The PTST data were obtained from a thermal camera on top of a mobile hydraulic mast installed in a relatively uniform suburban area (Sunset neighbourhood) of Vancouver, BC, Canada. This area has various long-term instrumentation for urban climate monitoring in place, including measurements of radiative and convective fluxes on top of a 26 m long-term flux tower named “Vancouver-Sunset” . The area is characterized by detached houses (Local Climate Zone 6, ) following an orthogonal street grid layout. Measurements and modelling took place in the 6100 block of Elgin Street between E 45th and E 46th Ave (49∘13′42′′ N, 123∘05′02′′ W, WGS-84), located 500 m to the NW of the “Vancouver-Sunset” flux tower. The selected canyon section has a total of 12 buildings uniformly aligned along a north–south road, which minimizes asymmetric solar irradiance interactions over the course of a day. The lack of tall vegetation in the canyon section simplifies the projection of measured longwave emittance from the PTST data set on to a urban surface model (USM) and reduces the geometric complexity and uncertainties associated with the movement of trees in wind. The canyon section studied had a canyon width of 33.3 m. A concrete road of 13 m width was located roughly in the centre of the canyon bounded with lawns (and sidewalks) on both sides. Houses in the canyon were all built between 1971 and 1976 and are of similar dimensions and materials, with a rectangular footprint oriented perpendicular to the street and low-pitched roofs with slopes from 10 to 15∘. Building peak heights vary from 6.2 to 7.1 m in a two-floor configuration, with an area-averaged roof area height of 6.23 m. Total building volumes range from 520 to 750 m3. Most buildings have extensive back porches often with a carport towards a 6 m wide back lane (asphalt, concrete and bare soil). The relative uniformity of the structures simplified the complex geometry and proved helpful when statistically filling obstructed areas. The model domain encompassed a west–east (cross-canyon) extent of 90 m and a north–south (along-canyon) extent of 92 m (Fig. ).

A pan and tilt device allowed the camera to record 360∘ scans at different tilt angles over the course of a 24 hour cycle at a temporal resolution of 60 min. The field of view (FOV) of the PTST data set corresponds roughly to that of a downward-facing hemispherical radiometer. In contrast to a radiometer that returns a single, integrated value over time, the spatially resolving PTST covers the lower hemisphere with >4×104 pixels over time (Fig. ).

A Thermovision A40M thermal infrared camera (FLIR Systems, Wilsonville, Oregon, USA) with a wide angle lens was mounted atop a mobile hydraulic mast in the centre of the canyon studied at a height of 17.95 m above ground level (2.88 zb). The system has a FOV of 61∘×48∘ corresponding to 320 by 240 pixels. Every hour, the camera was rotated in a 360∘ panorama at two different tilt angles, one at approximately 65∘ off-nadir, another at approximately 45∘ resulting in panoramic scans with a spatial resolution of 1.07×10-5 sr, which corresponds to panoramas of > 40 M pixels per scan. The panorama omitted a cone directly in the nadir, where the mast was located. Details of the scan pattern can be found in .

The Thermovision A40M uses an uncooled microbolometer sensor to retrieve TB from measurements of incoming longwave radiation. The microbolometer is sensitive to thermal infrared radiation between 7.5 to 15 µm although highest sensitivity is concentrated between 9.2 and 11.8 µm (> 90 % sensitive). The detectors have a radiometric resolution of 16 bits/pixel. At ambient T0 near 300 K, a sensitivity of 0.08 K is achievable, with an absolute accuracy of ± 2 K . Data from the thermal camera were recorded in digital format via FireWire on a PC. Each panoramic scan resulted in 250 frames at 320 by 240 pixels.

Two tripods with meteorological sensors were deployed to the north of the hydraulic mast on lawns to the east and west of the street and provided measurements of air temperature Ta and relative humidity RH at 0.3 m (HMP-35, Campbell Scientific Inc., Logan, UT, USA). Those were used for atmospheric correction (see Sect. ). Additionally, at “Vancouver Sunset” (49∘13′34′′ N 123∘04′42′′ W, WGS-84), a CNR1 4-Component Radiometer (Kipp and Zonen, Delft, Netherlands) provided measurements of hemispherical radiation fluxes at 26 m above the surface. Shortwave irradiance (K↓), and reflected shortwave radiation (K↑) were measured using two CM3 pyranometers, and longwave irradiance (L↓), and the sum of emitted and reflected longwave radiation (L↑) were quantified using two CG3 pyrgeometers (spectral sensitivity from 5 to 50 µm), all at 5 min temporal resolution.

