Assessment of an Urban Sensor View Model for thermal anisotropy
J.A. Voogt
Department of Geography, University of Western Ontario, London ON, Canada N6A 5C2
Received 8 September 2006; received in revised form 8 May 2007; accepted 10 May 2007
Abstract
The surface-sensor-sun relations model (SUM) of Soux et al. [Soux, C.A., Voogt, J.A., & Oke, T.R. (2004). A model to calculate what a remote
sensor ‘sees’ of an urban surface. Boundary-Layer Meteorology, 111, 109–132.] is modified to include a coupling of SUM with the actual building
structure of a study area, thereby allowing variable building heights and shapes to be represented within SUM as well as the provision for an interbuilding
spacing that provides a more realistic urban block structure in the internal SUM urban surface representation. Model simulations using
both modifications are performed and compared with airborne observations of surface temperature made over a Light Industrial area and a
downtown area of Vancouver, BC. The results are generally good, although there is a general tendency to underestimate the overall thermal
anisotropy. Use of mean facet temperatures in the validation limits validation statistics for one study area; improvements are made when facet
temperatures are updated from individual flight lines. Performing a sensitivity analyses on the contributions to the thermal anisotropy suggests that
surface structure and microscale temperature variability both make substantial contributions to the total anisotropy. This finding underscores the
importance of including microscale temperature variability in assessments of urban thermal anisotropy. Full hemispheric plots of directional
temperature and statistics for each study area are presented as an application of the model and show smooth variations in directional temperature
when averaged over the study area.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Urban surface temperature; Thermal anisotropy; Sensor view model
1. Introduction
Thermal remote sensors viewing urban areas must consider
directional variations of upwelling thermal radiation. These
variations are the result of microscale temperature patterns created
by the three-dimensional urban surface structure. This directional
variation is termed the effective thermal anisotropy of the surface.
Effective thermal anisotropy arises because of macroscale surface
structure and temperature patterns, rather than the non-lambertian
behaviour of individual surface components. The effective thermal
anisotropy is an impediment to the application of thermal
remote sensors over urban areas because it implies the measurements
are biased by view direction and time, and therefore not
fully representative of the thermal state of the surface. In recognition
of this problem, it has been common practice to limit the
viewing angle of remote thermal observations over urban areas to
nadir or near-nadir angles, thereby providing measurements restricted
primarily to the horizontal surface components of the
urban area. This may be termed a “birds-eye” or plan-view of the
urban surface (Voogt & Oke, 1997). While this perspective
provides a first-order approach to normalizing thermal remote
measurements over urban areas, it remains a biased measurement
that does not fully account for the three-dimensional structure of
the surface. Further, it limits the utility of some remote sensors
with significant off-nadir scanning capabilities.
In order to better understand urban thermal anisotropy, observational
or modeling approaches may be used. Direct observations
of urban thermal anisotropy are difficult to acquire relative
to those over other microscale surface covers such as crops, where
low towers and standard infrared thermometers may be used to
sample representative areas of the surface type of interest (e.g. see
the review by Paw U, 1992). Observations of urban anisotropy
typically require aircraft based sensors to provide suitable spatial
resolution and control over viewing direction, although towers
have been used in some select cases (Soux et al., 2004). Examples
of direct observation of urban thermal anisotropy include those of
Iino and Hoyano (1996), Nichol (1998), Voogt and Oke (1998a)
and Lagouarde et al. (2004). These studies have demonstrated the
Available online at www.sciencedirect.com
Remote Sensing of Environment 112 (2008) 482–495
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E-mail address: javoogt@uwo.ca.
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doi:10.1016/j.rse.2007.05.013
large absolute magnitude – up to 10 °C in highly urbanized
districts – of urban thermal anisotropy, where anisotropy is taken
to represent the maximum difference in sensor observed temperature
from any two view directions.
The high costs associated with direct observations of urban
thermal anisotropy generally preclude assessments of multiple
land uses, different cities, detailed temporal variations, especially
of night-time versus daytime effects, or seasonal variations.
To expand our knowledge, the construction of numerical
models that can represent the urban thermal anisotropy is
needed. One model explicitly developed to assess urban thermal
anisotropy is the SUM surface-sensor-sun relations model Soux
et al. (2004). This model calculates how a remote sensor views a
simple urban surface by calculating the radiative source area or
view factors of the urban surface components for a given remote
sensor position. The model design is sufficiently flexible to be
used for a range of scales. At the microscale, the model can
provide radiative source area assessment (Oke, 2004; Schmid,
1997) for tower mounted hemispherical radiometers common to
surface micrometeorological measurements. Radiative source
area analysis can be used to assess the impact of the surface
structure on, for example, net radiation (Offerle et al., 2003) or
the matching between radiative and turbulent flux source areas
(Schmid, 1997, Voogt & Oke, 2003). At larger scales, when
combined with surface temperature information, the model is
able to estimate the anisotropy of radiative temperature as seen
by a given sensor-sun-surface configuration.
The objectives of this paper are to:
• evaluate the performance of the SUM 3-D directional sensor
view model for two urban land use areas;
• investigate the sensitivity of the model results to the representation
of the urban surface structure and microscale
temperature variability;
• use the model to investigate the full anisotropic distribution
of upwelling thermal radiation over the two land use areas.
Fig. 1. Sensor IFOV projected onto a modeled urban surface using (Top) a simple surface representation, (bottom) GIS database for the light industrial study area.
483J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
The paper uses an updated version of the SUM model that
includes a provision to incorporate a more realistic surface
representation using individual building footprint data. The
overall goal is to provide a first full-scale test of the ability of the
model to estimate the thermal anisotropy at the urban land use
scale, and demonstrate the applicability of the model to describing
the full anisotropic behaviour of thermal radiation over
select urban surfaces.
