Urban Planning (ISSN: 2183–7635)
2017, Volume 2, Issue 1, Pages 19–30
DOI: 10.17645/up.v2i1.855
Article

Sky View Factors from Synthetic Fisheye Photos for Thermal Comfort
Routing—A Case Study in Phoenix, Arizona
Ariane Middel 1, *, Jonas Lukasczyk 2 and Ross Maciejewski 3
1

School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ 85281, USA;
E-Mail: ariane.middel@asu.edu
2 Department of Computer Science, University of Kaiserslautern, 67663 Kaiserslautern, Germany;
E-Mail: j_lukasczy09@informatik.uni-kl.de
3 School of Computing, Informatics & Decision Systems Engineering, Arizona State University, Tempe, AZ 85281, USA;
E-Mail: rmacieje@asu.edu

* Corresponding author
Submitted: 15 January 2017 | Accepted: 9 March 2017 | Published: 27 March 2017
Abstract
The Sky View Factor (SVF) is a dimension-reduced representation of urban form and one of the major variables in radiation
models that estimate outdoor thermal comfort. Common ways of retrieving SVFs in urban environments include capturing
fisheye photographs or creating a digital 3D city or elevation model of the environment. Such techniques have previously
been limited due to a lack of imagery or lack of full scale detailed models of urban areas. We developed a web based tool
that automatically generates synthetic hemispherical fisheye views from Google Earth at arbitrary spatial resolution and
calculates the corresponding SVFs through equiangular projection. SVF results were validated using Google Maps Street
View and compared to results from other SVF calculation tools. We generated 5-meter resolution SVF maps for two neighborhoods in Phoenix, Arizona to illustrate fine-scale variations of intra-urban horizon limitations due to urban form and
vegetation. To demonstrate the utility of our synthetic fisheye approach for heat stress applications, we automated a radiation model to generate outdoor thermal comfort maps for Arizona State University’s Tempe campus for a hot summer
day using synthetic fisheye photos and on-site meteorological data. Model output was tested against mobile transect measurements of the six-directional radiant flux density. Based on the thermal comfort maps, we implemented a pedestrian
routing algorithm that is optimized for distance and thermal comfort preferences. Our synthetic fisheye approach can help
planners assess urban design and tree planting strategies to maximize thermal comfort outcomes and can support heat
hazard mitigation in urban areas.
Keywords
climate-sensitive urban design; desert city; heat; MRT; outdoor thermal comfort; PET; sky view factor; thermal comfort
routing; urban form; walkability
Issue
This article is part of the issue “Urban Forms and Future Cities”, edited by Luca D’Acci (Erasmus University Rotterdam, The
Netherlands), Tigran Haas (KTH Royal Institute of Technology, Sweden) and Ronita Bardhan (Indian Institute of Technology
Bombay, India)
© 2017 by the authors; licensee Cogitatio (Lisbon, Portugal). This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY).

1. Introduction
Heat is the leading cause of weather-related mortality in the U.S and poses a significant threat to pub-

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

lic health (National Oceanic and Atmospheric Administration [NOAA], 2015). Exposure to extreme heat is expected to increase in the future, as rapid urbanization
continues and heat waves are projected to become more