Observations were made between 14 September 2008 at 13:30 and 15 September 2008 at 12:30. The weather during the field campaign was cloud free. A cloud-free situation with direct-beam irradiance maximizes thermal anisotropy and is usually the situation when thermal remote sensing is performed. During the study period, air temperatures ranged between 284.7 and 298.5 K in the canyon. Daily total measured K↓ was 31.9 MJm-2day-1, of which 4.9 MJm-2day-1 was reflected (K↑). Daily total measured L↓ was 29.4 MJm-2day-1, and L↑ was 37.1 MJm-2day-1.

Basic positional information of the urban surface was collected with a Trimble R7 differential GPS (DGPS) unit (Trimble, Sunnyvale, California, USA), with horizontal position accuracy <1 cm and vertical accuracy < 2 cm. The DGPS data were supplemented with Light Detection and Ranging (LiDAR) data flown during March 2007 by a fixed wing aircraft operating a TRSI Mark II discrete-return sensor . For the purposes of this project, only the ground returns of the LiDAR were used. Close-range photogrammetry was chosen to reconstruct buildings. In close-range photogrammetry, multiple images from varying directions of the same building are correlated to solve 3-D positions of points and lines. These features are then assembled into vector representations of buildings. The images collected for photogrammetry were taken at ground level and from atop the same hydraulic mast at multiple locations using a Nikon D100 digital single-lens-reflex (SLR) camera (Nikon, Tokyo, Japan), equipped with a 28 mm Nikkor lens. Eos Photomodeler (Version 6.2, Eos Systems, Vancouver, BC, Canada) was used to reconstruct vector building models from digital SLR images. Eos Photomodeler has been used previously for modelling of urban form with good performance . The street canyon was broken down into its component features, with each house being modelled individually, and then integrated together in 3-D Studio Max (Version 8, Autodesk, San Raphael, CA, USA) to form a complete canyon 3-D model. The resulting USM is visualized in Fig.  in form of a 3-D projection.

The material type defines the emissivity ε of a facet and other underlying material properties (e.g. thermal admittance). A survey of the ground-level photos and orthophotography was undertaken, creating an inventory of all material types in the canyon (Table ). Materials were manually marked on the triangles composing the USM using a material identifier code. Where material boundaries did not fit the topology of the model, additional triangles were added in order to correctly attribute materials. To each of the materials, a ε value was attributed based on . It was assumed that ε is isotropic; i.e. surfaces show a Lambertian behaviour in the longwave band. Also aging and weathering of surfaces was not considered in the attribution of ε to materials.

The sky view factor (ψsky) was calculated for each surface pixel using an ambient occlusion algorithm in 3-D Studio Max. In ambient occlusion, each pixel on a 3-D model is the source for a Monte Carlo ray casting simulation, where sampling rays are cast in all directions from the pixel with a cosine probability relative to the zenith. To test the ability of ambient occlusion algorithms to numerically determining ψsky in complex geometries, several idealized 3-D situations in which ψsky was known were compared against this algorithm. The results showed good correspondence with a maximum error in ψsky of 0.02, indicating that the ambient occlusion method was adequate .

Atmospheric correction were performed for each time step after projecting TB back onto the USM. A set of MODTRAN simulations were run for the current camera spectral range following the procedure outlined in . These corrections considered path length (ds), local air temperature (Ta, measured in canyon), sensor measured brightness temperature TB and relative humidity RH (measured in canyon). Due to the large number of Ta, TB and path length values, it was impractical to run a MODTRAN simulation for each combination. Instead, a number of scenarios were run by changing TB at 5 K intervals (for range 278–323 K), Ta in 2 K intervals (273–303 K), RH at 2 % intervals (40–80 %), and d at intervals of 10 m (15–75 m). The resulting look-up table was interpolated linearly between two TB values to match the actual TB of each pixel, while for all other parameters the nearest value was used. Corrections of individual pixels ranged between 0.7 and 8.6 K (road, midday, large ds) over the 24 h.