2. The SUM directional sensor view model
The SUM surface-sensor-sun relations model (Soux et al.,
2004) represents how a remote thermal sensor views an urban
surface. The remote sensor is specified in terms of instantaneous
field of view (IFOV), and angular and azimuthal viewing
geometry (all given in degrees) as well as sensor height and
relative position to the surface structure. The urban surface
structure is represented as a four dimensional array, where the
first 3 dimensions are the urban surface structure, and the fourth
stores particular attributes of each cell of the surface. The urban
surface is composed of roofs, walls, roads and alleyways,
although there is no formal restriction on the number of surface
components that may be represented.
The urban surface is represented here in two ways: a simple
repeating arrangement of buildings and streets (simple surface),
and through a spatial database (Geographic Information
System — GIS) of actual building footprints and heights (GIS
surface). The simple urban surface consists of a regularly repeating
series of rectangular-shaped buildings of equal dimensions
(including height) that is defined in terms of a building
width, length, height, street width, alley width, inter-building
spacing and a number of buildings along a “block” (Fig. 1a). In
the original model formulation (Soux et al., 2004) there was no
provision for an inter-building spacing. The GIS surface reads
in the building footprints and heights from a spatial database so
that the actual building layout is preserved and variable building
heights are accommodated (Fig. 1b). In this implementation,
building facets are assumed to be in one of four orientations 90°
apart relative to the primary street azimuth, which can be set to
any direction. Extension to variable wall azimuths is not limited
by the model formulation.
For each cell, the model determines whether the cell is shaded
or sunlit, and whether it is viewed based on the given sensor
viewing geometry. View factors for each viewed cell are calculated
using a contour integration approach, and then summed
and reported as totals for the sunlit and shaded components of
Fig. 2. Light industrial study area in Vancouver, BC. Canada showing: building GIS, site photo, building height frequency distribution and nadir thermal image
composite overlaid with building footprints.
484 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
each facet of the urban surface. The view factors are then
coupled with radiometric temperatures of the component
surfaces to provide an estimate of the sensor directional radiometric
(or brightness) temperature for a particular azimuth and
viewing angle.
3. Data and methods
3.1. Building data
Surface databases of building footprints for two study areas:
a light industrial (LI) area and a downtown (DT) area of
Vancouver BC Canada (Figs. 2 and 3) were constructed.
Building footprints in the LI study area were digitized from
1994 1:2000 scale aerial photos and confirmed with photos
taken during the observation period. Building heights were
estimated from field observations using an inclinometer in
August 1994. Building footprints and heights in the DT area
were taken from the 1984 City of Vancouver Planning
Department Downtown Peninsula Map and updated based on
the 1994 aerial photos, along with photos taken during the
observation period. Building heights along the main traverse
routes of the vehicle-mounted infrared thermometer array (Section
3.2) were updated from ground-based inclinometer measurements
made within a year of the observation period.
The LI area is characterized by relatively long rectangular
buildings of 3–4 stories with flat roofs, and largely devoid of
vegetation (b5% Masson et al., 2002). The DT area is characterized
by a few very tall massive buildings mixed in with a
high density of lower (4–6 storey) buildings, again with very
low amounts of vegetation. General characteristics of the sites
are shown in Table 1. The digitized vector polygons were
converted to a 1 m raster grid and coded as roofs, streets, alleys,
building interior or one of 4 wall orientations. The scale of the
downtown surface model was reduced by a factor of 3 (an
individual cell array represents 3×3×3 m) to reduce the array
size in the SUM simulations. The building footprints replicate
the configuration of the buildings, including representation of
adjoining walls of equal heights that are a common feature in
the LI area. A limited number of smaller scale building features
such as elevator shaft housings are included where they
formed a significant feature of the building roof in the LI study
area, but in general, the fine-scale details of the buildings
such as balconies, roof parapets, variable height roofs are not
included.
3.2. Temperature data
Temperature data is required for two purposes: to provide
input component surface temperature estimates for the modeled
urban surface and to provide a validation data set for the SUM
output. Radiometric temperatures were measured using two
systems: an airborne thermal scanner and a ground-based array
of infrared thermometers.
Fig. 3. Downtown study area in Vancouver BC Canada showing: building GIS, site photo and building height frequency distribution.
485J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
The airborne thermal scanner (AGEMA 880 LWB) was
equipped with a 12° field of view lens and was deployed from a
helicopter. Images were sampled along flight lines using both
nadir and 45° off-nadir viewing angles at azimuths orthogonal
to each of the four major street orientations (Voogt & Oke,
1998a). A circular area on each image equivalent to a conical
12° field of view was extracted for comparison with modeled
results (Fig. 4). A summary of the flights performed is shown in
Table 1.
The ground-based array of non-scanning infrared thermometers
was mounted on a vehicle that was traversed along all
the streets and alleyways in the study area. Thirteen traverses
were conducted on each of the two observation days, with
traverses set to coincide with times of the overflights (Table 1).
Sampling of road and wall surface temperatures was conducted
at ∼5 m intervals and the data was processed to remove
observations from non-building surfaces and to identify the
mean values of temperature distributions related to sunlit and
shaded components of wall and road surfaces. Full details of the
method are available in Voogt and Oke (1998b).
3.3. Methods
3.3.1. Viewing the surface
3.3.1.1. GIS surface. The position of the modeled sensor
IFOV projected on the GIS surface (Fig. 1) was set to reproduce
the observed position (as shown by the thermal infrared imagery)
for both the start and end points of the flight line. Between
these two points the modeled sensor position is incremented in
equal steps across the GIS domain. Where significant differences
in sensor viewing angle or azimuth occur along the flight line,
the simulation is broken into sections, with separate viewing
geometries for each section. At each sampling location the SUM
model output (view factors for each sunlit and shaded surface
component) is saved.
