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Complete urban surface temperatures Voogt, J. A. 2011

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VOLUME 36 SEPTEMBER 1997J O U R N A L O F A P P L I E D M E T E O R O L O G Y q 1997 American Meteorological Society 1117 Complete Urban Surface Temperatures J. A. VOOGT* AND T. R. OKE Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada (Manuscript received 16 September 1996, in final form 20 February 1997) ABSTRACT An observation program using ground and airborne thermal infrared radiometers is used to estimate the surface temperature of urban areas, taking into account the total active surface area. The authors call this the complete urban surface temperature. This temperature is not restricted by the viewing biases inherent in remote sensors used to estimate surface temperature over rough surfaces such as cities. Two methods to estimate the complete surface temperature are presented. Results for three different land-use areas in the city of Vancouver, British Columbia, Canada, show significant differences exist between the complete, nadir, and off-nadir airborne esti- mates of urban surface temperature during daytime. For the sites and times studied, the complete surface temperature is shown to agree with airborne off-nadir estimates of the apparent surface temperature of the most shaded walls. Some implications of using the complete surface temperature to estimate screen level air temperature and to calculate surface sensible heat flux are given. 1. Introduction Surface temperature is an important boundary condition for studies of the urban atmosphere. Its measurement in cities is difficult because of the complex structure of the urban–atmosphere interface. Furthermore, there are strong microscale variations of surface temperature that arise due to changes in radiant load with surface slope and aspect, shading, and variations in surface thermal and radiative properties. Studies of single urban canyons have used in situ ther- mocouple or thermistor thermometry to estimate surface temperatures. An alternative is to use infrared radiometry, where instruments indirectly estimate an apparent surface temperature based upon the radiance received from that area of the surface that lies within the instrument’s in- stantaneous field of view (FOV). An advantage of this approach is better spatial sampling over the microscale temperature variations that occur across an individual building facet. Such instruments can be used in single canyons or mounted on a vehicle to extend the scale of observation (Voogt 1995). Thermal infrared radiometry from aircraft or satellite platforms has often been advocated as a means of pro- viding more spatially representative measurements of sur- * Current affiliation: Department of Geography, University of Western Ontario, London, Ontario, Canada. Corresponding author address: Dr. James A. Voogt, Dept. of Ge- ography, University of Western Ontario, London, ON N6A 5C2, Can- ada. E-mail: voogt@sscl.uwo.ca face temperature over larger areas of cities than is feasible using ground-based studies. However, studies over ‘‘rough’’ natural and agricultural surfaces (e.g., Boissard et al. 1990; Paw U 1992) demonstrate that directional variations of thermal emittance (which may be termed effective anisotropy) pose difficulties in the interpretation of the results. Roth et al. (1989) suggested that urban areas may be prone to similar effects. Work by Voogt (1995) confirms the existence of strong effective anisotropy in thermal em- ittance at the land-use scale (102–106 m2) over urban areas. Remotely sensed urban surface temperatures are subject to strong variations due to viewing restrictions of the urban surface structure by the instrument and differential heating patterns created by sun-surface geometric configuration. These results imply that remote sensors undersample the urban surface. In this paper, we combine surface temperature obser- vations obtained using infrared radiometry from different observation platforms with surface structural information to produce an urban surface temperature that better takes into account the temperatures of all the surfaces present. We term this temperature the complete (urban) surface temperature Tc. Complete surface temperatures are com- pared with remotely sensed surface temperatures of urban areas to assess the degree to which remotely measured estimates of urban surface temperature differ from the tem- perature of the entire three-dimensional surface. 2. Definitions a. The complete urban surface From a climatological perspective, the surface is crit- ically important. It is where the principal sources and 1118 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 1. Schematic illustration of different definitions of the urban surface. (a) Complete, (b) ground level, (c) rooftop equivalent (‘‘black box’’), (d) bird’s-eye view, (e) ‘‘surface’’ (screen level) observed, and (f) zero-plane displacement. sinks of heat, mass, and momentum are located. Prop- erties of the surface control the partitioning and con- version of these entities, so the nature of the surface strongly conditions the behavior of the lowest layers of the atmosphere. Specification of surface properties and conditions is thus an important objective for study and a necessary prerequisite to gain understanding of the climate system. If the relatively young field of urban climatology is to gain insight, it has to grapple with definition and specification of the heterogeneous and highly convoluted three-dimensional urban–atmosphere interface. Surface representations in boundary layer meteorol- ogy simplify and approximate the actual nature of the surface (Fig. 1). What is required is the complete area comprising the boundary between the surface system and the air (Fig. 1a). Often what is used is the surface ‘‘seen’’ by a sensor. For example: a plane at the ground (Fig. 1b) or above roof level (Fig. 1c) that ignores the canopy or treats it as a ‘‘black box’’; a bird’s-eye view of an infrared thermometer placed above the system (Fig. 1d); planes of observation that coincide with the measurement level of a sensor, such as a screen-level thermometer to measure the air temperature (Fig. 1e); or a plane at some intermediate height in the canopy, which represents an effective surface, usually for the purpose of modeling the integrated system (Fig. 1f). The surface representation adopted generally is scale dependent; details of the surface structure are increas- ingly simplified as the total area increases. SEPTEMBER 1997 1119V O O G T A N D O K E TABLE 1. Definition of area component symbols. Symbol Description Ap Ao Ar Apr Aw Ab Av Apv Ac Plan (horizontal) area (obtained from map or aerial photo) Horizontal ground-level area (grass, roads, gardens) Roof area (actual) Plan