Landscape and Urban Planning 165 (2017) 162–171

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Landscape and Urban Planning
journal homepage: www.elsevier.com/locate/landurbplan

Research Paper

Optimizing green space locations to reduce daytime and nighttime urban
heat island effects in Phoenix, Arizona

MARK

⁎

Yujia Zhanga, , Alan T. Murrayb, B.L. Turner IIc
a
b
c

School of Geographical Sciences and Urban Planning, Arizona State University, Coor Hall, 5th Floor, 975 S. Myrtle Ave., Tempe, AZ 85287, United States
Department of Geography, University of California at Santa Barbara, Santa Barbara, CA 93106, United States
School of Geographical Sciences and Urban Planning, and School of Sustainability, Arizona State University, Tempe, AZ 85287, United States

A R T I C L E I N F O

A B S T R A C T

Keywords:
Urban heat island
Green space cooling
Location optimization
Environmental services trade-offs
Climate change mitigation

The urban heat island effect is especially significant in semi-arid climates, generating a myriad of problems for
large urban areas. Green space can mitigate warming, providing cooling benefits important to reducing energy
consumption and improving human health. The arrangement of green space to reap the full potential of cooling
benefits is a challenge, especially considering the diurnal variations of urban heat island effects. Surprisingly,
methods that support the strategic placement of green space in the context of urban heat island are lacking.
Integrating geographic information systems, remote sensing, spatial statistics and spatial optimization, we
developed a framework to identify the best locations and configuration of new green space with respect to
cooling benefits. The developed multi-objective model is applied to evaluate the diurnal cooling trade-offs in
Phoenix, Arizona. As a result of optimal green space placement, significant cooling potentials can be achieved. A
reduction of land surface temperature of approximately 1–2 °C locally and 0.5 °C regionally can be achieved by
the addition of new green space. 96% of potential day and night cooling benefits can be achieved through
simultaneous consideration. The results also demonstrate that clustered green space enhances local cooling
because of the agglomeration effect; whereas, dispersed patterns lead to greater overall regional cooling. The
optimization based framework can effectively inform planning decisions with regard to green space allocation to
best ameliorate excessive heat.

1. Introduction
As cities grow, changes in urban land cover and geometry/morphology/architecture coupled with intensifying human activities have
led to a modified thermal climate, particularly at night, forming an
urban heat island (UHI) (Fan & Sailor, 2005; Voogt & Oke, 2003). This
effect has significant implications for sustainability, with consequences
for energy and water consumption, emissions of air pollutants and
greenhouse gases, human health, and the emergence of regional heat
islands (Arnfield, 2003; Georgescu et al., 2014; Hondula et al., 2012,
2014; Huang, Zhou, & Cadenasso, 2011; Sailor, 2001). The UHI effect is
intense in Phoenix, Arizona, amplified by rapid and extensive urbanization with resulting temperature increases approximating 0.5 °C per
decade (Grimm et al., 2008). Summers in Phoenix are characterized by
peaks in energy use and increased residential water consumption as
well as the emergence of extreme UHI “riskscapes” (Harlan, Brazel,
Prashad,
Stefanov, & Larsen,
2006;
Jenerette,
Harlan,
Stefanov, & Martin,
2011;
Ruddell,
Harlan,
GrossmanClarke, & Buyantuyev, 2010; Wentz, Rode, Li, Tellman, & Turner,

⁎

2016).
Green space, an area partially or completely covered by grass, trees,
shrubs, and/or other vegetation in the form of parks, golf courses, large
gardens, and yards, can effectively reduce temperature through shading
and evapotranspiration (Balling & Lolk, 1991; Chang, Li, & Chang,
2007; Spronken-Smith & Oke, 1998). Recognizing the potential to
mitigate UHI, the City of Phoenix has launched a master plan that
aims to increase the amount of green space (City of Phoenix, 2010).
Consequently, an important question is where to site new green space in
order to best realize potential cooling benefits. Improvements in
measuring and modeling cooling benefits of green spaces are required,
however, to make informed decisions.
On the measurement side, air temperature based studies have found
that green space can be 1–3 °C, and sometimes even 5–7 °C, cooler than
surrounding built-up areas (Chow, Pope, Martin, & Brazel, 2011;
Spronken-Smith & Oke, 1998; Upmanis, Eliasson, & Lindqvist, 1998),
with cooling impacts extending as much as several hundred meters
beyond green space boundaries (Bowler, Buyung-Ali, Knight, & Pullin,
2010; Eliasson & Upmanis, 2000; Spronken-Smith, Oke, & Lowry,

Corresponding author.
E-mail addresses: yzhan169@asu.edu (Y. Zhang), amurray@ucsb.edu (A.T. Murray), Billie.L.Turner@asu.edu (B.L. Turner).

http://dx.doi.org/10.1016/j.landurbplan.2017.04.009
Received 26 July 2016; Received in revised form 26 March 2017; Accepted 12 April 2017
Available online 31 May 2017
0169-2046/ © 2017 Elsevier B.V. All rights reserved.

