples affixed to the inside of the chamber (Figure C.1) continuously record the surface temperature of the concrete at five-second intervals. The thermocouples are deemed accurate to within 0.01°C. The water  Figure C.1: Blackbody calibration chamber.  bath is continuously mixed by hand and with a submerged stirrer, to ensure all thermocouples measure to within 0.2 °C of one another. The bottom of the cylinder is sealed so that no light penetrates inside, thereby creating a black-body surface, the temperature of which is monitored. One at a time, the IRTc sensors are positioned at the bottom of the concrete cylinder, looking up towards the inside of the cylinder. The IRTc sensors are held in place for approximately 45-60 seconds, with surface temperature measurements recorded every five seconds. After all sensors have cycled through, the temperature of the cylinder is increased by adding progressively 192  warmer water to the surrounding bath. Calibration curves are constructed by comparing the average thermocouple temperature (Tcav) to the average IRTc reading (Tirtc) over the same time period. Second-order polynomial relations were found to be a best fit (r2 ≥ 0.9998) to the data. Resulting calibration coefficients used to correct the scale model dataset are given in Table C.2.  Table C.2 IRTc calibration coefficients using Tirtc = aTcav2 + bTcav + c. The r2 values for all data fits are ≥ 0.9998. Instrument  a  b  c  Temperature range (°C)  2087  0.0039  0.891  1.3482  12 - 60  2088  0.0038  0.0895  1.3365  13 - 59  2089  0.0036  0.9094  1.0805  13 - 59  2090  0.0035  0.8977  1.4334  13 - 58  2091  0.004  0.8687  1.7859  13 - 57  2092  0.0036  0.8906  1.5132  13 - 57  2093  0.0036  0.8515  2.4883  13 - 55  2094  0.0041  0.8892  1.3819  13 - 57  2095  0.0039  0.8791  1.6545  13 - 57  2096  0.0029  0.9288  0.9831  12 - 56  2097  0.0032  0.9289  0.9534  13 - 56  2098  0.003  0.9564  0.4374  13 - 56  2099  0.0039  0.9061  0.1726  13 - 61  2100  0.0039  0.9039  0.2562  13 - 61  2101  0.0036  0.9002  0.4511  13 - 60  2102  0.004  0.9057  0.1441  13 - 61  2103  0.0036  0.9078  0.2249  13 - 60  2104  0.0037  0.9006  0.3148  13 - 60  193  Appendix D  SUM MODEL OUTPUTS  The following figures summarize SUM model outputs that were used in analyses throughout the thesis. Figures D.1 – D.6 describe the surface view factors calculated for a 160°-FOV downfacing radiometer located approximately in and above east-west and north-south oriented canyons at heights 0.5 to 6 times the building height for all three scale model configurations and at three approximate times during the day (0900, 1200, and 1500 LAT). Figures D.7 and D.8 are stacked bar plots of the contribution of roof, wall, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb, and 3.5zb at each of the 16 sensor locations for the λS = 0.63 and λS = 0.42 scale model configuration (respectively). Similarly, the stacked bar plots in Figures D.9 – D.11 shows the modeled contribution of roof, street intersection, north-, south-, east-, west-facing walls, and north-south and east-west oriented road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at each of the 16 sensor locations (see Figure 6.1) for the three scale model configurations. Figures D.12 – D.20 are stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb, 2.5zb and 3.5zb at each of the 16 sensor locations for the three scale model configuration, at 0900, 1200, and 1500 LAT.  194  d)  6 S wall (sunlit)  5.5 5  z/zb  N-S street (sunlit)  3  2.5 2  1.5  1.5  1  1 0.5  0.1  0.2  0.3  0.4  0.5  0.0  e) S wall (sunlit)  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4 z/zb  3  Intersection (shaded)  3.5 3  2.5  2.5  2  2  1.5  1.5  1  1  0.