or apparent roof area: for flat roofs Ar 5 Apr; equivalent to building plan area Wall area (total or with an additional subscript denoting facet direction) Building area (sum of roof and wall areas) Vegetation area (three-dimensional tree representation) Plan or apparent vegetation area (horizontal projection), subdivided into trees with trunk heights (htk 5 0, .0) Complete surface area FIG. 2. Illustration of component areas composing a typical urban building unit. The surface representation adopted here includes ma- jor structural features such as buildings and trees (or sizable shrubs). In general, the surface representation does not include details at length scales less than that of a building or tree. Landform relief is ignored. Com- ponent areas are listed in Table 1 and shown schemat- ically in Fig. 2. b. The complete urban surface temperature The complete urban surface temperature Tc is an area- weighted temperature. Component surface temperatures may be combined in proportion to their areal fraction of the complete surface. The complete surface longwave emission Lc may be written n L 5 f L , (1)Oc i i i51 where fi are the fractional areas with emission Li. An equivalent radiant temperature may be calculated from (1) assuming blackbody emission and using the Stefan– Boltzmann law or other temperature-emittance relations defined for particular spectral regions (e.g., Singh 1985), depending upon the characteristics of the instruments used to obtain Li. Heilman et al. (1981), Kustas et al. (1990), and Sun and Mahrt (1995) have used similar definitions to describe a composite temperature that they use to represent the apparent temperature of the surface as observed (rather than the complete surface) by a ther- mal remote sensor. To obtain Lc from (1) requires the specification of surface classes, their representative temperatures, and the fractional area of each surface class. While this pro- cedure can be implemented for agricultural crops that have relatively few component temperatures, this task becomes more difficult as surface complexity and the variety of materials present increases. To overcome this difficulty, we reduce the number of components in (1) to represent major surface orientations and use temper- ature frequency distributions to represent the actual vari- ation of temperature due to microscale variations in sur- face properties. As defined, Tc is not directly observable, although it may be possible to approximate it using hemispherical or wide FOV estimates of upwelling longwave radiation. These may provide a useful approximation because they reduce the directionality of the measurement and inte- grate both horizontal and vertical surfaces of all ori- entations. However, view factors for individual surfaces will be biased toward horizontal surfaces and those sur- faces most directly beneath the sensor. 3. Study areas The observational program was carried out using three primary study areas within the city of Vancouver, British Columbia, Canada. The sites selected included a light industrial (LI) area comprised of one- and two-story warehouses with flat roofs and workshops; a downtown office/commercial zone (D) with massive, tall buildings; and a suburban residential (R) neigh- bourhood composed of one- and two-story single family dwellings (Fig. 3). In the R study area, vegetation cover (gardens, street trees, and parks) is extensive. Most streets have regu- larly spaced trees bordering the roadway. Although less frequent, trees are randomly distributed in backyards and alleys. Both the suburban and downtown sites were almost devoid of vegetative cover. A descriptive sum- mary of the sites is given in Table 2. 1120 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 3. Study areas in Vancouver, British Columbia, Canada. (a) Light industrial, (b) downtown, and (c) residential. TABLE 2. Study site description. Bracketed designations for the sites are used in the text. Site Descriptiona Building heights Streetb pattern Area (km2) Subareac (m2 3 103) No. of buildings Downtown (D) Office and commercial towers (C1) 6–20 stories NE–SW NW–SE 0.56 453 274 Residential (R) Single-family dwellings (R2) 1–2 stories N–S E–W 1.0 170 409 Light industrial (LI) Rectangular, closely spaced buildings (I2) 1–3 stories E–W N–S 0.65 618 733 a Auer (1978) land-use category in brackets. b Street pattern refers to the primary orientation of streets and cross streets. The direction of the long axis of the block is listed first. c Subarea refers to the portion of the study area in which complete surface area calculations were made. 4. Methods a. Estimating the complete surface area 1) BUILDINGS The three-dimensional area of buildings Ab, made up of roof area Ar and wall area Aw (Fig. 2), is calculated using the digitized outlines of buildings taken from high-resolution (1:2500) aerial photography. Large rooftop structural elements such as elevator shaft hous- ings are included, but structural details with length di- mensions less than one-half the shortest building facet are omitted. Roofs may be planar or consist of two or four angled surfaces. Building heights in the LI area were estimated in stories (to the nearest 0.5) with a story assigned as 3.7 m (12 ft). In area D, building heights (in stories) were obtained from Vancouver Planning Department (1984) maps. Building heights along the traverse route were updated from observations made using an Abney level. An eight-block subarea of the R study area was chosen for detailed analysis. Here, 271 houses (an average of 34 per block) and 139 garages (approximately 17 per block) were digitized. The height [in stories, to the near- est 0.25, using 3.05 m (10 ft) per story], roof type (flat, gabled, four-sided), and roof pitch were estimated for each building. Vertical facet surface area calculations for buildings with gabled roofs include the gables (tri- angular wall area above the level of the eaves on the end walls). The area A of a polygon represented by a series of xi, yi points (i 5 1, N) can be determined from Stoke’s theorem as N211 A 5 x y 2 y x 1 x y 2 x y , (2)O i i11 i i11 N 1 1 N1 22 i51 where the x, y values are the digitized points for each building or surface object. Vertical facet areas are ob- tained by calculating the length of a vector (side of the polygon) and multiplying this by the assigned height of the building. Where adjacent buildings share a common wall, com- mon vectors are identified. If the heights of the buildings differ, the area of the exposed wall is calculated. Wall SEPTEMBER 1997 1121V O O G T A N D O K E FIG. 4. (a) Definition of tree structural measures. (b) Modeled shapes for the tree types in the study area: B: bushes/shrubs, C: coniferous, D: deciduous, E: evergreen (nonconiferous), F: flowering (mainly cherry). orientation is derived from the sign of (2) in combination with the slope (determined from the coordinates of the points relative to a reference point) of the line repre- senting the wall segment. 