19

intense, more frequent, and longer lasting (Jones et al.,
2015). Past research has shown that daytime heat can
be reduced through microclimate-responsive urban design that acknowledges the cooling potential of urban
form and vegetation (Erell, Pearlmutter, & Williamson,
2012; Lenzholzer & Brown, 2016). Dense urban forms
can create local cool islands during the day and are particularly effective at mitigating heat in hot desert environments where water is scarce (Middel, Häb, Brazel,
Martin, & Guhathakurta, 2014; Pearlmutter, Bitan, &
Berliner, 1999).
Heat is most commonly expressed as air temperature, but temperature alone is not a comprehensive
indicator of outdoor thermal comfort or stress. Thermal comfort is influenced by numerous environmental
factors, including temperature, radiation, humidity, and
wind speed; and personal factors, such as clothing and
activity level (Ng & Cheng, 2012; Nikolopoulou & Lykoudis, 2006; Vanos, Warland, Gillespie, & Kenny, 2010).
In outdoor spaces, radiation is one of the most important variables affecting thermal comfort; perceived thermal comfort can vary several degrees in the shade and
sun (Mayer & Höppe, 1987; Middel, Selover, Hagen, &
Chhetri, 2016). Thermal conditions in urban areas vary
widely due to complex shading patterns from buildings
and trees that determine solar access at the pedestrian
level. Therefore, air temperature maps fail to accurately
represent the significant variation of thermal conditions
in built environments.
In urban climate research, the Sky View Factor (SVF)
has been widely used as approximation of the 3D urban
geometry to assess the urban heat island (UHI) and longwave radiative heat loss in cities at night (Brandsma &
Wolters, 2012; Gál, Lindberg, & Unger, 2009; Oke, 1981;
Unger, 2004). SVF is defined as the fraction of visible sky
on a hemisphere and ranges from zero to one, denoting
the ratio of the radiation received (emitted) by a planar
surface to the radiation emitted (received) by the entire
hemisphere (Johnson & Watson, 1984). SVF is relevant
to human thermal comfort, as it affects Mean Radiant
Temperature (MRT), a synthetic parameter that summarizes the direct and reflected short and longwave radiation fluxes a human body is exposed to. MRT is one
of the most important meteorological variables in the
assessment of thermal comfort and the basis for many
human thermal comfort indices (Johansson, Thorsson,
Emmanuel, & Krüger, 2014; Lee, Holst, & Mayer, 2013;
Thorsson, Lindberg, Eliasson, & Holmer, 2007).
Numerous models have been developed to calculate
SVF and MRT in urban settings at different spatial scales
and with varying data requirements. Matzarakis, Rutz
and Mayer (2007, 2010) developed RayMan to model
SVF and MRT from hemispherical photos and meteorological observations. The model has been shown to perform reasonably well in homogeneous urban environments (Lee & Mayer, 2016), yet it is limited to a single
point in space. The SkyHelios model (Matzarakis & Matuschek, 2011) simulates continuous SVFs for small ur-

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

ban areas, but requires a geometric obstacle file. More
recently, studies have presented continuous SVF calculations using 3D city models (Chen et al., 2012; Gál et
al., 2009; Unger, 2009; White, Hu, Langenheim, Ding, &
Burry, 2016), but these calculations usually do not incorporate vegetation. Tree canopy cover significantly reduces SVF at the pedestrian level and is an important
shade source that should be incorporated in view factor
analyses and outdoor thermal comfort assessments. The
SOLWEIG model has been successfully applied to calculate SVF and MRT for urban areas using digital surface
models (DSMs) as representation of the urban morphology (Chen, Yu, Yang, & Mayer, 2016; Lindberg & Grimmond, 2011; Lindberg, Holmer, & Thornsson, 2008). Although trees have recently been added into SOLWEIG,
the use of DSMs does not allow to model complex urban
forms, such as building overhangs and shade structures.
We developed a methodology to calculate SVFs for
large urban areas at high spatial resolution using synthetically generated fisheye images from Google Earth.
Our approach calculates SVFs for large urban areas incorporating the full 3D environment, including vegetation,
and is independent of available 3D building databases or
DSMs. As an example, we produced 5 m resolution SVF
maps for two neighborhoods in the Phoenix metropolitan area overlaid over Google Earth terrain. To show the
utility of our approach for thermal comfort and walkability assessments, we generated thermal comfort maps of
Arizona State University’s Tempe campus for a hot summer day in August 2016 using Google Earth hemispherical images and meteorological data from an on-site field
campaign. We then utilized a routing algorithm for pedestrian navigation that is optimized for distance and individual outdoor thermal comfort preferences.
2. Methods
To assess intra-urban SVF variations in select neighborhoods in the Phoenix metropolitan area, we retrieved
data from Google Earth on a 5 m resolution grid to generate synthetic 180° hemispherical views of the sky from
3D buildings, trees, and terrain. We removed the sky portion of the fisheye photos and calculated the SVF for
each location on the grid through equiangular projection.
Subsequently, we calculated MRT and a thermal comfort
index using the synthetic fisheyes as input for an automated radiation model to inform our case study.
2.1. Retrieving Data from Google Earth
Google Earth version 7 allows users to render a 3D mesh
of the ground that includes buildings, trees, shrubs, and
other obstacles. The 3D mesh is generated from oblique
imagery collected during Google overflight campaigns at
a 45° angle in each cardinal direction and down. The
aerial imagery is automatically converted into a 3D city
model using stereo-photogrammetry and serves as texture for the 3D mesh so that the scene can be rendered.