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  3.5  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  6 5.5  z/zb  3  2  View factor  0.5  0.0  0.1  0.2  0.3  0.4  0.5  0.0  f)  6 S wall (sunlit)  5.5  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  3.5  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  1200 LAT  View factor  z/zb  3.5  2.5  0.0  c)  N-S street (shaded) Intersection (shaded)  0.5  b)  E-W street (shaded)  4  E wall (shaded) W wall (shaded)  3.5  Intersection (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5  W wall (sunlit)  4.5  6 5.5  N wall (sunlit) E wall (sunlit)  z/zb  a)  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  View factor  0.4  0.5  1500 LAT  0.0  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.1 Surface view factors ‘seen’ by the 160°-FOV down-facing radiometer located approximately in/above an east-west canyon at heights 0.5 to 6 times the building height for the λS = 1.25 scale model configuration for three approximate times during the day: 0900 LAT (top row), 1200 LAT (middle row), and 1500 LAT (bottom row). Left-hand panels (a-c) show view factors of each sunlit and shaded wall component. The right-hand panels (d-f) show view factors of sunlit and shaded intersections and east-west and north-south oriented streets. 195  d)  6 S wall (sunlit)  5.5 5  z/zb  N-S street (sunlit)  3  2.5 2  1.5  1.5  1  1 0.5 0.1  0.2  0.3  0.4  0.5  0.0  e)  6 S wall (sunlit)  5.5  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4 z/zb  3 2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  3.5  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  View factor  z/zb  Intersection (shaded)  3  2  0.0  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  0.4  0.5  0.0  0.2  1200 LAT  View factor  c)  0.4  0.6  0.8  1.0  View factor  f) 6  6 S wall (sunlit)  5.5  N-S street (sunlit)  5  W wall (sunlit)  4.5  z/zb  3  E-W street (shaded) N-S street (shaded)  4  E wall (shaded) W wall (shaded)  3.5  Intersection (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5.5  N wall (sunlit) E wall (sunlit)  5  z/zb  N-S street (shaded)  3.5  2.5  0.5  b)  E-W street (shaded)  4  E wall (shaded) W wall (shaded)  3.5  Intersection (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5  W wall (sunlit)  4.5  6 5.5  N wall (sunlit) E wall (sunlit)  z/zb  a)  3  2.5  2.5  2  2  1.5  1.5  1  1  0.5  Intersection (shaded)  3.5  0.5  0.0  0.1  0.2  0.3  View factor  0.4  0.5  1500 LAT  0.0  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.2 Same as D.1 except for north-south canyon.  196  d)  6 S wall (sunlit)  5.5 5  z/zb  3 2.5  2 1.5  1  1 0.5 0.1  0.2  0.3  0.4  0.5  0.0  e) S wall (sunlit)  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  3.5  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  6 5.5  z/zb  Intersection (shaded)  3  2  View factor  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  0.4  0.5  View factor  0.0  f) S wall (sunlit)  3.5  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  1200 LAT  6 5.5  z/zb  N-S street (shaded)  3.5  1.5  0.0  c)  E-W street (shaded)  2.5  0.5  b)  Intersection (sunlit)  4  E wall (shaded) W wall (shaded)  3.5  N-S street (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5  W wall (sunlit)  4.5  6 5.5  N wall (sunlit) E wall (sunlit)  z/zb  a)  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  View factor  0.4  0.5  0.0  1500 LAT  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.3 Surface view factors ‘seen’ by the 160°-FOV down-facing radiometer located approximately in/above an east-west canyon at heights 0.5 to 6 times the building height for the λS = 0.63 scale model configuration for three approximate times during the day: 0900 LAT (top row), 1200 LAT (middle row), and 1500 LAT (bottom row). Left-hand panels (a-c) show view factors of each sunlit and shaded wall component. The right-hand panels (d-f) show view factors of sunlit and shaded intersections and east-west and north-south oriented streets. 