To retrieve each pixel's T0,px from measured TB,px we used the broadband equation showing that longwave flux density L↑,px observed from a surface is the sum of emittance and longwave reflected radiation : L↑,px=σTB,px4=εpxσT0,px4+(1-εpx)L↓,px, where εpx is the pixel's emissivity previously attributed based on material. Equation  was then solved for T0,px: T0,px=σTB,px4-(1-εpx)L↓,pxσεpx4. A pixel's incoming longwave radiation L↓,px is approximated as the sum of longwave radiation from the sky weighted by the pixel's sky view factor (ψsky), and the longwave radiation from the canyon, weighted by the pixel' ground view factor (1-ψsky). L↓=ψskyLsky+(1-ψsky)σT0,C4 Lsky is the directly measured incoming broad-band longwave radiation at the tower “Vancouver Sunset” for the given time step. The approximation in Eq. () assumes that atmospheric irradiance is isotropic, and that the surrounding urban facets all have a uniform surface temperature equal to T0,C. In this equation we first approximate T0,C by TB,C. The correction was iteratively applied as the temperature correction changes the value of T0,C. This correction was performed repeatedly until the corrected surface temperature T0,px for one iteration was not significantly different from T0,px for the previous iteration (difference of less than 0.25 K). This was accomplished within 5 iterations.

As the thermal camera is at a fixed location, it is evident that not all pixels in the texture maps can be seen by the camera. Secondly, selected areas were removed by manual inspection because of minor misalignments along edges. The mean visibility of roofs and ground in the entire domain are 95 and 72 %, respectively. The visibility of E–W walls is only 46 % (lane-facing walls of buildings cannot be seen). For N–S walls, the visibility is good in the four nearest houses (≈ 90 %); however it is very poor (< 10 %) for all houses further away from the thermal camera. Hence, the PTST data set is also a preferred view; however its panoramic nature means that it contains data from all relevant facets of the urban canopy. However for simulating alternative projected FOVs the USM needs to be populated on all sides with temperatures.

The gap filling of unseen pixels was based on an adaptive search algorithm. For each pixel requiring interpolation, four predictors were extracted: the pixel facet type (roof, wall, ground), pixel material type, pixel orientation (azimuth and slope) and pixel ψsky. Each of these factors affects TB of a surface. A search algorithm then looked at all measured pixels in the same texture sheet that matched the features to those belonging to the pixel to be filled. Matched pixels had to have identical facet type and material to the originating pixel. Sky view factor and orientation had variable thresholds: the orientation threshold was based on the slope of the pixel. Pixels with a high slope required an orientation value that was very close (within 5∘), while pixels with a low slope had a more relaxed threshold (within 15∘). The pixels used to statistically fill the obstructed target pixel had to experience a difference in ψsky of less than 0.03.

If similar pixels could not be found on the same object (i.e. house), the sheets for all other houses and the ground were examined. This was key in areas where only one side of the house was visible to the thermal image, as pixels for the opposite side would all be unattributed. This gap filling assumes that the houses have similar thermal behaviour in each direction from the tower. The same wall orientation is visible on the other side of the scanning camera (i.e. panorama) and houses with pixels matching the orientation could be always found. If similar pixels were still not found, the ψsky and orientation thresholds were relaxed by 5 %, and the search was repeated. In this way all pixels were matched.

If a simulation of a sensor at a high altitude is desired, the single domain of 92 by 90 m is insufficient. The domain was therefore repeated in the x and y directions, to create an effectively infinite suburban residential area conserving the anisotropy of the measured area. The resulting domain was then repeated approximately 50 times in both horizontal directions (45 000 houses). Though not completely infinite, it approximates an infinite plane for the view directions as simulated for a hemispherical downwards-facing sensor. The tiled surface is not completely representative of a city: it has no east–west streets, but serves adequately as an idealized suburban surface with the given data set. The characteristics of the cyclic domain are summarized in Table .

In 3-D Studio Max, a pinhole-type camera was placed facing downward at 104 m above the tiled surface. A FOV of 1∘ was used for the camera with rendered pixel dimensions of 256 by 256 pixels (Fig. a). These parameters approximate a sensor pointing down at nadir with a projected FOV of 30 m. For oblique views, the camera was angled so that each frame faced the same centre point of the tiled surface (but the projected FOV was larger). Camera azimuths (Ω) from 0 to 360∘ at an interval of 30∘ were simulated with off-nadir angles (ϕ) from 0 to 70∘ at intervals of 10∘. This resulted in a total of 96 different view simulations for each of the 24 hourly steps.