20

As the current Google Earth Application Programming Interface (API) does not provide a function to export rendered images, we used a NodeJS server to remotely control a browser that runs the Google Earth plugin and
takes screenshots of the browser window through the
operating system API. First, our algorithm requests map
tiles from the Google Maps service for an area of interest
defined by an array of map tile coordinates and a sampling resolution, in our case 5 m, to determine sampling
locations. Buildings and water bodies are excluded from
the sampling. The algorithm generates a Keyhole Markup
Language (KML) file with the coordinates of the locations
to steer the virtual camera in Google Earth. Then, the
camera takes a tour along the predefined route, and the
operating system API takes a screenshot after the Google
Earth plugin finishes loading the 3D mesh at each camera location. The camera view angle is set to 90° and the
height is set to 1.1 m above ground level. 1.1 m is the
recommended height for human thermal comfort applications, as it represents the center of gravity of the human body for standing subjects (ISO 7726, 1998). The algorithm takes five screenshots at each location—one in
each cardinal direction and one upwards (Figure 1a).

Watson, 1984); vector-based methods that calculate the
SVF from projected building envelopes on the sky using
a 3D building database (Chen et al., 2012; Gál et al. 2009;
Gál & Unger, 2014; Unger, 2009); raster-based methods
that use digital elevation models (DEMs) or DSMs to estimate SVFs based on pixel heights or shadow casting (Gál
et al., 2009; Lindberg & Grimmond, 2011; Lindberg et al.,
2008; Ratti, Baker, & Steemers, 2005; Zakšek, Oštir, &
Kokalj, 2011), and photographic methods that use fisheye imagery of the upper hemisphere (Bradley, Thornes,
& Chapman, 2001; Chapman & Thornes, 2004; Grimmond, Potter, Zutter, & Souch, 2001; Holmer, Postgård,
& Eriksson, 2001). The hemispheric horizon limitation is
usually projected on a 2D plane to calculate the amount
of visible sky in the scene. The most widely used projection technique is the equiangular projection by Steyn
(1980), where the projected image is divided into concentric annuli of equal width and then evaluated. We use
a modified version of the manual Steyn-method for digitized fisheye photographs that was proposed by Chapman, Thornes and Bradley (2001). We partition the synthetic fisheye picture into n annular rings (default n = 36)
and calculate the SVF by summing up the contribution of
each ring:

2.2. Fisheye Projection
After data retrieval, we generate synthetic fisheye images using an angular fisheye projection of the surroundings on a 2D plane (Figure 1b). For the projection, we
treat the images as a cube map and perform ray casting
in WebGL. Specifically, we represent the fisheye image
as a unit square with center c = (0, 0) and calculate for
each point p = (u, v) with length r = ‖p‖ ≤ 0.5 the corresponding position on the unit hemisphere. Points with
r > 0.5 are not part of the fisheye and are therefore colored white. For all other points, the position on the hemisphere is given by
⎛
⎞
⎜⎜sin(θ)ur ⎟⎟
v = ⎜⎜⎜ sin(θ)vr ⎟⎟⎟
⎝
⎠
cos(θ)
with latitude θ = r π and normalized direction vector
⎧ p
⎪
⎪
if r > 0
⎨ r
(ur , vr ) = ⎪
⎪
⎩ (0, 0) otherwise
Subsequently, the vector v is used to sample the cube
map, yielding the final fisheye image. The hemispherical
view is then converted to black and white (white = sky;
black = obstacles) using a deterministic sky color gradient (Figure 1c).
2.3. Sky View Factor Calculation
Several methods are available to calculate the SVF based
on fisheye images: The SVF can be calculated using analytical methods that derive the horizon limitation from
geometric properties of the urban canyon (Johnson &

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

SVF =

π(2i − 1) pi
π n
􏾜 sin 􏿶
􏿹􏿶 􏿹
2n i=1
2n
ti

where pi /ti is the ratio between the number of sky pixels
to the total number of pixels in ring i (Figure 1d).
2.4. Thermal Comfort Modeling
Physiologically Equivalent Temperature (PET) is a widelyused thermal comfort index that is based on MRT, reported in °C, and expresses how people experience
weather conditions, incorporating the radiative environment and personal characteristics, such as age, clothing,
and metabolic rate (Höppe, 1999; Mayer & Höppe, 1987).
The 1D RayMan model (Matzarakis et al., 2007, 2010) has
been extensively employed to estimate MRT, PET, and
other thermal comfort indices from fisheye photographs,
meteorological, and personal factors (Coutts, White, Tapper, Beringer, & Livesley, 2016; Herrmann & Matzarakis,
2012; Johansson & Emmanuel, 2006; Krüger, Minella, &
Rasia, 2011; Lin, 2009; Lin, Matzarakis, & Hwang, 2010;
Oliveira, Andrade, & Vaz, 2011; Thorsson, Lindqvist, &
Lindqvist, 2004), following equations outlined in the German VDI engineering standards (Verein Deutscher Ingenieure, 1994). We automated the Windows GUI using a
script that simulates keystrokes to remotely execute the
RayMan tool and batch process thousands of georeferenced synthetic fisheyes for a given day and time. The
results are collected in a CSV file and can subsequently be
imported in ArcGIS using the fisheyes’ latitude-longitude
coordinates to generate high resolution MRT and PET
maps for further analysis.