3.3.1.2. Simple surface. The urban surface parameters are
chosen to best approximate observed dimensions of the area as
derived from GIS analyses, and to preserve the non-dimensional
complete to plan area ratio (Ac/Ap), and roof to plan area ratio
(Ar/Ap). The SUM model is then run to sample the position of
the projected IFOVon the surface across one full wavelength of
the surface structure in both the x and y directions with the
results saved for each sampling location.
3.3.2. Assigning surface temperatures
To estimate the sensor directional radiometric temperature,
the calculated view factors are combined with radiometric
temperature information for each surface derived from one of
the methods described below. Temperatures are converted to
equivalent 8–14 μm radiation during the summation using the
method of Verhoef et al. (1997).
3.3.2.1. Facet average method. The facet average method of
specifying facet temperatures results in a single temperature for
each surface component (e.g. sunlit road, shaded road, sunlit
east wall, shaded, east wall, etc.) Wall temperatures are derived
from mean vehicle traverse data while roof and ground surface
temperatures are derived from a separate set of thermal images
taken from a nadir viewing angle and merged into a single
composite image (Voogt & Grimmond, 2000). The GIS database
is then used to extract mean temperatures of building roofs
and ground (primarily road) surfaces. An adjustment for
warming and cooling of roof surface temperatures between
the time of the nadir flight lines and off-nadir lines is made for
the morning and late afternoon flights over the LI area. The
adjustment is based on the time series of roof surface temperature
made by a single infrared thermometer mounted on one of
the study buildings (see Masson et al., 2002).
Table 1
Characteristics of the study sites and general observing parameters
Study site Light Industrial Downtown
Code LI DT
Building height Avg. 7.3 m Avg. 27 m;
median 15 m
Ac/Ap 1.4 2.2
Ar/Ap 0.38 0.37
Date 15 Aug 92, YD 228 16 Aug 92,
YD 229
Flight altitude:
nadir (m)
647 m 689 m
Flight altitude:
off-nadir
457 m 488 m
Number of flights 3 2
Off-nadir view
directions
N, S, E, W NW, SE, NE, SW
Flight Times (LST)
Ground-traverse
Flight 1: 0900–1000 Flight 4 1015–1110
Traverse 228.4 0925–0949 Traverse 229.5 1030–1107
Flight 2: 1245–1330 Flight 5 1505–1545
Traverse 228.7 1255–1318 Traverse 229.10
1509–1605
Flight 3 1605–1645
Traverse 228.11 1630–1651
Solar Geometry
(zenith/azimuth
angles)
F1 48.9–45/121.5–129.9 F4 41.3–38.9/140.8–150.3
F2 36.8–37.9/200.2–206.8 F5 51.2–54/241.7–246.3
F3 61.3–64.2/257.4–261.1
Fig. 4. Off-nadir thermal image acquired over the LI study area. The circle
indicates the limits of the modeled conical IFOV.
486 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
Separation of shaded and sunlit road surfaces is accomplished
by inspection of the image histogram. Separation could
be accomplished using a shading routine coupled with the GIS,
but tests using Flight 2 showed that the shaded area determined
in this manner was under-represented, in part due to the lack of
representation in the GIS by small scale structures. The binary
building “mask” image was filtered with different filter sizes
(Table 2) to assess variability arising from inaccuracies in the
match between the thermal image composite and the GIS
building footprint. Following filtering, the images were reclassified
so that all non-integer pixels were set to 0, thereby
reducing the size of the defined surface. The difference between
filtered and non-filtered surfaces is largest for roof surfaces and
is minor for road surfaces. The relatively large change in shaded
road temperature may be due to the filter size beginning to
exceed the size of most shaded areas, which is relatively small at
this time of day. Additional filtering of the roof mask shows
decreasing variability of temperature (reduced edge effects) as
filter size grows, and a decrease in the temperature change as
filter size increases, indicating a greater likelihood that the mask
incorporates only roofs. Based on this analysis, 3×3 filtered
results are used for horizontal surfaces.
3.3.2.2. Multiple facet average method. The multiple facet
average method was used for some model tests in the Light
Industrial study area. It is similar to the facet average method
except that in place of a single average temperature for each
facet, a distribution of facet averages is created. For wall surfaces,
vehicle traverse results are averaged for each street in the
study area, yielding 11 averages for north and south walls and 5
averages for east and west walls. Averages for horizontal surface
components were derived from a series of operations based
on the nadir thermal composite image and the GIS surface. First,
a mask of the component of interest (roof, sunlit ground, shaded
ground) was multiplied by the nadir thermal composite image
and unmasked areas assigned the mean temperature of the mask
component. This image was then processed with a 155×155
filter to yield an approximate mean temperature for the component
at a scale representing the projected IFOVof the airborne
sensor. Finally, the filtered image was sampled with a regular
rectangular grid and masked for edge effects to yield 572
sample points.
3.3.2.3. Image sampling method. Component surface temperatures
were also determined by detailed sampling of images
along each off-nadir flight line of the early afternoon flight over
the LI area for comparison with the facet average method.
Images were selected to give complete coverage of the flight
line within the bounds of the observed images. Images selected
were not included as part of the observed database. All roof,
sunlit road, shaded road and wall surfaces that could be
identified within a given domain for each image were digitized
and the mean, standard deviation and area were saved. Digitized
areas were corrected for “double-counted pixels” that sometimes
occurred due to digitizing inaccuracy and/or the vector to
raster conversion process. Using the individual statistics for
each sampled image, a mean weighted temperature for each
component of each flight line was calculated.