197  d)  6 S wall (sunlit)  5.5 5  z/zb  3.5  2 1.5  1  1  0.5  0.5 0.1  0.2  0.3  0.4  0.5  0.0  e) S wall (sunlit)  z/zb  3  2.5 2  1.5  1.5  1  1  0.5  0.5 0.2  0.3  0.4  0.5  View factor  f)  z/zb  2.5  0.6  0.8  1.0  View factor  6 E-W street (sunlit) N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  E wall (shaded) W wall (shaded)  3  0.4  4.5  S wall (shaded) N wall (shaded)  3.5  0.2  5  W wall (sunlit)  4  Intersection (shaded)  5.5  N wall (sunlit) E wall (sunlit)  4.5  N-S street (shaded)  1200 LAT S wall (sunlit)  5  E-W street (shaded)  0.0  6 5.5  Intersection (sunlit)  3  2  0.1  N-S street (sunlit)  3.5  2.5  0.0  1.0  E-W street (sunlit)  4  E wall (shaded) W wall (shaded)  3.5  0.8  6  4.5  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  6 5.5  z/zb  Intersection (shaded)  3  2  View factor  z/zb  N-S street (shaded)  3.5  1.5  0.0  c)  E-W street (shaded)  2.5  2.5  b)  Intersection (sunlit)  4  E wall (shaded) W wall (shaded)  3  N-S street (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5  W wall (sunlit)  4.5  6  5.5  N wall (sunlit) E wall (sunlit)  z/zb  a)  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5  0.0  0.1  0.2  0.3  View factor  0.4  0.0  0.5  1500 LAT  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.4 Same as D.3 except for north-south canyon.  198  d)  6 S wall (sunlit)  5.5 5  W wall (sunlit)  z/zb  E wall (shaded)  3  W wall (shaded)  Intersection (shaded)  3 2  1.5  1.5  1  1  0.5  0.5  0.1  0.2  0.3  0.4  0.0  0.5  View factor  e) S wall (sunlit)  3.5  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  6 5.5  z/zb  N-S street (shaded)  3.5  2  0.0  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  0.4  0.5  View factor  0.0  f) S wall (sunlit)  3.5  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  1200 LAT  6 5.5  z/zb  E-W street (shaded)  2.5  2.5  c)  Intersection (sunlit)  4  N wall (shaded)  3.5  N-S street (sunlit)  4.5  S wall (shaded)  4  E-W street (sunlit)  5  E wall (sunlit)  4.5  b)  6 5.5  N wall (sunlit)  z/zb  a)  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  View factor  0.4  0.5  0.0  1500 LAT  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.5 Surface view factors ‘seen’ by the 160°-FOV down-facing radiometer located approximately in/above a east-west canyon at heights 0.5 to 6 times the building height for the λS = 0.42 scale model configuration for three approximate times during the day: 0900 LAT (top row), 1200 LAT (middle row), and 1500 LAT (bottom row). Lefthand panels (a-c) show view factors of each sunlit and shaded wall component. The right-hand panels (d-f) show view factors of sunlit and shaded intersections and east-west and north-south oriented streets.  199  d)  6 S wall (sunlit)  5.5 5  z/zb  3.5  2.5 2  1.5  1.5  1  1  0.5  0.5 0.2  0.3  0.4  0.5  View factor  e) S wall (sunlit)  z/zb  3.5 3  E-W street (shaded) N-S street (shaded) Intersection (shaded)  3 2.5 2  1.5  1.5  1  1  0.5  0.5  0.1  0.2  0.3  0.4  0.5  View factor  0.0  f) S wall (sunlit)  3.5  z/zb  3  N-S street (sunlit) Intersection (sunlit) E-W street (shaded) N-S street (shaded)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  1200 LAT  6 5.5  z/zb  Intersection (sunlit)  3.5  2  0.0  c)  N-S street (sunlit)  4  2.5  1.0  E-W street (sunlit)  4.5  E wall (shaded) W wall (shaded)  0.8  6  S wall (shaded) N wall (shaded)  4  0.6  View factor  5  W wall (sunlit)  4.5  0.4  5.5  N wall (sunlit) E wall (sunlit)  5  0.2  0900 LAT  6 5.5  Intersection (shaded)  0.0  z/zb  b)  N-S street (shaded)  3  2  0.1  E-W street (shaded)  3.5  2.5  0.0  Intersection (sunlit)  4  E wall (shaded) W wall (shaded)  3  N-S street (sunlit)  4.5  S wall (shaded) N wall (shaded)  4  E-W street (sunlit)  5  W wall (sunlit)  4.5  6 5.5  N wall (sunlit) E wall (sunlit)  z/zb  a)  Intersection (shaded)  3.5 3 2.5  2  2  1.5  1.5  1  1  0.5  0.5 0.0  0.1  0.2  0.3  View factor  0.4  0.5  0.0  1500 LAT  0.2  0.4  0.6  0.8  1.0  View factor  Figure D.6 Same as D.5 except for north-south canyon.  200  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  11  12  11  12  11  12  13 ROADS  14  15  16  Actual  13 ROADS  14  15  16  Actual  13 ROADS  14  15  16  Actual  z m /z b = 2.5  b) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  Figure D.7 Stacked bar plots of the contribution of roof, wall, and road surfaces to the overall FOV of a 150°FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 0.63 scale model configuration. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 201  z m /z b = 1.5  a) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5  6  7  8  ROOFS  9  10  11  12  WALLS  13  14  15  16  Actual  14  15  16  Actual  14  15  16  Actual  ROADS  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5  6  7  8  ROOFS  9  10  11  12  WALLS  13 ROADS  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4  5 6 ROOFS  7  8  9 10 WALLS  11  12  13 ROADS  Figure D.8 Same as D.7 except for the λS = 0.63 scale model configuration.  