21

screenshots in 5 direc
ons

hemispheric projec
on

sky detec
on

SVF calcula
on

(a)

(b)

(c)

(d)

Figure 1. Sky View Factor calculation pipeline. Starting with five images of 90° field of view (a), we apply an angular hemispheric fisheye projection (b), detect sky regions (c), and calculate the Sky View Factor using 36 annular rings (d).
3. Sky View Factor Results
We evaluated the accuracy of our SVF approach in two
steps. First, we compared the synthetic hemispherical images created from Google Earth to fisheye photos generated from Google Street View panoramic images using
the SVF as accuracy metric. Second, we compared our
SVF results to outputs from other algorithms using the
same set of fisheye photos. After validation, we generated 5 m resolution SVF maps for two contrasting neighborhoods in Phoenix.
3.1. Evaluation of Sky View Factors
To assess the accuracy of the Google Earth fisheye images compared to real world photos, we generated
18,367 fisheye images from Google Street View panoramas across the Phoenix metropolitan area (Figure 2) using the Google Street View API. The fisheye generation
process is similar to Google Earth, but requires a more
sophisticated sky detection algorithm due to varying sky
and cloud conditions. We used a modified Sobel filter algorithm for edge detection and a procedure developed
by Laungrungthip, McKinnon, Churcher and Unsworth
(2008). We then generated Google Earth fisheye photos at the Google Street View locations, using a camera
height of 2.5 m to approximate the height of a Street
View car. A comparison of SVFs calculated from Google

Earth and Google Street View yielded an average difference in SVF of 0.022 with a standard deviation of 0.084.
The largest differences in SVF were caused by two reasons. First, the Google Street View panoramas were acquired more recently than the Google Earth 3D mesh for
Phoenix, which was generated several years ago. Thus,
some buildings exist in Street View, but not in Google
Earth, and vice versa. Second, Google Street View offers
panoramas of building interiors that cannot be rendered
in Google Earth. Filtering out 2,579 indoor panoramas
and extreme cases of time discrepancies yielded a 0.01
average difference in SVF with a 0.028 standard deviation. This error is minimal and we conclude that the rendered output of Google Earth yields adequate results.
We evaluated the accuracy of the SVF calculations
by computing the SVFs of 527 randomly selected Google
Earth fisheye images in the Phoenix metropolitan area
using our implementation of Chapman et al. (2001),
the RayMan Pro model v2.1 by Matzarakis et al. (2007,
2010), the SkyViewFactor-Calculator v1.1 by Holmer et
al. (2001), and the unweighted, naive approach of counting pixels. Since the SkyViewFactor-Calculator uses the
well-established Steyn-method (Steyn, 1980), we chose
the Holmer et al. SVF implementation as reference. As
shown in Figure 3, our implementation of Chapman et al.
(2001) produces SVFs that are not significantly different
from the well-established Steyn-method. We confirm the
findings of Hämmerle, Gál, Unger and Matzarakis (2011),

SVF = 0.82

SVF = 0.82

SVF = 0.44

SVF = 0.38

(1a)

(1b)

(2a)

(2b)

Figure 2. Comparison of fisheyes and Sky View Factors generated from Google Street View images (1a, 2a) and Google
Earth 3D meshes (1b, 2b).
Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

22

1.0
0.9

SVF of each method

0.8
0.7

Holmer (annulus)
Holmer (pixel-based)
Rayman 2.1
pixel count
our implementa
on

0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

SVF Holmer (annulus)