2) TREES Trees (in the R area only) were categorized into five types, based upon geometric form and relative abun- dance: B: bushes, C: evergreen (coniferous), D: broad leaved (deciduous), E: evergreen (nonconiferous), and F: flowering deciduous. For surface area calculations, trees have been rep- resented by the following simple shapes: cones (conif- erous) (Li and Strahler 1985), spheres or cylinders (de- ciduous) (Jupp et al. 1986; Goel 1988) or, more gen- erally, by ellipsoids (Campbell and Norman 1989). A wide variety of tree forms can be represented by ellipse parameters if the possibility of truncated ellipses is in- cluded (Charles-Edwards and Thornley 1973; Goel 1988). Ellipsoids were used to represent the tree types pres- ent in the residential study area. Tree height hr, maxi- mum crown radius rc, and height to the base of the foliage (equivalent to trunk height htk) were estimated from ground surveys for all trees in the study subarea. The position of the ellipse centroid (height of maximum crown radius hr) was estimated as a fraction Fhf of the total foliage height hf where hf is the difference between hi and htk. Here, Fhf was estimated to be 0.25, 0.1, 0.5, 0.25, and 0.1 for types B,C,D,E, and F, respectively. Tree structural parameters are graphically portrayed in Fig. 4a. The ellipse semi-axes are represented by c and rc (equivalent to a). When z 5 c, the tree canopy is represented by a complete ellipse; when z , c, the ellipse is truncated. Calculated shapes for select ex- amples of each tree type in area R are presented in Fig. 4b. Crown radius is assumed to be symmetrical (i.e., circular) in the x and y planes; the tree shapes are el- liptical in the x, z plane only, so the resulting shapes are most precisely described as prolate and oblate sphe- roids. Estimates of total tree surface areas calculated using the ellipsoidal representations versus those based on cones, cylinders, and spheres (assigned to represen- tative tree types) agree to within 4%. The representation of trees as simple geometric ob- jects fails to account for gaps in the foliage, which re- duce the projected surface area. The actual ‘‘viewed’’ or apparent surface area emitting outside the canopy in a particular direction is theoretically defined as the pro- jection of the total canopy foliage onto a plane orthog- onal to the direction of view. Lang and McMurtrie (1992) describe the theoretical basis for the commonly required case of foliage projected onto a horizontal plane below the canopy. The complete surface area of a tree canopy Ay may be defined as the area of foliage projected onto the bounding surface of the geometric shape representing the tree. This is the area of foliage that emits directly to the surroundings. Theoretical cal- culation of this value is complex. As an approximation we define a ratio Fgap that is the reduction factor required to account for the gaps in the canopy foliage. The ratio Fgap allows the complete can- opy area to be calculated from the simple geometric area, which in turn can be estimated from basic struc- tural parameters. Calculation of Fgap is theoretically dif- ficult and requires details of the canopy foliage density, orientation, and clumping. Values of Fgap obtained from the literature often refer to forest canopies rather than single trees and are generally based upon a cumulative projection of the leaf area index (LAI) onto a horizontal plane beneath the canopy. These values therefore do not account for the anticipated variations in Fgap for pro- jections in the vertical plane. The Fgap estimates for mod- el poplar stands based upon downward cumulative LAI (Chen et al. 1993) are in the range of 0.3–0.2 for a deciduous LAI of 4, which is the estimated maximum in the study area (Kramer and Kozlowski 1979; Grim- mond 1988). For this study it was considered acceptable to use crude approximations for Fgap based upon field obser- vations. Tree types B–F were estimated to have Fgap values of 0.15, 0.2, 0.3, 0.2, and 0.45, respectively. If the structure of individual trees differed significantly from the average for their type, an estimated field value replaced the default value. 3) COMPLETE SURFACE AREA The complete active surface area Ac of each study site is estimated by adding the (three-dimensional) areas of vegetation Ay and buildings Ab to that of the exposed ground area Ao: Ac 5 Ay 1 Ab 1 Ao. (3) 1122 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y The area of exposed horizontal ground surfaces (Ao; grass, roads, etc.) is determined as a residual from A 5 A 2 [A 1 A ],o p pr pv(h 50)tk (4) in which Ap is the total plan area (calculated from a topographic map), Apr is the plan area of roofs (assumed equivalent to buildings), and is the plan area ofApv(h 50)tk vegetation elements for which the canopy intersects the ground (most common for bushes but also some conif- erous trees). The exposed ground area Ao includes hor- izontal surfaces below tree canopies where ht . 0 (Fig. 2). b. Infrared thermometry 1) VEHICLE TRAVERSES OF VERTICAL FACET SURFACE TEMPERATURE An array of infrared thermometers (Everest Intersci- ence Model 4000A, hereafter referred to as EIRT) was mounted on a truck to sample the temperatures of ver- tical surfaces (primarily building walls). The EIRT has a 158 FOV. The sensors were mounted in pairs facing outward from the vehicle. Traverses in the LI and R areas, where building heights were low, were conducted with one pair of sensors facing outward from each side of the vehicle. One sensor of each pair was level, while the other was mounted at a 108 elevation angle to sample the upper portions of the buildings. This configuration allows both sides of the street to be sampled with one traverse. In the D area, all sensors were oriented to face in the same direction with elevation angles of 08, 158, 308, and 458 in order to better sample the temperatures of the tall buildings. In both configurations, a single, downward-facing EIRT was used to obtain the road surface temperature, and air temperature was monitored using shaded and aspirated fine-wire thermocouples. Spatial sampling was conducted along a traverse route that covered all streets and alleyways (within a select area) in the LI and R study areas. Traffic considerations confined the traverse route in area D to streets only. A difficulty with the sampling methodology is that there is no record of what the sensors see when a sample is registered. Because of the unevenness of building heights and their spacing, samples are made up of not only building walls but also mixed FOV scenes composed of building and sky com- ponents or, in some cases, sky alone. This presents dif- ficulties in the interpretation of the data, particularly for sunlit facets that have a wide range of surface temper- atures. In this study the spectrum of temperatures re- corded during a traverse is truncated, so that the low temperature end, characteristic of mixed building and sky or sky scenes, is removed. 