Hemispherical sensors were rendered as circular areas with diameter 256 pixels (Fig. b). The sensor was positioned directly above several points in three different transects from west to east throughout the canyon. For each position, varying heights were chosen (Fig. ), from 2 to 10 m (at 2 m intervals) and from 10 to 100 m at 4 m intervals (up to approximately z/zb = 10). A total of 270 hemispherical radiometer positions were rendered for a total of four time steps (13:30, 18:30, 00:30, and 06:30). These 6 hour intervals gave a reasonable assessment of the canyon temperature patterns over time for the available computational time. The imported Lpx,h was then corrected for angle-of-incidence effects (cosine response) and averaged to recover a single signal of Lh for each radiometer position. Similar to the narrow FOV sensors, the simulated hemispherical sensor signals consider only emittance, and treat the surface as a black body. Note that measured Lh from a real broad-band pyrgeometer at different heights would additionally be impacted by atmospheric effects between the surface and the measurement level that are not considered in the current study.

Figure compares the surface temperature inferred from a narrow FOV sensor at nadir (T0,d(ϕ=0)) to T0,C. T0,C is lower than T0,d(ϕ=0) in the daytime and is higher following sunset in a situation that favours strong radiative cooling (many facets with high ψsky, clear skies, both of which are present in this situation). The largest difference is present near solar noon (solar altitude 43∘); at this time horizontal surfaces, especially those with large ψsky, are warm relative to vertical surfaces and dominate the radiance received by a narrow FOV sensor. The reverse is true at night, where wall T0,f are likely to be higher (see Fig. ) than T0,f of horizontal facets, in particular those of roofs, due to their low thermal admittance.

A maximum difference T0,d(ϕ=0)-T0,C of +2.0 K is observed at 13:30 (overestimation by the sensor), and values are closest at 10:30. Over the course of the day, the root mean squared error (RMSE) of T0,d(ϕ=0)-T0,C is 1.2 K. compared T0,C to T0,d(ϕ=0) of a hardware scale model over the course of a day. The maximum overestimation T0,d(ϕ=0)-T0,C is reported at solar noon and has a value of around +2.5 K, which is similar to this study (+2.2 K). During nighttime, the T0,d(ϕ=0)-T0,C differences for the lowest density configuration in range between -0.5 and -1 K, which is again comparable to values found here (-0.9 to -1.4 K, underestimation).

The large number of view directions simulated allows the systematic examination of the difference between directional and complete surface temperatures for oblique sensor views. The difference T0,d-T0,C is plotted in polar form in Fig. . In these polar plots, each pixel represents a temperature value for a view direction as plotted by the off-nadir angle (ϕ) and azimuth from geographic north (Ω) of the sensor location. At the centre of the plot lies the value at nadir (ϕ=0).

In the daytime situations, the effects of anisotropy are clearly visible, particularly before solar noon (Fig. b). Here in half of the hemisphere, T0,d underestimates T0,C (opposed to solar position) and in the other half T0,d overestimates T0,C (same side as solar position – the solar position is represented by a cross in b). Generally over the day, the hotspot of highest T0,d is following the solar position (see also Supplement). When the position of the sun is close to the direction of the sensor, the signal is mostly overestimated. The daytime hotspot has a slight lag from the sun's position (approximately 1 h).

This pattern of higher visible T0,d from the direction of the sun persists until the sun moves below the horizon (by 17:30) at which point the difference between west and eastern facets begins to be reduced, but is still sustained a few hours (Fig. , right). By 18:30, most modelled views show a T0,d lower than T0,C. The south-facing regions remains warm due to residual heat stored that is now released.

Moving into the nighttime, a continued decay of the daytime hotspot is evident until 21:30 (see Supplement). Until this point, views from the south continue to be consistently warmer, underestimating T0,C by only 0.5–1.1 K. For most other views, there is a consistent underestimation of T0,C by T0,d by between -1.0 and -2.2 K. Generally, anisotropy is lower at night. After the hotspot disappears, most of the view directions show similar values for a given ϕ. Moving onto the morning, a hot spot develops in intensity by 08:30 and causes very large T0,d to T0,C differences of -2.4 K when looking from the west.

Throughout all simulations, we find overestimations of T0,C by T0,d of up to +2.9 K (17:30) and underestimations by up to -2.6 K (08:30) (Fig. ). The simulated values of T0,d can be also used to determine the anisotropy (maximum temperature difference between the most extreme view directions), which is the distance between the minimum and maximum whiskers in Fig. .

The effective anisotropy shows expected behaviour following observational results from , with high anisotropy in the daytime (up to 3.5 K) and little anisotropy at night (< 1.0 K). The trend also follows that of the residential neighbourhood in , which showed higher differences in measured brightness temperatures from differing view directions in morning and late afternoon situations (10:00 and 17:00) compared to midday situation (14:00). Magnitudes are similar as well though the simulated Elgin Street anisotropy is lower by approximately 1.5 K at 10:00 and 17:00. All of these studies took place in Vancouver neighbourhoods with similar urban structure, so an agreement is expected and supports the findings here. Aircraft measurements of thermal anisotropy from Marseille, France in also follow this trend, with maximum anisotropy during the morning (08:00 to 10:00). However, their anisotropy is much larger (up to 10.5 K) likely due to the different urban form and fabrics, different thermal sensor types, and potentially also differences in the ratio of direct to diffuse shortwave irradiance.