Figure 3. Our Sky View Factor implementation compared to other algorithms.
showing that the RayMan model significantly underestimates SVFs, especially in the midrange, when Lambert’s
law is not considered for the pixel weighting. Lastly, simply calculating the ratio between sky and non-sky pixels
yields inaccurate results, since this approach does not account for angular distortion.
3.2. High-Resolution Sky View Factor Maps in 3D
To illustrate the spatial variability of horizon limitations
in urban areas, we created SVF maps at 5 m resolution and 1.1 m height from synthetic Google Earth fisheye photos for two contrasting neighborhoods in the
Phoenix metropolitan area—a residential area in the
City of Phoenix (Ahwatukee, Lakewood community) and
Phoenix Downtown (Figure 4). The residential subdivision is a neighborhood with detached single family
homes, approximately 2.4 km by 1.8 km, and can be
classified as an Open Lowrise Local Climate Zone (Stewart & Oke, 2012). The Downtown area is 2 km by 3 km
and classified Open to Compact Highrise. The SVF maps
were created in ArcGIS and exported as KML for display
in Google Earth, clamped to the ground, with 3D terrain
activated. While the core Downtown area exhibits low
SVFs (< 0.40) near office buildings, SVFs in the central
business district are generally high due to wide streets
(number of fisheyes: 168,266; mean SVF: 0.76; standard
deviation: 0.17). The Ahwatukee suburb is characterized
by even higher SVFs (number of fisheyes: 97,393; mean
SVF: 0.86; standard deviation: 0.14), except to the northwest, where a 3-story apartment complex lowers SVFs to
0.50. The close-up views of the areas clearly highlight the
importance of trees for SVF calculations.

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

4. Case Study: Thermal Comfort Maps for Pedestrian
Routing
We demonstrate the utility of our synthetic fisheye approach through a case study that highlights how urban
form and vegetation impacts thermal comfort and walkability. As a study area, we chose Arizona State University’s main campus, located in the City of Tempe, Arizona. Tempe is an ideal urban area for heat stress studies, because it is located in the Sonoran Desert and has
a semi-arid climate with hot and dry summers. Average maximum air temperature peaks at 40.4°C between
June and August, and monthly precipitation is less than
1 mm in June (Western Regional Climate Center, 2016).
Most of Arizona State University’s Tempe campus is designated as a walk-only zone during weekdays from 8:00h
to 16:00h; no one may ride, drive, or park wheeled vehicles. With over 50,000 students and faculty on campus,
increasing pedestrian thermal comfort through heat mitigation measures is especially important during the summer months. For this study, we selected a 3 × 3 Google
Maps tile area (ca. 750 m × 750 m) that encompasses the
north-west corner of the main campus and corresponds
to an open low- to midrise Local Climate Zone with a
mean SVF of 0.52 ± 0.18 (Figure 5).
We ran the automated version of RayMan for 19,600
synthetic fisheye photos in the study area at 1.1 m height
on a 5 m grid for August 7, 2016, a week before classes
started. Weather conditions were hot and clear, with a
daily maximum temperature of 43°C, minimum temperature of 30°C, average dew point of 14°C, and light wind
(< 1.5 ms−1 ). As meteorological model input, we used
observations from an hourly microclimate transect that

23

0
0.25 0.5
0 0.25 0.5

1 km
1 km

SVF
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Figure 4. High-resolution Sky View Factor maps (1.1 m height) for Phoenix Downtown, Arizona, USA (top) and a residential
subdivision in Phoenix, Arizona, USA (bottom) superimposed on Google Earth 3D terrain; bird’s eye view and two tilted
close-up views.
Arizona State University, Main Campus

0

125

250 m

Sky View Factor

a

b
SVF
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Figure 5. Aerial photo (a) and high-resolution Sky View Factor map at 1.1 m height (b) for the north-west corner of Arizona
State University’s Tempe campus.
was conducted on campus between 8:00h and 19:00h on
August 7, 2016. Air temperature, relative humidity, and
wind speed were logged at 1.5 m and 2 s intervals during the transect, linearly time-detrended to the full hour,
and spatially averaged to yield representative mean values for the study area. For the thermal comfort routing
application, we focused on 9:00h in the morning and
17:00h in the late afternoon, shortly after peak air temUrban Planning, 2017, Volume 2, Issue 1, Pages 19–30

perature, and assumed a walking 35 years old male in a
t-shirt and shorts (Table 1).
4.1. Thermal Comfort Model Performance
The fine-scale modeling results for Arizona State University’s campus highlight direct radiation as an important
driver of MRT. Shade, i.e. the absence of direct incom24

Table 1. Meteorological data for August 7, 2016, and personal characteristics used as input for thermal comfort modeling.