2) AIRBORNE INFRARED THERMOGRAPHY An AGEMA 880 LWB thermal scanner operating in the 8–14-mm waveband was mounted in a helicopter and used to obtain thermal images over each of the study areas from nadir and 458 off-nadir sensor angles. The imagery was corrected for atmospheric effects using the LOWTRAN-7 atmospheric radiation program (Kneizys et al. 1988) in conjunction with meteorological obser- vations from airsondes (AIR Inc.) launched adjacent to the site. No correction for the effects of surface emis- sivity was made. Roth et al. (1989) suggest spatial tem- perature errors of up to 1.5 K are possible due to vari- ations in urban–rural surface emissivity for satellite- based studies. Temperature variations due to emissivity differences are expected to maximize at scales on the order of meters and to decrease as averaging occurs over larger ground resolution element. High-resolution ther- mal imagery requires emissivity information beyond the scope of this project, and use of an overall urban emis- sivity (e.g., Arnfield 1982) does not necessarily imply complete correction of apparent surface temperatures on a pixel-by-pixel basis. Flights were conducted at times when surface tem- perature contrasts between opposing street canyon facets were large. These times were selected to determine the presence and magnitude of effective anisotropy (direc- tional variations in apparent surface temperature) over the study area (Voogt 1995). For the north–south and east–west street orientations of the LI and R areas, this led to flights in the morning, slightly after solar noon, and in the late afternoon. In the D study area, where the street pattern is aligned northwest-southeast and northeast-southwest, flights were conducted in the late morning and midafternoon. c. Estimating the complete surface temperature The complete surface temperature, defined by (1), requires specification of surface emittance for each of the area components included in the summation. If areas are defined on the basis of having different temperatures, the procedure becomes difficult to implement in urban areas where there is a wide variety of surface types to consider (e.g., Quattrochi and Ridd 1994). Rather than defining myriad surface types and prescribing their rep- resentative temperatures, an alternate approach was de- vised. It uses frequency distributions of apparent tem- perature either from the airborne AGEMA imagery or in combination with the vehicle traverse EIRT data. 1) COMBINATION OF NADIR AIRBORNE AND TRAVERSE TEMPERATURE DISTRIBUTIONS One method to estimate Tc is to combine the apparent surface temperature distributions of horizontal surfaces from airborne nadir scanner imagery with those of ver- tical facets obtained from the vehicle traverse (Fig. 5). This horizontal–vertical combination circumvents the need to subdivide the horizontal surface into component fractional areas and estimate mean temperatures or tem- perature distributions for each. The observed nadir tem- SEPTEMBER 1997 1123V O O G T A N D O K E FIG. 5. Conceptual representation of the procedure to calculate the complete surface temperature distribution for an urban area by com- bining airborne nadir and ground-based vertical facet temperature distributions. FIG. 6. (a) Frequency distributions of surface temperature for com- ponents in the Industrial area, 1030 PDT 15 August 1992. Vertical facet distributions are from the vehicle traverse. (b) Composite tem- perature distribution of the LI study area from the airborne nadir imagery and the complete surface temperature composited from (a).perature distribution is assumed to represent the various components in their correct proportions. The component frequency distributions (nadir and four vertical) are combined with weights according to their fraction of the complete surface area. In the residential area where trees obscure some portion of the horizontal surface, an additional weighting for the obscured horizontal surface is included. The temperature for this surface was ob- tained from ground observations made by personnel equipped with handheld infrared radiation thermometer (IRT). Figure 6a illustrates the component temperature dis- tributions from the airborne and vehicle observations from a morning flight over the LI area. These are com- bined as illustrated in Fig. 5 to create the complete surface temperature distribution presented in Fig. 6b. The mean emittance of the complete distribution is es- timated using (1), where fi are the frequencies for each emittance class and Li is the emittance for the class. Then Tc is obtained by inversion of the Stefan–Boltz- mann law. A disadvantage of this approach is the need to truncate or otherwise modify the distribution of sur- face temperatures obtained from the vehicle traverse to remove mixed building and sky values. This procedure has the advantage of including most observations that fully view wall surfaces, but it also retains some ob- servations of mixed sky and warm wall surfaces, which yield a combined temperature greater than the truncation temperature. The resulting distribution slightly under- estimates areas of high surface temperature. A second difficulty is that the method assumes that the distribution of vertical facet temperatures is representative of all vertical surfaces. In practice the traverse method re- stricts observation to facets that may be viewed from positions along the route and are within the range of elevation angles of the EIRT. Facets orthogonal to the street are not sampled except on the ends of the block. Unfortunately, close interbuilding spacing means that end facets have greater exposure to direct solar radiation than for similarly oriented facets within the block. Cal- culations for the R area indicate 57%–80% of the area of interbuilding walls are shaded during the times of the morning and late afternoon flights, depending upon the building height and spacing. During the early afternoon flight, 35%–55% are shaded. 2) COMBINATION OF NADIR AND OFF-NADIR AIRBORNE An alternative to the use of the vehicle traverse data is to use vertical facet surface temperature distributions extracted from the off-nadir airborne scanner imagery. 