202  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  15  16  Actual  15  16  Actual  15  16  Actual  E-W ROADS  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  E-W ROADS  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS EAST WALLS  6  7 8 9 10 11 NORTH WALLS SOUTH WALLS INTERSECTIONS  N-S ROADS  12 13 14 WEST WALLS E-W ROADS  Figure D.9 Stacked bar plots of the contribution of roof, street intersection, north-, south-, east-, west-facing walls, and north-south and east-west oriented road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 1.25 scale model configuration. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 203  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  15  16  Actual  15  16  Actual  15  16  Actual  E-W ROADS  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  E-W ROADS  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS EAST WALLS  6  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  E-W ROADS  Figure D.10 Same as D.9 except for the λS = 0.63 scale model configuration.  204  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  15  16  Actual  15  16  Actual  15  16  Actual  E-W ROADS  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS  6  EAST WALLS  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  E-W ROADS  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2  3  4 5 ROOFS EAST WALLS  6  7 8 9 10 11 12 13 14 NORTH WALLS SOUTH WALLS WEST WALLS INTERSECTIONS  N-S ROADS  E-W ROADS  Figure D.11 Same as D.9 except for the λS = 0.63 scale model configuration.  205  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 11 ROOF  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.12 Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 1.25 scale model configuration, at 0900 LAT. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 206  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.13 Same as D.12 except for 1200 LAT  207  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.14 Same as D.12 except for 1500 LAT  208  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.15 Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 0.63 scale model configuration, at 0900 LAT. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 209  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.16 Same as D.15 except for 1200 LAT  210  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 11 ROOF  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.17 Same as D.15 except 1500 LAT  211  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c) 1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.18 Stacked bar plots of the contribution of sunlit roof, street intersection, walls, and road surfaces to the overall FOV of a 150°-FOV radiometer located at 1.5zb (a), 2.5zb (b) and 3.5zb (c) at each of the 16 sensor locations (see Figure 6.1) for the λS = 0.42 scale model configuration, at 0900 LAT. The right-most bar is the actual surface contribution according to the complete definition of the surface, AC, which is used as a reference distribution. 212  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1 2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTIONS SUNLIT EAST WALL  z m /z b = 3.5  c)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.19 Same as D.18 except 1200 LAT  213  z m /z b = 1.5  a)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 2.5  b)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD  5  SUNLIT NORTH WALL  6 7 8 SUNLIT E-W ROAD  9  SUNLIT WEST WALL  10 ROOF  11  12  13  SUNLIT SOUTH WALL  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  z m /z b = 3.5  c)1.0  Proportional Area  0.8  0.6  0.4  0.2  0.0 1  2 3 4 SUNLIT N-S ROAD SUNLIT NORTH WALL  5  6 7 8 SUNLIT E-W ROAD SUNLIT WEST WALL  9  10 ROOF  11  12  SUNLIT SOUTH WALL  13  14 15 16 Actual SUNLIT INTERSECTION SUNLIT EAST WALL  Figure D.20 Same as D.18 except 1500 LAT.  214  

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