The difference between the domain area and all the digitized
component surfaces is the residual area. The residual temperature
associated with this area typically represents vegetated
areas, partially sunlit areas, low emissivity areas, or other areas
that could not be precisely identified. The residual temperature
was used to modify the area-weighted sunlit road and shaded
ground temperatures using (all symbols defined in the Glossary)
Trd ¼ ½ArdTrd þ FrdðTresAresފ=ðArd þ AresFrdÞ ð1Þ
Tshd ¼ ½AshdTshd þ FshdðTresAresފ=ðAshd þ AresFshdÞ ð2Þ
This modification essentially apportions the non-sampled
(residual temperature) to the horizontal surfaces (sunlit road and
shaded area). The existing SUM surface component categories
then better represent the entire ground surface temperature
distribution; an alternative approach would be to provide more
Fig. 5. Component surface temperatures for the off-nadir flight lines of the early
afternoon flight over the LI area. Symbols represent mean values derived from
detailed sampling of individual images for each flight line with a view direction
as indicated near the bottom of the image. Lines represent the single mean
temperature from the facet average method for roofs, and sunlit and shaded
components of streets and alleyways. Modified road and shade temperatures
incorporate the residual image area.
Table 2
Horizontal surface temperature components for an early afternoon flight over the
Light Industrial study area derived from analysis of the nadir thermal image
composite
Surface Roof Road Road (sunlit) Road (shaded)
T¯ σ T¯ σ T¯ σ T¯ σ
No filter 318.87 6.51 311.05 7.14 314.00 3.68 298.89 4.67
3×3 319.46 6.12 311.20 6.99 313.97 3.54 298.76 4.74
5×5 319.69 5.99 311.66 6.56 313.98 3.42 298.93 4.81
7×7 319.78 5.93 312.21 5.93 314.00 3.29 299.37 4.75
487J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
categories of ground surface components (e.g. surface vegetation,
gravel, sidewalks etc.) within SUM.
The results of the facet average and detailed sampling
methods are shown in Fig. 5 and may be summarized as:
• roof temperatures are well approximated by the use of the
facet average method;
• when differentiated in the facet average method, alleys are
cooler than streets for both sunlit and shaded components;
• modifications to road and shaded temperature components
(Road(m), Shade(m)) using the residual temperature cool the
road and warm the shaded component (Fig. 5);
• sunlit wall temperatures derived from image sampling are
warmer than those observed from the truck-mounted infrared
thermometers;
• view directions to the north have relatively warm shaded
surfaces but these form a very small fraction of the field of
view and do not strongly impact the results (0.15 °C difference
in modeled temperature for a 5 °C change in shaded
surface component temperature).
4. SUM model evaluation
The SUM model evaluation is carried out using the GIS
surface viewing method and the facet average method for specifying
the component surface temperatures. The modeled radiometric
temperature is then compared to the mean temperature
from the images, derived from a circular portion of the image
(Fig. 4) to coincide with the SUM sensor projected IFOV. All the
simulations for each flight line are averaged and compared to the
mean temperature of the images for that flight line, and model
validation statistics are calculated on the basis of these averages.
4.1. Light Industrial area
Results of the model comparison for the Light Industrial
area (Fig. 6), suggest a tendency for a slope b1; i.e. an overestimation
for view directions where more shaded surfaces are
seen e.g. southerly and easterly view directions for the morning
flight, southerly view direction for the early afternoon flight and
an underestimation for view directions that include the most
strongly sunlit facets. The southerly view direction for the early
afternoon flight in particular is characterized by a substantial
overestimation, and this is reflected in the poor statistical validation
measures (Table 3). Together, these deficiencies result in
a substantial underestimate of the overall thermal anisotropy of
the surface — as expressed by the range of the modeled versus
observed values. The variability of the observed temperatures,
represented by averages of different flight lines and their
associated standard deviations (error bars) is larger than that of
the modeled results, indicating the importance of temperature
variability for surface components relative to the variation in
surface structure alone. During the morning and late afternoon
flights, some temporal variation of surface temperatures between
flight lines is expected (e.g. as shown in Fig. 5) and may
account for some of the variability in the observed temperatures.
Fig. 7 compares the modeled versus observed directional
temperature of the early afternoon flight over the LI area using
both the image sampling method and facet average method for
providing component surface temperatures. A substantial improvement
in statistical agreement is achieved for all parameters
(Table 3). The improvement comes about through large changes
in the modeled temperatures for the south view direction and
also to some extent for the north view direction. A comparison
Fig. 6. Comparison of observed and modeled directional radiometric temperatures of four 45° off-nadir viewing directions for the a) 0930 LSTand b) 1300 LST flights
over the Light Industrial area.
Table 3
Validation statistics for each of the overflights
Flight Flt 1 Flt 2 Flt 2⁎ Flt 3 Flt 4 Flt 5
Area LI LI LI DT DT
Time (LST) 0930 1300 1630 1100 1530
Statistic
b (slope) 0.33 0.35 0.9 0.53 0.77 0.80
a (intercept) 21.3 26.7 4.0 16.1 6.9 6.0
RMSE (Root Mean Square Error) 1.34 1.71 0.38 0.67 1.52 1.09
RMSEs (Root Mean Square Error
systematic)
1.31 1.69 0.22 0.64 1.20 0.69
RMSEu (Root Mean Square Error
unsystematic)
0.26 0.25 0.31 0.19 0.94 0.84
MBE (Mean Bias Error) 0.16 0.97 −0.04 0.14 0.66 0.37
MAE (Mean Absolute Error) 1.22 1.37 0.31 0.58 1.24 0.93
d (Index of Agreement) 0.74 0.70 0.99 0.90 0.96 0.96
Model results obtained using the GIS surface viewing method and facet average
method for assigning surface temperatures. Flt 2⁎ represents statistics calculated
using detailed sampling of image component temperatures.