1124 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y TABLE 3. Major surface component areas for each study area: LI: Light Industrial, D: Downtown, and R: Residential. All areas have units of m2 3 103. Area Symbol Area (LI) % of Ac Area (D) % of Ac Area (R) % of Ac Plan (2D) Ground level Roof Wall (N or NE) Wall (S or SE) Ap Ao Ar Aw(N, NE) Aw(S, SE) 618 380 237 69 70 71 44 27 8 8 453 287 167 138 137 46 29 17 14 14 170 121 53 23 23 56 40 17 8 8 Wall (E or NW) Wall (W or NW) Wall (misc.) Vegetation Aw(E, NW) Aw(W, NW) Aw(M) Ay 55 54 9 6 6 1 134 133 13 13 17 17 52 6 6 17 Complete Total Active (3D/2D) Ac Ac/Ap 875 1.4 995 2.2 306 1.8 These overcome some of the difficulties with the tra- verse vehicle data but have their own limitations. Re- sults from the extracted data depend on the completeness with which component surface areas are sampled be- cause temperature patterns are the sole means of defin- ing the spatial dimensions of the facets. In the R and D areas, where interbuilding spacing is small, it may be difficult to obtain the temperature of facets due to the small area seen at the off-nadir angle. Tree canopy temperatures are estimated for each view direction in the R area. The difference in area between Ay and Apv was divided equally among the four view directions; the vertical plan area of vegetation is in- cluded in the nadir weighting. A weighting for the ob- scured horizontal ground area is also included. 5. Results a. Complete surface areas of the study sites Component surface areas, calculated from the data- base of surface structure, for each of the study areas are presented in Table 3, and frequency distributions of building height are shown in Fig. 7a. Heights are dis- tributed approximately normally in the LI and R areas, with only a few instances of tall (.4 stories) buildings. In area D, the distribution is strongly asymmetric with greatest frequencies in classes centered between 5 and 15 m and a long tail of frequencies extending toward higher building heights. In the LI area combined wall areas constitute 28% of Ac and horizontal surfaces (including rooftops) make up the remaining 71%. Greater areas of north- and south- facing facets are exposed compared to east- and west- facing because many of the buildings along the blocks share common east and west walls and therefore have no east or west exposure (Fig. 3a). In area D, vertical facets combine to form 54% of Ac, a value greater than the fraction of horizontal surfaces (46%) and much greater than the horizontal roof area (17%, Table 3). The percentage wall area in area R is similar to that of the LI area; this result is likely due to the high incidence of common building walls in the LI area which reduces the relative wall area. Surface area calculations for the R site include the effect of roof pitch so that both plan roof area and actual roof area are available. The mean roof pitch in area R is approximately 208, although the distribution is skewed, with substantial numbers of both houses and garages observed to have higher roof pitch angles. Roof types are fairly equally split among gabled and four- sided types; only a minor proportion have flat roofs. As a measure of building density the ratio of roof to plan area yields values of 38%, 37%, and 31% for areas LI, D, and R, respectively. The active area ratio Ac:Ap, is a measure of the increase in effective surface area in contact with the atmosphere due to the three-dimen- sionality of the urban interface. In the study areas the increase is about 40% in LI, 80% in R, and about 120% in D (Table 3). Trees are a major contributor to the large Ac:Ap value calculated for the R area. Results of the survey of tree structural parameters are presented in Table 4. Deciduous trees are the most fre- quently occurring type, accounting for 59% of the total. The overall mean tree height (not including type B) is 7.7 m. This is only approximately 50% of the height adopted by Schmid (1988). The difference between the two estimates is attributed to the small spatial domain in the current study and the abundance of relatively small street trees. A two-dimensional projection of the canopy area, less the two-dimensional area of trees where foliage intersects the ground, yields the obscured horizontal surface area (12547 m2, 4.1% of Ac). b. Viewed and nonviewed surfaces A summary of surface areas broken down into those surfaces generally seen or viewed by remote sensors (i.e., horizontal, unobstructed surfaces) and those most often unseen or undersampled (e.g., building walls or obstructed horizontal surfaces) is given in Table 5. Also included are results from a typical high-rise housing estate in Singapore (Nichol 1996). The results highlight SEPTEMBER 1997 1125V O O G T A N D O K E FIG. 7. Frequency distribution of building heights in (a) LI, (b) D, and (c) R study areas. TABLE 5. Proportions of ‘‘seen’’ and ‘‘unseen’’ areas. Singapore results from Nichol (1996). Area Vancouver D LI R Singapore Seen (2D) Ground Roofs Tree canopies 0.63 0.37 0.62 0.38 0.64 0.28* 0.08 0.77 0.17 0.16 Unseen Walls ‘‘Below’’-tree canopies 1.20 0.40 0.47 0.30** 0.54 0.16 Total active surface 2.2 1.4 1.8 1.7 * Plan projected roof area, which is slightly less than the total roof area and accounts for the missing 0.03 required for the sum to equal 1.8. ** Calculated as ground area below tree canopy plus the difference between 3D tree canopy area and the plan projected tree canopy area. TABLE 4. Statistical summary of the dimensions of tree structural parameters from field surveys. Units are in meters. Tree type Code n Mean ht s Med. Mean rc s Med. Mean htk s Med. Bush Coniferous Deciduous Flowering deciduous B C D F 81 78 289 43 2.4 8.6 7.7 6.2 1.2 4.1 3.2 1.8 2.4 9.1 7.6 6.1 1.1 3.1 3.4 3.0 0.4 2.2 1.6 1.3 0.9 2.4 3.1 3.0 0.1 1.8 3.2 2.7 0.3 1.7 1.8 1.5 0 1.4 3.1 2.1 the importance of building walls and obscured areas as a component of the complete urban surface. The Vancouver sites all show similar values for the proportion of open ground (roads, grassed areas, etc.). Roofed areas are largest in the LI and D areas of Van- couver. Roof pitch in residential areas increases the ef- fective roof area relative to the building plan area. Tree canopies are not included in the analysis of the D and LI areas, but this should not be a significant omission. The value for the R area is based upon the tree structural information gathered by field surveys rather than areal estimates from aerial photographs. Wall areas make up the most significant proportion of unseen areas with the fraction highest in area D. Wall areas for the LI and R areas are similar; the LI area is probably reduced somewhat because of the large num- ber of buildings that share adjoining walls. Despite the smaller plan vegetated area, the ‘‘below’’-tree canopy area for site R is larger than Singapore because this area includes a portion of the three-dimensional vegetated area (see Table 5). c. Complete surface temperatures of the study sites 1) COMPARISONS OF ANDT Tc c1 2 The mean vertical facet temperature distributions ob- tained from the airborne and vehicle platforms for all flights over the LI and D study