09:00h
17:00h

Air
Temperature
[°C]

Relative
Humidity
[%]

Wind
Speed
[ms−1 ]

33.6
41.6

35.8
23.1

0.9
0.6

Age

Gender

Weight
[kg]

Height
[m]

Clothing
[clo]

Metabolic
Rate [Wm−2 ]

35

Male

75

1.75

0.5

110

ing shortwave radiation, causes discontinuities in MRT, illustrated by two separate color-schemes for shaded and
unshaded locations on the map (Figure 6). Shaded locations range from 49.0°C to 50.0°C MRT (49.4°C to 50.1°C
MRT) in the morning (afternoon), while sun-exposed areas are upwards of 58.6°C MRT (57.2°C MRT). The map
further suggests that MRT is slightly increased near vertical urban features. Although an increase in emitted longwave radiation is expected from sun-facing walls that are
or have been exposed to direct radiation, and therefore
become a source of radiant heating, the same does not
necessarily apply to permanently shaded surfaces and
trees. This is a known limitation of the RayMan model;
it assumes the same thermal properties for all solid surfaces in the fisheye image and the lower hemisphere,
which can lead to an overestimation of longwave radiation from surfaces.
To test model performance, we compared the RayMan simulated MRT results to six-directional radiant flux
density observations from an on-campus field measurement campaign on August 7, 2016 (Figure 6). 3D radiant
flux densities were sampled at 20 locations across cam-

pus every hour from 8:00h to 19:00h using three Hukseflux 4 component net radiometers mounted on a mobile instrument platform at 1.1 m height above ground.
The sampling sites were traversed within 45 minutes, including a one minute stop at each location to account for
sensor lag. MRT was calculated from the observations following ISO 7726 (1998). The sites were selected to span
a wide variety of sun-exposure and surface cover combinations (Table 2). Exposure settings include open sites,
shade from trees, east-west canyons, and a building overhang; surface cover varies between concrete, grass, soil,
and gravel.
A comparison of modeled and observed MRT shows
considerable differences for most locations (Table 2). Although RayMan explains 84.4% of the variance in MRT,
the model consistently overestimates shaded and underestimates sun-exposed sites (RMSE=7.33; MBE=3.69;
MAE=6.83; d=0.72). This indicates that the model accurately captures the differences in MRT between shaded
and sun-exposed locations due to incoming shortwave
radiation, but has difficulties to resolve the heterogeneity of urban form. Our results are in agreement with

August 7, 2016, 09:00 h

0

125

250 m

shaded

August 7, 2016, 17:00 h

a

b
MRT
[˚C]

shaded

sun-exposed
sun-exposed
Figure 6. Simulated mean radiant temperature (MRT) map of the study site for 09:00h (a) and 17:00h (b) on August 7, 2016,
with on-site mean radiant temperature observations.

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

25

Thorsson et al. (2007) who found that RayMan underestimates sun-exposed sites under clear conditions in
Göteborg, Sweden, and with Lee and Mayer (2016) who
found that RayMan overestimates low and underestimates high MRT observations in Freiburg, Germany. Yet,
RayMan performed better in our setting than during
a field experiment in Glasgow by Krüger, Minella and
Matzarakis (2014) who reported RMSE values upwards
of 10°C in a comparison of various methods to estimate
MRT. Despite the divergence between observed and
modeled MRT values, we conclude that RayMan yields
reasonable estimates to demonstrate the utility of our
thermal comfort routing application. Improving MRT simulations is beyond the scope of this paper, but implementing a refined radiation scheme for our synthetic fisheye approach is part of ongoing work.
4.2. Pedestrian Routing
Based on the RayMan model output for PET, we suggest walking routes across campus that are tailored to
thermal comfort preferences. We employed the Dijkstra (1959) algorithm to calculate the shortest path between two locations in the study area and incorporated
a weighting that accounts for PET preferences of an individual. The “comfort over distance” parameter α controls
the importance of thermal comfort for navigation, i.e.
α = 0 yields the shortest path and α → ∞ yields the most
comfortable path, minimizing average PET of a route. For
our case study, we selected a route starting at the Ira

A. Fulton Schools of Engineering Brickyard north-west of
the Tempe campus and ending at the Memorial Union in
the campus center. The Brickyard building complex is located on Mill Avenue, a pedestrian-friendly street in the
heart of Tempe with many restaurants, cafes, bars, and
shops. The Memorial Union offers student support services and is a major activity hub at the campus core. We
calculated the shortest path (α = 0), a more comfortable
path (α = 2), and the most comfortable path (α → ∞)
from the Brickyard to the Memorial Union for August 7,
2016, 9:00h and 17:00h (Figure 7). With increasing willingness to walk further, optimal comfort routes divert
from the shortest path to navigate pedestrians through
shade from buildings and trees instead of exposing them
to the sun. Routes also vary by time of day, as the sun position changes shade patterns from buildings and trees.
At 9:00h, shade is generated to the west of urban features and the most comfortable route leads through a
tree-lined north-south canyon between midrise buildings. At a walking speed of 1.4 ms−1 , the route is 65 m
and 48 s longer than the shortest route (995 m, 11 min
and 48 s), lowers sun exposure by 7.5%, and increases average thermal comfort from 43.4 to 42.9°C PET (Table 3).
At 17:00h, when shade is generated to the east at a low
sun angle, the most comfortable path leads along the
east side of a group of high-rise buildings through an almost completely shaded north-south canyon. The route
is 97 m longer than the shortest path (997 m, 11 min and
54 s), adding 1 min and 6 s to the trip but reducing sun
exposure by 10%.