488 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
of the component surface temperatures (Fig. 5), as well as the
average view factor for each component, shows that for the
south view direction, the improvement in modeled values is
derived largely as a result of the variability of sunlit road and
roof temperatures, especially a decrease in these values for two
flight lines relative to the mean values used in the standard
approach. For the north view direction, the most significant
differences are due to underestimation of the south-facing wall
temperature and alley temperatures by the standard method,
whereas for the east view direction, sunlit street, roof and wall
temperatures are approximately equally responsible. This assessment
suggests the original differentiation of the streets from
alleys is not particularly important relative to the provision of
surface temperatures for non-road surfaces (the inclusion of the
“residual” temperature). Some variability in roof temperature,
especially a consistent difference between south and north
viewing directions, may be related to shading by microscale
roof surface structures within the sampled roof area.
4.2. Downtown area
A comparison of modeled and observed directional radiometric
temperatures over the downtown study area show relatively
good agreement (Fig. 8, Table 3). There is a tendency, as
for the LI area, for the warmest temperatures to be underestimated
and the coolest temperatures overestimated, however
the effect is more muted than in the LI area. Use of the simple
urban surface structure that approximates Ac/Ap and Ar/Ap
yields similar results, but with a greater tendency to overestimate
cool temperatures and underestimate the warmest directional
temperatures (results not shown). The spatial variability
of results is much reduced through the use of the regular urban
surface structure.
4.3. Summary
It is clear from the model evaluation that the modeled
results are highly sensitive to specified input facet temperatures.
Three specific factors related to the input temperature
were found to be important. First, temperatures of the sunlit
walls as derived from analysis of the thermal imagery are
warmer than those estimated by the ground-based truck
traverses. This is likely related to the ground-based sampling
of surfaces deeper (and more likely to be shaded) within the
street canyons, and which may also be affected by reflection
of cold sky radiance from low emissivity building surfaces.
These temperatures may be correct for the viewing position,
but may be hidden from airborne view by awnings or other
small scale surface features that are not incorporated in the
SUM model surface representation. Thus, use of surface
temperatures derived from vehicle-mounted instruments in the
SUM model may impart a low temperature bias, especially for
the most sunlit walls. Second, the temperature distributions on
streets of different orientations can be quite different. SUM at
present does not account for street orientation, however the
shading history of a surface can substantially modify the
modal values for sunlit and shaded components of the surface;
use of an average value leads to poorer agreement. Third, the
specification of “alley” surfaces for the downtown area is
confined to the very narrow streets and courtyards between
buildings, and forms a relatively small proportion of the
overall area. The sunlit temperature component of these
surfaces is likely to be cooler due to a shorter warming period
because of greater shading in these confined areas.
Fig. 7. Comparison of observed and modeled directional radiometric
temperatures of four 45° off-nadir viewing directions for the early afternoon
flight (1300 LST) over the Light Industrial area using both the image sampling
method (solid symbols) and facet average method (open symbols) to determine
component surface temperatures.
Fig. 8. Comparison of modeled and observed directional radiometric temperature of four 45° off-nadir viewing directions for the downtown study area a) at 1100 LST
(Flight 4) and b) 1530 LST (Flight 5). Model results use the GIS surface and facet average temperature methods.
489J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
In order to further assess the sensitivity of the modeled
anisotropy to input surface conditions a number of sensitivity
tests were conducted to identify the contribution of variations in
surface structure and surface temperature to the urban thermal
anisotropy. These are discussed next.
5. Sensitivity analysis
5.1. Sensitivity to surface structure and temperature
The sensitivity of the modeled sensor temperature to both
surface structure and surface temperature was examined by
comparing the observed temperature distribution to four separate
model simulations (Table 4). The first two simulations
examine the effect of the two urban surface representations (GIS
and simple surface) and use a fixed average temperature for
each of the surface components. The third simulation keeps the
surface geometry, as represented by the average view factor for
each surface component, fixed and combines this with temperature
variability for each of the surface components. The final
simulation combines variable surface geometry using the GIS
surface with temperature variations from the image sampling
method for each surface.
Results, shown as box plots, are presented in Figs. 9 and 10.
It is clear that the simple urban surface representation given by
the internal SUM surface geometry provides relatively little
variation and substantially underestimates the full anisotropy of
the surface (shown by the superimposed vertical arrow). The
use of the GIS surface increases the variability of the modeled
temperature in each view direction but the overall anisotropy
increase compared to the simple geometry is relatively small
(mostly an increase in the maximum temperature for the north
view direction). Compared to the observed temperature variability,
the GIS surface accounts for approximately 60% of the
total anisotropy. Facet temperature variability alone accounts
for roughly the same amount of modeled temperature variability
as the GIS surface structure (Fig. 10). The combined simulation,
in which view factors derived from the surface GIS and variable
facet surface temperatures from the image sampling method covary,
shows variations of the same order, or in some cases
larger, than the observed. The increase in variability here comes
from the full combination of temperature with view factors —
in reality not all surface structures would exhibit the full range
of temperature variability tested. The simulations suggest that
surface geometry and facet temperature variability (due to surface
material variations) have roughly equal contributions to the
overall observed temperature variability.
5.2. Sensitivity to omission of small scale surface structure
Another factor that may contribute to the deficiency in the
validation of Fig. 6 is an underestimation of the shaded area
viewed, possibly due to small scale surface structures that are
not represented in either the simple urban surface or the GIS
database. To determine if this interpretation has merit, a number
Table 4
Model sensitivity simulations of sensor-detected temperature
Simulation name Surface geometry Surface temperature method
Fixed urban surface Simple surface Facet average
GIS surface GIS surface Facet average
T variation only GIS surfacea
Multiple facet averageb
Combined GIS surfacec
Image samplingd
Notes:
All tests performed using data from the early afternoon flight over the Light
Industrial area.
a
The view factors for each component are averaged for all sampling locations.
b
Samples are combined with mean view factors to yield 11×572 modeled
temperatures for north and south view directions and 5×572 temperatures for
east and west view directions (see Section 3.3.2 for details).
c
View factor calculations are performed at 36–57 sensor positions for east
and west view directions, 41–80 for north–south view directions to coincide
with airborne observations.
d
Between 4–7 images per flight line are sampled, each generating a set of
facet temperature averages.