areas are compared in Fig. 8. Comparison with the R area is not possible be- 1126 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 8. Comparison of apparent wall surface temperatures for the D and LI areas obtained from vehicle traverses and the airborne thermal scanner. Symbol letters refer to facet orientation. FIG. 9. Comparison of complete surface temperatures calculated using combined airborne nadir and vehicle traverse data ( ) vs thatTc1 using airborne nadir and off-nadir data ( ).Tc2 cause the vehicle traverse includes building facet and vegetation temperatures, whereas these components were extracted separately in the remotely sensed im- agery. Agreement is generally good when facet tem- peratures are cool (i.e., they are mostly shaded). At high- er temperatures there are significant biases, particularly in the D area. This bias is attributed to differences in viewing location between the two observation plat- forms. From the perspective of the airborne scanner, warm bias may be attributed to one or more of the following: A preferential view of the top (fully irradi- ated) portion of walls, inability to view below the level of any awnings (which shade the lowest portions of the building walls), obscuration of the lower wall when can- yon geometry (i.e., H/W) is large, and specular reflec- tion of radiation from warm street and canyon surfaces by facets with low emissivity. Vehicle traverse results have a cool bias using a similar reasoning. Differences in the LI area may be related to sampling biases induced by the particular building geometry. The vehicle traverse and airborne scanner sample north and south facets equally well since the street pattern allows full access by the traverse vehicle. However, many east and west walls along a block cannot be viewed from the traverse vehicle since they do not directly face onto a street. Further, these facets tend to be warmer because they have greater solar access earlier in the morning and evening than do the end-of-canyon walls, which are more subject to shading by buildings on the opposite side of the street. A similar vehicle sampling bias exists for the R area; however, here the very narrow inter- building spacing and pixel smearing also prevents good sampling of the wall surfaces using the image extraction technique. The biases in facet temperature are reflected in the comparison of and for each site (Fig. 9). TheT Tc c1 2 differences between estimates are largest in area D (up to 28C) where the sampling biases are greatest. In the R area, uses combined 08 and 108 EIRTTc1 temperature distributions from the traverse vehicle, and it is assumed that an adequate sampling of both the house and tree temperatures is obtained. Truncation of the traverse distribution was specified using a graphic analysis of the traverse and extracted temperature dis- tributions, and looking for evidence of the tree canopy signal in the traverse (especially 108 EIRT) distribution. This was related to a local minimum in the frequency distribution. Estimates of combine extracted temperature dis-Tc2 tributions for vertical facets and tree canopies. Off-nadir tree canopy temperature distributions show variations in the mean of approximately 38C between the most directly irradiated direction and the most shaded for each flight over the R area. This is similar to the mag- nitude observed by Balick et al. (1987), McGuire et al. (1989), and Sun and Mahrt (1995). 2) COMPARISON OF COMPLETE AND REMOTELY SENSED TEMPERATURES Comparison of complete temperature estimates with the airborne nadir and off-nadir mean apparent tem- peratures (denoted generally as Tr, or specifically by Tnadir or Toff-nadir) allows us to determine the degree to which remotely sensed observations are biased. In gen- eral, the most apparent difference between the complete and nadir temperature distributions is the enhancement of low temperature frequencies. This occurs because, except for the most directly irradiated facet, all vertical surfaces have temperature distributions that are cooler than those in the horizontal. Temporally, the difference between the nadir and vertical distributions is strongest SEPTEMBER 1997 1127V O O G T A N D O K E FIG. 10. Comparison of complete apparent surface temperatures , (solid triangles labeledTc1 C) with mean image apparent surface temperatures labeled by view direction (V: nadir), and traverse air temperatures (Tat, denoted by solid diamonds) for all study areas and flight times. near solar noon when, because of the relatively small zenith angle, even the most directly irradiated facet has a distribution significantly cooler than the horizontal. At times earlier and later in the day, the most directly irradiated wall has a frequency distribution only slightly cooler than that of the horizontal, so Tc estimates are closer to Tnadir. Following sunset and with conditions favoring strong radiational cooling, it is possible that Tc may become warmer than Tnadir or Toff-nadir. Under these conditions, the sky view factor (as controlled by surface geometry) and surface thermal properties exert a strong control on the resulting surface temperature pattern: roofs, treetops, and horizontal open areas, especially those with low thermal admittance, become cool, while the lower por- tions of the building walls and nearby horizontal sur- faces remain warm. Remotely observed apparent surface temperatures may therefore be cooler than the complete surface if the view is biased toward horizontal, unob- structed surfaces. For off-nadir viewing geometries, re- sults may be sensitive to the particular surface geometric configuration. No nighttime observations are available from this study to test these hypotheses. Complete, nadir, and off-nadir temperatures in each view direction for each of the study areas and all flight times are presented in Fig. 10, where Tc is represented by . All observations at nadir, and most of those atTc1 off-nadir, are warmer than Tc. The single observations that most closely match Tc are those off-nadir obser- vations with view angles in the direction of the most shaded facet (north or northeast walls). On all occasions, Tair is considerably (38–128C) lower than Tc. It is evident from Fig. 10 that urban surfaces are characterized by strong directional variations of appar- ent surface temperature (anisotropy), especially between surfaces viewed with the sensor in an up-sun, versus a down-sun, direction. The variations between complete and remotely observed temperatures can be large when the remote sensor views the surface in the direction of the most directly irradiated vertical surface; maximum observed differences for the LI, R, and D areas were 68, 108, and 78C, respectively. These differences are large in comparison to other influences upon remotely observed surface temperature. Our