Table 2. Site description and comparison of simulated vs. observed mean radiant temperature for 20 locations in the study
area for August 7, 2016 at 9:00h and 17:00h.
09:00 h
Stop
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

17:00 h

Exposure

Location

Surface
Cover

MRTobs
[°C]

MRTcalc
[°C]

MRTcalc −
MRTobs [°C]

MRTobs
[°C]

MRTcalc
[°C]

MRTcalc −
MRTobs [°C]

shade
sun
shade
shade
shade
shade
sun
shade
shade
shade
shade
shade
shade
shade
shade
shade
shade
shade
sun
shade

under tree
E-W walkway
under tree
under tree
under tree
under tree
intersection
under tree
under palm trees
under tree
under overhang
under tree
under tree
under tree
under tree
under tree
under tree
under tree
E-W canyon
under tree

concrete
concrete
soil
grass
grass
gravel
concrete
concrete
concrete
soil
concrete
concrete
concrete
grass
concrete
concrete
concrete
concrete
concrete
concrete

44.3
68.2
46.4
38.6
45.1
40.5
67.4
40.9
44.2
39.3
33.6
57.0
43.0
40.0
41.5
41.6
43.0
48.3
64.9
41.6

49.6
59.6
49.8
49.8
50.0
49.4
58.9
49.6
50.0
49.8
49.4
49.2
49.4
49.3
49.4
49.5
49.5
49.3
59.5
49.9

−15.3
1−8.6
−13.4
−11.3
−14.9
−18.9
1−8.5
−18.7
−15.8
−10.5
−15.8
1−7.8
−16.4
−19.3
−17.9
−17.9
−16.6
−11.0
1−5.4
−18.3

43.8
68.2
38.7
41.2
42.1
46.3
66.6
45.5
48.3
43.9
36.0
46.1
44.6
43.2
41.7
43.9
47.3
47.2
67.2
39.3

49.9
57.5
49.4
49.6
49.9
49.7
57.4
50.0
50.0
49.9
49.9
49.7
49.8
49.8
49.9
49.8
49.8
49.8
57.7
49.9

−16.1
−10.7
−10.7
−18.4
−17.8
−13.4
1−9.2
−14.5
−11.7
−16.0
−13.9
−13.6
−15.2
−16.6
−18.2
−15.9
−12.5
−12.6
1−9.5
−10.6

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

26

August 7, 2016, 09:00 h

0

125

August 7, 2016, 17:00 h

250 m

shaded

a

b
PET
[˚C]

sun-exposed

shaded

sun-exposed

Figure 7. Thermal comfort map (Physiologically Equivalent Temperature, PET, in °C) for Arizona State University’s Tempe
campus for August 7, 2016, 09:00h (a) and 17:00h (b); Shortest path (dotted line) from the Ira A. Fulton Schools of Engineering (Brickyard) to the Memorial Union, slightly longer, but more comfortable route (dashed line), and most comfortable
path (solid line).
Table 3. Route statistics on length, walking duration (at 1.4 ms−1 ), average thermal comfort (PET), and sun exposure for
three thermal comfort preferences (α = 0, 2, α → ∞) at two different times of day (9:00h and 17:00h) on August 7, 2016.
09:00h

17:00h

α=0

α=2

α→∞

α=0

α=2

α→∞

995
11.8
43.4
50.5
6.0

1020
12.1
43.2
45.0
5.5

1057
12.6
42.9
43.0
5.4

997
11.9
48.7
37.1
4.4

1016
12.1
48.5
33.3
4.0

1094
13.0
48.3
27.4
3.6

Length [m]
Duration [min]
Average PET [°C]
Sun Exposure [%]
Sun Exposure [min]

Considering the hot dry thermal conditions on August 7, detours from the shortest path are short and reasonable, and at the same time significantly reduce sun
exposure, especially in the late afternoon when sun angles are low. Thermal comfort differences in the shortest and most comfortable path are expected to be more
pronounced for longer distances and in more heterogeneous urban forms. Results will also differ in other climatic conditions where humidity or wind speed might
play a more significant role in determining thermal comfort and during the winter when deciduous trees have
lost their leaves.
5. Discussion and Conclusions
We developed a methodology to generate synthetic fisheye images based on Google Earth 3D data for urban
areas at fine spatial resolution. The hemispherical im-