Fig. 9. Box plot of modeled directional temperature for the simple and GIS urban
surface as well as the observed sensor temperature. Boxes represent the 25th,
50th, and 75th percentiles, error bars the 10th and 90th percentiles and symbols
the 5th and 95th percentile. The arrow represents the range of temperatures
equivalent to the anisotropy.
Fig. 10. Box plots of observed and modeled directional temperature. The plots
labeled “T variations” use the mean view factor for each view direction derived
from the GIS surface viewing method and combine this with variations in
temperature across the LI study area obtained from the multiple facet average
method. The combined modeled results use the image sampling method for
specifying facet temperatures and combine these with all the modeled view
factors along the flight line using the urban surface GIS (see Table 4 and Section
3.3.2 for details) Box plot parameters are as defined in Fig. 9.
490 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
of additional tests were made. First, the summed view factors
for all shaded components seen by the sensor was compared to
the fraction of pixels from all images that fall below a threshold
shaded/sunlit temperature value (Fig. 11). This test was performed
for both morning and early afternoon flights over the LI
area. The temperature contrast between shaded and non-shaded
areas is greatest in the morning since the area that converts from
sunlit to shaded is relatively small. If the total shaded view
factor is less than the area of temperatures that correspond to
shaded areas it may suggest that the images are characterized by
more shade than is represented in the surface GIS. The effect
would be maximized for view directions towards the solar
azimuth. Inspection of Fig. 11a suggests that the total shaded
view factors may be slightly low for the east and south view
directions for Flight 1. Much smaller view factors (and fractions
of shaded pixels) are noted for north and west view directions.
Modeled view factor ranges are very small whereas the
fractional area of temperatures less than the threshold is larger;
this larger fraction incorporates variability in surface characteristics
as well as surface structure. For the midday flight, the
most apparent differences are from the west and east viewing
directions (nearly orthogonal to the solar azimuth). The west
view direction at this time is newly shaded, hence the relatively
large modeled shaded view factor. However the temperature
range remains large from the differential heating of surfaces
with different radiative and thermal properties through the
morning, so these newly shaded surfaces tend to exhibit a range
of temperatures depending on their particular surface properties.
The heating and cooling history of the surface thus tends to
lower the fraction of pixels less than the fixed threshold. In
contrast, the east view direction is towards newly sunlit walls,
so the shaded view factor total is lower, but these surfaces have
yet to warm significantly, so the fraction of “shaded” surfaces
based on the threshold temperature remains large. There is little
difference between the modeled shaded view factor and the
fraction of cool surfaces for the south view direction for which
relatively few pixels will have changed status from sunlit to
shaded.
A second test used a regular surface geometry with the
complete area (Ac) set to match that of the LI study site and then
added small structures to the building roof. These structures
represent elevator shaft housings or small penthouses that may
not have been included in the original GIS. Three sizes of
structures were tested (Table 5). The structures occupy between
12–30% of the plan roof area and 13–25% of the total building
area (vertical and plan surfaces). Initial simulations simply
added the roof structure to the base building structure leading to
an increase in the overall complete surface area of the study
domain. A second set of simulations was conducted with the
largest and smallest of the roof structures in which the building
height and/or roof structure height was adjusted to keep
the complete surface area and Ac/Ap fraction approximately
constant.
When roof structures are added (without attempting to
preserve the complete surface area) the shaded view factor
increases for view directions towards the Sun (Fig. 12a) compared
to the no roof structure case. When the roof structure is
added and the building height is adjusted so that Ac/Ap is
preserved (Fig. 12b), only minor changes in the shaded view
factor are noted (less than 0.01) and these are not likely to be
significant. These results suggest that omission of small scale
structures from the surface GIS is potentially important in cases
where the base building structure is well represented (e.g. from
Fig. 11. Box plots for: (a) Flight 1 and (b) Flight 2 comparing the total view
factor for shaded surfaces in each of the off-nadir viewing directions with the
fraction of pixels within the projected IFOV that fall below a threshold that
approximates the sunlit/shaded temperature boundary.
Table 5
Dimensions (m) of test surfaces used to assess the view factor of additional small
roof structures (RS) to buildings (B)
Surface HB HRS WRS LRS Ac/Ap Ar(RS)/Ar(B) Ac(RS)/Ac(B)
Buildings onlya
7 – – – 1.428 – –
Small RS 7 3 6 12 1.490 0.117 0.132
Medium RS 7 3 8 14 1.504 0.194 0.185
Large (RS) 7 3 10 16 1.518 0.302 0.248
Small RS, scaled by Ac 6 3 6 12 1.429 0.117 0.144
Large RS, scaled by Ac 6 2 10 16 1.427 0.302 0.226
Height, width and length of roof structure (HRS, WRS, LRS) and height of
building (HB) for each simulation are specified as well as complete (Ac), plan
(Ap) and roof (Ar) areas for both buildings and roofs structures.
Areas are calculated for one complete “wavelength” of the surface.
a
Surface structure (all values in m): buildings 30×23, 3 buildings/block;
streets 22, alleys 12, inter-building spacing 9.
491J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
building footprint information) but when roof top structures are
not included, and are a notable feature of the structures. If the
building, omitting the actual roof top structure, has a similar
complete surface area to that including the roof top structure,
then the view factors are similar. However, this does not take
into account the different relative position of shadows cast by a
simplified building relative to that with a roof structure; in the
former case, the shaded view factor of the main building wall
and ground area is increased, in the latter, the shadow is projected
first onto the roof, then at larger zenith angles onto the
ground. The shading influence on the roof top versus ground
surface may be important to anisotropy depending on the relative
temperature differences involved.