estimate of the effect of emissivity is 1.58–2.58, which is an upward adjust- ment of the 1.58 estimate by Roth et al. (1989) due to anticipated larger variations in surface emissivity at smaller observational scales. Further errors due to the presence of specularly emitting surfaces in the thermal infrared are possible, especially in downtown environ- ments. These would generate nonisotropic radiance dis- tributions, but detailed analysis of their effect has yet to be undertaken. Variations due to atmospheric ab- sorption and emission along the path length viewed by the sensor are on the order of 48–78 (assuming midla- titude summer conditions) as determined from obser- vations and model simulations (LOWTRAN-7). Spatial variations in atmospheric properties over large cities have been estimated to contribute infrared signals equiv- alent to about 1 K (Carlson 1986). The influence of view direction on the relationship between Tc and remotely measured mean apparent sur- face temperature for each of the study areas is given in Fig. 11. So that results from all three study areas may be viewed simultaneously, the flight data over the D study area have been combined by assigning facets as 1128 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y FIG. 11. Comparison of complete surface temperature with mean apparent temperature for each view direction. Data for all flights conducted over each study area are plotted. The con- vention for plotting data from area D northeast is congruent to north, southeast is congruent to east, northwest is congruent to west, and southwest is congruent to south. northeast is congruent to north, southeast is congruent to east, northwest is congruent to west, and southwest is congruent to south. The relationship between andTc1 Tr from south and east view directions shows remarkable linearity despite variations in time, surface structure, and temperature. In particular, the south view direction (which is most shaded) yields almost a 1:1 relationship and most observations agree within 18C. The exceptions are LI and R shortly after solar noon, when the differ- ence is about 28C. This suggests that there is value in using the remotely sensed mean temperature in the di- rection of the most shaded vertical facets to directly estimate Tc. From a predictive view point, it may be preferable to consider the relation between Tc and nadir observations, since most available remote sensors operate in this con- figuration. Using Tnadir, Toff-nadir, and the total active area Ac: Ap of each site as independent variables, linear re- gressions were performed on the results of Fig. 11. Re- sults are presented in Table 6. When only one indepen- dent variable is used, Toff-nadir in the most shaded direc- tion performs slightly better than does Tnadir. The ad- dition of Ac:Ap was found to be a statistically significant independent variable (a 5 0.99) and slightly improves the model statistics over those obtained from Tnadir alone. The generality of the predictive relations is limited by the small sample size, limited temporal domain, view angle restrictions, and differences in building orienta- tion of the current study. In practice, there is also the fact that Tc is most different from Tr for a single view SEPTEMBER 1997 1129V O O G T A N D O K E TABLE 6. Results of linear regression analysis for prediction of Tc1 from Model A: Tnadir, Model B: Toff-nadir (most shaded direction), and Model C: Tnadir, (Ac:Ap). Model performance statistics [rmse measures and d, the index of agreement (Willmott 1981)] are calculated from modeled Tc vs observed Tc. Regression parameter Model A Model B Model C Constant Coefficient 1 Coefficient 2 r2 Total sum of squares Resid. sum of squares 2.3581 0.8370 0.96 149.2 5.91 0.585 0.957 0.99 149.2 1.49 9.990 0.755 22.8039 0.99 149.2 1.47 F rmse rmse (systematic) rmse (unsystematic) d (index of agreement) 146 0.860 0.171 0.843 0.998 596 0.431 0.043 0.429 0.989 251 0.429 0.043 0.427 0.998 FIG. 12. Comparison of (a) air and nadir apparent surface tempera- tures and (b) air and complete surface temperatures. direction shortly after solar noon (Fig. 10). This is rel- evant given that many remote sensing missions are flown near midday in order to capture the spatial dis- tribution of surface temperature at the time of maximum surface temperature. 6. Application of complete surface temperatures a. Complete surface and air temperature relations Remote measurements of apparent surface temper- ature are often compared with surface-layer air tem- perature measurements (Dousset 1989; Henry et al. 1989; Stoll and Brazel 1992; Gallo et al. 1993; Lee 1993; Nichol 1996) with the goal of generating es- timates of air temperature from thermal imagery. Re- sults vary for the reasons discussed by Roth et al. (1989), namely, remote sensors incorporate a biased view of rough surfaces, air and surface temperatures have a complex coupling through flux divergence in the lowest layers of the atmosphere, and there are mismatches in the scales of observation used for re- mote and in situ measurements. Estimation of complete surface temperatures ad- dresses the problem of observational bias in the re- mote thermal measurements. The results here indicate that large differences exist between daytime apparent surface and air temperatures when compared at the land-use scale (Fig. 12a). Both traverse (canopy level) air temperatures and, where available, fixed tower measurements several meters above mean canopy height are plotted. Data from the LI and R sites exhibit similar diurnal trends (nonlinear) in the pattern of Tair versus Tr (nadir) or Tc. The use of Tair measured just above the canopy layer yields a slight reduction in the differences between the LI and R site. No such observations were available over the D study area. The use of Tc in place of Tnadir only slightly enhances the predictive capabilities for estimating Tair (Fig. 12b). We conclude there is little utility in using simple regression techniques to predict Tair from remotely sensed surface temperature. The physical linkage be- tween the surface and the air is far too complex, es- pecially in urban areas, to be amenable to such anal- ysis (see also Stoll and Brazel 1992). b. Surface temperatures and the surface energy balance Much interest has been generated in the use of re- motely sensed variables to predict the surface energy balance and the partition of net radiation into sensible, latent, and conductive heat components. Remotely measured surface temperature is used in formulations to estimate net radiation and sensible heat flux (e.g., Hall et al. 1992). Net radiation can be determined using remote sens- ing to estimate each component of the radiation bal- ance: downwelling shortwave and longwave radia- tion, surface albedo, and upwelling longwave radia- tion. If this is