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

ages can be used to derive urban form and climate metrics such as SVF, duration of sun exposure, MRT, and
the thermal comfort index PET. Our approach is novel
in that it combines several advantages of existing approaches. First, urban form and climate metrics can be
calculated automatically for large urban areas independent of available 3D building databases, DSMs, or DEMs.
Second, trees are included in the 3D urban geometry;
trees are important shade providers at the pedestrian
level that must be considered in fine-scale outdoor thermal comfort applications. Our synthetic fisheye images
compared well to real world hemispherical photos retrieved from Google Street View, but are currently more
difficult to generate, because the most recent Google
Earth API does not support direct access.
The presented SVF approach integrates well with
existing thermal comfort models that use fisheye photographs to model radiation fluxes. However, refinement

27

of the physical properties and sun-exposure of the solid
surfaces in those fisheye-based models is needed to resolve the heterogeneity in urban areas and estimate thermal comfort more accurately.
In a heat mapping case study, we demonstrated the
utility of our synthesized fisheye images for pedestrian
thermal comfort routing on Arizona State University’s
Tempe campus. We introduced the “comfort over distance” parameter α that minimizes average PET exposure for a route based on a pedestrian’s willingness to
walk further. Integrating personalized thermal comfort
preferences as a weighting factor, we estimated a pedestrian’s exposure time to direct sun given a route, walking speed, and overall thermal comfort. The current routing algorithm minimizes average PET with increasing α,
but the duration, frequency, and magnitude of personal
exposure to heat affects thermal comfort as well (Kuras
et al., in press). The time spent walking above a certain PET threshold presents an alternative metric similar to the Extreme Degree-Minute approach employed
by Karner, Hondula and Vanos (2015) that could be implemented as weighting factor. Our algorithm can further be extended to provide more individualized thermal comfort routes incorporating multiple weighting factors, e.g., traffic-related air pollution and accessibility to
cooling facilities such as water fountains, shops, and cooling centers.
Our individualized thermal comfort maps demonstrate how urban form, represented here by the SVF, impacts walkability and pedestrian outdoor thermal comfort. As navigational aid, these maps have the potential to significantly reduce thermal stress on pedestrians.
They can help the public to better prepare for outdoor
activities by visualizing how thermal conditions “feel”
and how they vary within the urban area. Thermal comfort maps can also provide useful information for urban
planners. They can be employed to assess neighborhood
walkability, determine hotspots, and support heat hazard mitigation efforts, e.g., inform targeted tree planting
in cities to maximize thermal comfort outcomes.
Thermal comfort outcomes are significantly influenced by how we design cities, i.e. the layout and types
of buildings, streets, and vegetation. Thermal comfort
maps from synthetic fisheye photos provide important
insights that, integrated into urban planning processes,
can inform future city design to create more climatesensitive outdoor spaces.
Acknowledgments
This research was sponsored by University of Kaiserslautern, grant ”Microclimate Data Collection, Analysis,
and Visualization”.
Conflict of Interests
The authors declare no conflict of interests.

Urban Planning, 2017, Volume 2, Issue 1, Pages 19–30

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About the Author
Ariane Middel (PhD, University of Kaiserslautern) is an Assistant Research Professor in the School of
Geographical Sciences and Urban Planning at Arizona State University. Her research interests are directed toward understanding the dynamics of urban climate to develop climate adaptation and heat
mitigation strategies, specifically addressing the challenges of sustainable urban form and design under climatic uncertainty in rapidly urbanizing regions. She was recently elected as a Board member of
the International Association for Urban Climate (IAUC).
Jonas Lukasczyk (M.Sc., Technische Universität Kaiserslautern) is a PhD student in the Visual Information Analysis group at TU Kaiserslautern. His work focuses on topological visual analysis of spatiotemporal data. For more information on his current work visit www.jluk.de.

Ross Maciejewski (PhD, Purdue University) is an Assistant Professor in the School of Computing, Informatics and Decision Systems Engineering at Arizona State University (ASU). His recent work has
explored the extraction and linking of disparate data sources analyzing combinations of structured
geographic data to unstructured social media data focusing on public health, dietary analysis, social
media, and criminal incident reports. He is a Fellow of the Global Security Initiative at ASU and the
recipient of an NSF CAREER Award. For more information visit vader.lab.asu.edu.

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