A simple test using the internal SUM surface geometry was
used to compare results between two model runs that used an
identical surface layout (i.e. building footprint and building
arrangement along the streets), but with different mean building
heights, one set at the mean for the study area as derived from
the GIS analysis (7 m) and the second set to (a somewhat
arbitrary) 10 m. Altering only the building height preserves the
plan area ratios of roof and ground area but increases the wall
and complete areas. This scenario represents cases where the
GIS captures the main urban surface structure, but misses
features that have a small plan area and a relatively large vertical
surface area which could cast significant shadows. Such features
might include fences, hedges or utility poles. Using the
same facet component temperatures for both simulations, the
results (Fig. 13) show that the sensor observed temperatures
are decreased most for view directions towards the solar
azimuth (S and E directions). The difference in the direction
most closely matching the solar azimuth (W) is very small. At
this time of day there is also a relatively large change in the
temperature for the north view direction due to the increase in
shaded area of north–south streets. This change would be
smaller as the solar azimuth approaches 180°. The changes
illustrated in Fig. 13 would act to improve some, although not
all, of the modeled-observed differences shown in Fig. 6. The
results for actual small scale surface structures on the ground
may be more muted as there is a chance they may exist within
already existing shaded areas.
6. Sum model assessment for other viewing directions
The SUM model provides the ability to extend the analysis to
other viewing angles and azimuths not sampled by the airborne
scanning system. As a demonstration of this capability, model
simulations are performed for the LI (early afternoon flight,
Flight 2 — Table 3) and DT (late morning, Flight 4) study
areas at 5 degree increments in off-nadir angle (up to 55°) and
10 degree increments of sensor azimuth.
The LI simulation takes into consideration the sensitivity
analysis that shows the importance of representing both the
surface structure and temperature variability by using the surface
building GIS and coupling this with: a) for horizontal
surface temperatures, the nadir thermal image composite of the
study area at 1 m resolution, geo-referenced to the building GIS
database (Fig. 2), and b) assigning wall temperatures to
buildings such that the temperature frequency distribution
Fig. 12. Box plots of shaded view factors for select view directions of Flight 1
when additional roof structures (RS) are added to modeled buildings.
(a) Simulations of three roof structure sizes added to buildings. (b) Simulations
of the large and small roof structures where building heights are set so as to
preserve the complete area for each simulation.
Fig. 13. Modeled sensor observed temperature using identical surface layouts for
two different building heights. Variability of the modeled temperature comes
from moving the sensor position such that the modeled IFOV is moved across
the surface in 2 m increments.
492 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
observed by the vehicle traverses is preserved for each of the
wall orientations. A separate frequency distribution is used for
sunlit and shaded components of each wall, where necessary
(south and west-facing walls at this time).
The domain that contains the modeled sensor IFOV is a
350 m×350 m square with the sensor position adjusted so that
the IFOV is centred on the middle of the domain for all viewing
angles. The horizontal area of the sensor IFOV varies from
approximately 7×103
m2
for a nadir view (∼95 m diameter) to
27×103
m2
(an ellipse with length 233 m and width 148 m) at
50° off-nadir angle for the specified 450 m observing height.
Seventy different domain positions were tested within the area
that includes the composite nadir temperature image.
To summarize the results, statistics for each sensor view
direction (each off-nadir angle and azimuth presented in the
polar plot) were calculated (Fig. 14). The polar plots include
interpolation of results in both viewing angle and direction
(3 intermediate points) to increase the resolution of plotted
points. The mean temperature (Fig. 14a) smoothes the variability
of the individual polar plots and shows a hot spot for
viewing azimuths centred around the northerly viewing direction
and decreasing gradually as azimuths increase or decrease
towards the east and west respectively. Nadir viewing directions
remain relatively warm, not surprising for this time of day with
peak roof and road temperatures, and a relatively open canyon
geometry. The coolest temperatures are for large off-nadir
viewing angles in the direction of the solar azimuth that view
the largest shaded areas (projected onto streets in a north and
slightly eastern direction at this time). Large off-nadir viewing
angles in southeasterly azimuths are also very cool, and cooler
than those in a direct southerly direction. The increase for the
southerly direction is likely related to the north–south streets
which are very warm at this time of day. A comparison with the
results of Lagouarde et al. (2004) show a smaller variation of
temperature across the polar plot and a tendency for the nadir
viewing direction to be close to the warmest view direction.
These findings are in agreement with the expectation of
Lagouarde et al. (2004) for less dependency of the anisotropy
on canyon geometry and more on individual surface material
characteristics for land use types such as the LI study area where
building heights and canyon height to width ratios are relatively
low. The smoothness of the polar plots represents the averaging
that occurs over the projected IFOV. The ground resolution of
the current simulations is much larger compared to the 6.6–
16.2 m resolution for nadir and 50° off-nadir angles used in
Lagouarde et al. (2004).
The standard deviation for each view direction (Fig. 14b)
tends to be largely symmetrical about the nadir point as is the
range image (Fig. 14c). This effect is due to the relatively small
size of the projected IFOV for the nadir view direction relative to
the off-nadir viewing angles and the sensitivity of the modeled
temperature to the exact positioning of the IFOVon the surface,
where it may be easily dominated by one surface type with (e.g.
sunlit rooftop or sunlit or shaded street). Interestingly, the nadir
standard deviation is very similar to that obtained by Lagouarde
et al. (2004) who report an average standard deviation of nadir
temperature of 1.2 °C for their city centre site in Marseille. The
smallest variability is noted for large off-nadir view angles
towards the north where a maximum view of warm south-facing
walls that have the largest range of temperatures represented in
the wall temperature frequency distribution.
The simulation for the downtown area uses mean facet
temperatures coupled with the building GIS. Off-nadir angles
Fig. 14. Statistics for the modeled directional radiometric temperature (°C) over
the Light Industrial study area (early afternoon flight) for each viewing direction
(5° increments in off-nadir angle and 10° increments of azimuth angle) shown as
polar plots. a) Mean value for each viewing position, b) standard deviation,
c) range. S indicates the position of the Sun.