At 13:30 there is a strong variation in Lh with pyrgeometer position across the canyon as indicated by the different coloured profiles in Fig. a. The 18 profiles converge near 500 Wm-2 at z/zb=7.5 to a RMSE between all profile locations at the same height of less than 1 Wm-2. The pattern of variability between sensor positions across the canyon cross section is repeated for all three canyon slices (y=-30,0,30 m, see Fig. ) with only minor differences.

Below zb, pyrgeometer positions over lawns exhibit lower Lh (lower T0 due to transpirative cooling of lawns that cover the largest view fraction in the FOV). The pyrgeometer positions on opposite sides of the street exhibit different behaviour: the positions over the western lawn experience higher Lh due to the warmer nearby house east-facing walls and also the warmer grass temperatures on the west lawns at noon (2.5 K warmer than lawns on east side). West lawns and the east-facing walls receive more incoming shortwave radiation during the morning when they are not shaded. For the pyrgeometer positions over the eastern lawn, Lh increases continuously with height, particularly above z/zb=1.0, as at this point roofs will begin to contribute to the sensor view. Being substantially warmer than lawns, the roofs will increase the measured Lh. The western lawn shows a different pattern, with rapidly increasing Lh until z/zb=1.5 at which point Lh beings to decrease with height.

The profiles of simulated pyrgeometer positions over road and lane facets are behaving roughly similar, with the road having slightly higher temperatures due to a larger area covered by concrete being present and the higher ψsky of this position compared to the simulated lane. This causes Lh over the road at low z/zb to be larger. For the lane, its lower ψsky will reduce heating due to lower solar irradiance (shadowing). In addition, facets visible in the lane include recessed areas such as garages and porches which receive less irradiance throughout the entire day. We would expect these recessed areas to reduce overall Lh. Both road and lane locations show a decrease in Lh with height.

Directly above the roofs, Lh varies greatly across the canyon and for many positions is higher than the converged value far above the canopy, as the view factor comprises mostly hot roofs while walls are less visible. Roofs have been shown to be warmer throughout the experiment in the daytime (see Fig. ), and also exhibit a range of different albedo and thermal admittance values and that explain differences along the canyon and between the east and west rows. Most profiles of Lh decrease rapidly with height. Only above-roof positions (those at x=-30 and x=+30 m) show larger variability of Lh with location in the along-canyon direction as opposed to the other positions (lawns, road). This variability is driven by differences in roof materials from house to house, with asphalt roofs giving consistently higher Lh temperatures than metal roofs, likely due to differences in albedo.

At 00:30 (Fig. b), the vertical profiles of simulated Lh (Fig. 5.16) experience a similar shape for locations over the road and over lawns with a local maxima in the range 1<z/zb<2. Near-surface positions above lawns remain the lowest Lh of all profiles. Modelled Lh increases immediately and rapidly with height above the two lawn positions as warmer night-time walls come into the FOV of the radiometers. For both positions over lawns, Lh decreases with height above z/zb = 1.5 as roofs come to dominate the FOV. It is however interesting to note the variation between the profiles above the east and west lawns. Above the eastern lawn the profile of Lh decreases more slowly with height. This is likely a remnant from afternoon heating delivering irradiance to warm the west-facing walls of the eastern row of houses for longer in the evening. Cooling of house facades and lawns on the western side of the canyon has a head start, so Lh over western lawn positions decrease faster. Even with this difference, by z/zb=6.3, the RMSE between all positions converge near 387 Wm-2. There is no significant variation in the observed profiles over lawns at the different horizontal slices.

Above roads and lanes, the profiles show that Lh is increasing until z/zb = 1.0 and then decreasing. There is no significant variation in the observed profiles over roads and lanes at the three different along-canyon cross-sections.

Above-roofs, Lh shows substantial variation depending on position along the canyon due to different daytime heating (albedo) and thermal admittance (roof isolation). In general however the magnitude of the variation is less than during the daytime: temperature differences between different roofs are lower. Profiles of Lh above western houses show an increase with height until convergence with all other profiles at z/zb = 6.3.