undertaken over cities, estimation of 1130 VOLUME 36J O U R N A L O F A P P L I E D M E T E O R O L O G Y the upward flux of longwave radiation should consider the effective anisotropy that exists in thermal emis- sions over these surfaces [see Fig. 10 and Voogt (1995)]. Complete surface temperatures could be use- ful as a means of accounting for the anisotropy of rough surfaces. Calculation of the surface sensible heat flux QH can be accomplished using C (T 2 T )a aero airQ 5 , (5)H rah where Ca is the volumetric heat capacity of air, rah is the resistance to heat transfer for the surface, Taero is the surface aerodynamic temperature, and Tair is the air temperature just above the surface. The difficulty in applying remote sensing to the estimation of QH via (5) is that Tr, as measured by a remote sensor, is in general different from the aerodynamic temperature (Hall et al. 1992; Norman et al. 1995; Sun and Mahrt 1995). This occurs primarily due to the effects of surface emissivity and directional dependence on viewing angle [the effective anisotropy; Norman et al. (1995)]. Differences between Tr and Taero are im- portant because QH is sensitive to even small errors in the difference [Taero 2 Tair; see, for example, Nor- man et al. (1995) and Kohsiek et al. (1993)]. Here, we calculate variations in QH for site R when Tr and Tc are used in place of Taero. The calculations use the method of Kustas et al. (1989). The site has a rough- ness length of z0 5 0.52 m and a zero-plane displace- ment length of 3.5 m (Steyn 1980); other input con- ditions were obtained from observations taken at the sunset tower, which is located in site R (Roth and Oke 1993) during the time of the remote sensing over- flights. The parameter kB21, the added resistance of a surface to heat transfer (e.g., Garratt 1992; Brutsaert 1982), has been shown to have a reasonably constant value of 2.5 over a range of vegetative surfaces, in- cluding partial canopy covers, but bluff-rough sur- faces are characterized by much higher values. Koh- siek et al. (1993) report kB21 5 3.68 over a mixed short vegetation and stone surface, with the sugges- tion that a rock surface may have values on the order of 8–10. The urban residential area has a combination of solid and permeable roughness elements with a partial canopy cover, so kB21 may be intermediate between the values for vegetation and bluff bodies. We performed calculations by setting kB21 at constant values of 2.5, 5, and 10; using values for bluff-rough surfaces from Brutsaert (1982); and using the back- calculated kB21 required to match the observed QH and rah for the site (S. Grimmond 1997, personal com- munication). The use of the bluff-body curve pre- sented by Brutsaert (1982) yields kB21 in the range of 22–27. Matching kB21 to the tower observations of QH and rah (which solves for the required temper- ature gradient) yields kB21 ø 3. The results show QH may vary from 12 to 85 W m22 8C21 for the observed range of Tr and Tc, de- pending upon the time of day, atmospheric conditions, and kB21. These values are of similar magnitude to those given by Norman et al. (1995). Differences in QH due to the method of calculation of Tc are generally 10%–20%. When Tnadir is used in place of Tc, differ- ences are 15%–31% in the morning and rise to 15%–40% later in the day as the difference Tnadir 2 Tc increases. Variations in calculated QH due to the use of off-nadir remotely measured temperatures of- ten exceed 50% when comparing Toff-nadir in the up- and down-sun directions and can be greater than 100% when comparing the most directly irradiated facet with Tc. In accordance with the close agreement be- tween the temperature of the most shaded facet and Tc, differences in QH are minimized (generally less than 5%) for this temperature pair. Comparison of QH(obs) and QH(est) using rah calculated from the tower site data suggests that the required temperature gradient for Eq. (5) is too large, partic- ularly at midday. The use of Tc in place of Tr improves QH estimates; however, Tc remains warmer than the temperature required (Taero) to satisfy QH(est) 5 QH(obs). The required temperature is approximately 28–2.58 cooler than Tc in the morning and late afternoon and 78 cooler in the early afternoon. It is possible that this difference may be due partly to an underestimation of the shaded portion of the complete surface esti- mate, which is less apparent in the morning and late afternoon when Tnadir incorporates more shaded sur- faces than in the early afternoon. A more detailed comparison of the tower-mounted flux estimates for the LI and R sites and those derived using remotely sensed and complete surface temperatures is under way. 7. Conclusions This work presents the first attempt to calculate a complete surface temperature that takes into account both the horizontal and vertical surfaces in urban ar- eas and thus recognizes the thermal impact of the three-dimensionality of the system. Complete surface temperature estimates are shown to generally differ from remotely sensed estimates of urban surface tem- perature whether they view the city from nadir or off- nadir. These findings are true for the three land-use types studied. Off-nadir observations in the direction of the most shaded facet agree most closely with Tc and provide a useful first approximation to its esti- mation. The limited data available suggest this ap- proximation is least valid at midday. During the day- time, complete surface temperatures are greater than air temperature by several degrees. Currently, our findings serve primarily as a warning of the dangers of using remotely observed surface temperatures without regard to the geometric nature SEPTEMBER 1997 1131V O O G T A N D O K E of the surface being observed and the viewing con- ditions. We emphasize the need to match scales of observation with those of analysis and to recognize, for a given application, which surfaces and which physical variables are of importance (e.g., air, surface, or aerodynamic temperature). Work is under way to develop and assess methods to estimate Tc from re- mote temperature observations and to further consider the effect of scale. Further work requires looking at the usefulness of complete surface temperatures to the estimation of air temperature and energy balance flux- es over urban areas, and how significant the role of surface emissivity is in these matters. Acknowledgments. Thanks are due to Drs. R. Spron- ken-Smith and S. Grimmond for assistance with the field observations. Drs. S. Grimmond and M. Roth provided helpful suggestions regarding the surface energy balance calculations. The AGEMA scanner was made available by the Ontario Laser and Ligh- twave Research Centre. P. Chalk assisted with the preparation of the figures. 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