493J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
are restricted to 50° to allow a slightly smaller domain for
sampling within the GIS building domain. Results (Fig. 15) are
based on 31 separate sampling positions of the modeling domain,
with separations of 90 m to provide full coverage of
the GIS domain and reduce overlap between neighbouring
sampling positions. Anisotropy is ∼10 °C, much larger than for
the LI area and in line with observations (Voogt & Oke, 1998a).
The warmest temperatures are observed when viewing towards
the NW, in accordance with the most-directly sunlit walls at this
time (nearly directly opposite the solar azimuth) and noting the
orientation of the streets that are aligned NE-SW and NW-SE in
this study area (Fig. 3). The coolest temperatures are offset
towards the south and southwest, rather than directly towards
the solar azimuth. Given the near coincidence of the solar
azimuth with the street orientation at this time, views along the
NW-SE roads in the direction of the solar azimuth may include
the relatively warm sunlit streets at this time, but viewing
azimuths slightly more towards the south and west will more
likely include the shaded sides of buildings. The asymmetry
between temperatures observed at view angles orthogonal to the
solar azimuth likely indicates the warming of walls with a
south-westerly orientation at this time. Nadir view temperatures
are intermediate between the warm and cold extremes at higher
off-nadir angles. This effect represents the larger role of walls in
the directional temperature and the narrower canyon geometry
that reduces the ground-level temperatures compared to that of
the roofs. The patterns of variability expressed by the standard
deviation (Fig. 15b) and range (Fig. 15c) are more complex than
those of the LI area and are likely affected by the particular
configuration of buildings, especially large tall buildings and
open areas, within the study domain. Standard deviations for
large off-nadir view angles in the direction of the most sunlitfacets
(330, 60°) are low (and perhaps lower than if some
measure of wall temperature variability had been included); in
the opposite directions, variability increases presumably due to
shading patterns and is spread from nadir to large off-nadir
viewing angles.
Overall, these simulations confirm that the limited view
direction sampling (nadir plus orthogonal to the road network
pattern at 45° off-nadir view angle) used to obtain the airborne
observations of Voogt and Oke (1998a,b) should incorporate the
majority of the anisotropic temperature range.
7. Summary
The SUM model can generate reasonable estimates of the
directional radiometric temperature, but results are highly
dependent on the ability to provide appropriate facet temperatures
and the specification of these temperatures can be difficult.
The model results for both study areas suggest some consistent
biases that lead to the underestimation of the effective anisotropy
for the surface compared to observed values. The effect is
more evident in the Light Industrial study area. Extension of
results, using the SUM model, to full hemispheric plots, shows
spatial variability for the tested sensor specifications, but when
composited over a number of positions in the study area, the
averaged results by view direction are smoothly varying and in
accordance with expectations for the given surface structure and
solar position.
The use of actual surface structure from GIS data improves
the model's ability to capture the spatial variability related to
the thermal anisotropy compared to the use of the SUM
model's regular internal urban structure, but this variability is
still reduced relative to that from observations due to the use
of mean temperature values for all the modeled surface facets.
Fig. 15. Same as Fig. 14 except for 31 positions over the Downtown study area
using data coinciding with Flight 4 (Table 3). Note the street orientation is
aligned at 45–225°/135–315°.
494 J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495
Detailed analysis and sensitivity testing for one study area
shows that representation of the microscale temperature variability
of the surfaces is needed for the model to correctly
represent the full anisotropy of the surface. This finding is in
agreement with the expectations of Lagouarde et al. (2004)
who noted that a range of surface material characteristics and
more open canyon geometry make the individual surface
characteristics relatively more important in determining the
overall thermal anisotropy of such areas, compared to those
of urban or residential land uses. An important implication
of this finding is that the specification of surface temperatures,
for example from model output, must include microscale
variability, and not simply represent facet averages, if the full
range of anisotropy is to be represented. At present, most
urban surface energy balance models that can be used to
estimate urban surface temperatures for use in assessing
anisotropy with a view direction model such as SUM provide
only facet averages of temperatures based on mean thermal
and radiative surface characteristics.
The application of the SUM model is limited by the need to
have detailed observations of the radiometric temperatures of all
component surfaces. Work on coupling SUM to a three-dimensional
surface energy balance model (Krayenhoff & Voogt,
2007) that is capable of representing the full microscale variability
of urban surface temperatures is underway and some
initial tests have been conducted (Voogt & Krayenhoff, 2005).
Acknowledgements
This research was supported by funding from the Natural
Sciences and Engineering Research Council of Canada. Thanks
are due to E.S. Krayenhoff, A. Soux and M. Van De Wiel for
discussions on model development and to J-P. Lagouarde, D.
Aldred and E.S. Krayenhoff for assistance with developing
routines for the polar plots.
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Glossary
Abbreviations and symbols used in the text
Abbreviation: Description
Sites
DT: Downtown study area
LI: Light Industrial study area
Acronyms
GIS: Geographic Information System
IFOV: Instantaneous field of view (°)
LST: Local standard time
RS: Roof structure
SUM: Surface-sensor-sun relations model
Symbol: Description (Unit)
Ac: Complete (3-D) area (m2
)
Ap: Plane (2-D) area (m2
)
Ar: Roof area (m2
)
Ard: Road area (m2
)
Ares: Residual area (m2
)
Ashd: Shaded area (m2
)
Frd: Fraction of road area in a sampled image
Fshd: Fraction of shaded area in a sampled image
Tr: Directional radiometric temperature (°C)
Trd: Road (sunlit) temperature from image analysis (°C)
Tres: Residual temperature from image analysis (°C)
Tshd: Shaded (horizontal) surface temperature from image analysis (°C)
495J.A. Voogt / Remote Sensing of Environment 112 (2008) 482–495