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Y. Zhang et al.

rainfall is about 210.82 mm. With rapid urbanization during the last 50
years, the mean daily air temperature has increased by 3.1 °C and the
nighttime minimum temperature by 5 °C (Brazel, Selover,
Vose, & Heisler, 2000). The city and metropolitan area confront major
urban heat island effects and related water withdrawal problems, which
are expected to be amplified by climate change over the coming years.
To address sustainability challenges, Phoenix adopted a master plan
in 2010 that aimed to create a healthier and more livable city through
strategic investment in more green space (City of Phoenix, 2010).
Existing green space in the city varies in size, shape and vegetation
cover, exhibiting different levels of cooling effects during the day and
the night. As illustrated in Fig. 1, green space is distributed rather
unevenly across the city. Low-income, ethnic minority neighborhoods
tend to have less and smaller-sized green spaces, generally with sparse
vegetation cover (Harlan et al., 2006). The aerial imagery in Fig. 1
shows the detailed study area, which is 8,800 ha in size. This area is
low-income and has a mixture of low and high vegetation cover
neighborhoods.
Associated data utilized in this study includes thermal temperature
readings and a fine-scale land cover classification. The land surface
temperature was derived from Advanced Spaceborne Thermal Emission
and Reflection Radiometer (ASTER) data layers. The ASTER image
consists of six bands for short-wave infrared, at 30 m resolution, and
five bands of thermal infrared, at 90 m resolution (Yamaguchi et al.,
1998). The ASTER_08 product was used for surface temperature
extraction. In order to address the diurnal cooling effect variation, a
consecutive night and day cloud-free image pair were selected (under
clear and clam weather conditions) for a summer period: June 17, 2010
(22:00 at local time) and June 18, 2010 (11:00 at local time),
respectively. Daytime and nighttime temperatures for these dates at
90 m resolution are shown in Fig. 2. The study area consists of 11,466
(126 by 91) pixels. The mean surface temperature of the area is
55.60 °C and 29.85 °C for day and night, respectively. According to
the National Weather Service and the Arizona Meteorological network,
five weather stations are located within the extent of the utilized ASTER
image, and one is within the reported study area (Fig. 1). Table 1 shows
the comparison between air temperature and corresponding LST values.
This highlights significant daytime differences between the surface and
air temperatures, because LST responds to direct solar radiation (Cao
et al., 2010; Hartz, Prashad, Hedquist, Golden, & Brazel, 2006). During
nighttime, the surface temperatures are slightly higher than air
temperatures. Calm wind conditions enhance the positive association
between LST and air temperature, whereas strong winds decouple the
relationship (Stoll & Brazel, 1992).
Both daytime and nighttime effects are examined because of their
combined impacts on human wellbeing, energy and water use, and
environmental performance. The well-known consequences of extreme
summer temperatures in the Phoenix area include human health
(Harlan et al., 2006), increased demands on energy for cooling and
water for landscaping (Wentz et al., 2016), and impacts on year-round
tourism favored by the commercial sector (Gober et al., 2009). Perhaps
less known are the nighttime UHI effects. These include extending
energy use for cooling into evening, owing to daytime heat storage
(Grimmond & Oke, 2002), and throughout the night, as well as providing a higher temperature base from which the daytime UHI effect builds
(Stoll & Brazel, 1992). Interestingly, higher nighttime temperatures
during the winter reduce the occurrence of frost and its dampening
effect on insects and anthropods, which in turn increase pesticide use,
among other impacts (Ruddell, Hoffman, Ahmad, & Brazel, 2013).
In addition, a 1 m land cover classification of metropolitan Phoenix
was utilized. This data layer was created using aerial imagery from the
National Agricultural Imagery Program. The 1 m aerial images have
four bands (RGB and NIR) and were acquired for summer 2010. The
images were classified using the object-based method, implemented
using the eConigtion software (Li et al., 2014). The resulting land cover
data layer included 12 land cover classes with an overall accuracy of

2000). Air temperature measurements are not suitable for citywide
studies, however, due to their small sample size and limited spatial
coverage (Bowler et al., 2010). Derived from remotely sensed thermal
infrared imagery, land surface temperature (LST) measures surface UHI
(SUHI). LST shows significant correlation with air temperature and
provides complete spatial coverage across an entire cityscape (Fung,
Lam, Nichol, & Wong, 2009; Klok, Zwart, Verhagen, & Mauri, 2012;
Nichol, Fung, Lam, & Wong, 2009). Extensive research has explored
relationships between SUHI and urban land cover, especially with
regard to vegetation (Buyantuyev & Wu, 2010; Li, Li, Middel,
Harlan, & Brazel, 2016; Myint, Wentz, Brazel, & Quattrochi, 2013; Ren
et al., 2013; Weng 2009; Zhou, Huang, & Cadenasso, 2011). Studies
have suggested that land cover composition and configuration of the
green space are strong predictors of its cooling effect (Cao, Onishi,
Chen, & Imura, 2010; Li et al., 2013; Lin, Yu, Chang, Wu, & Zhang,
2015; Maimaitiyiming et al., 2014; Ren et al., 2013 Ren et al., 2013).
Furthermore, local context and adjacent green space also have impacts
on cooling (Cheng, Wei, Chen, Li, & Song, 2014; Lin et al., 2015;
Spronken-Smith & Oke, 1998, 1999). Explicit linkages between cooling
effects and the locations of green spaces are missing, however, causing
difficulties for location model construction.
On the modeling side, micro-climate numerical models deal with
surface energy balance, simulating thermodynamic processes for canopy layer UHI assessment (Chow et al., 2011; Erell,
Pearlmutter, & Williamson, 2012; Fernández, Alvarez-Vázquez, GarcíaChan, Martínez, & Vázquez-Méndez, 2015; Middel, Chhetri, & Quay,
2015; Ng, Chen, Wang, & Yuan, 2012). Results from such models are
rich in temporal scale but are limited in spatial extent, thus fail to
capture intra-urban temperature variations. Combining broader scale
spatial data, multi-objective optimization models have been applied
recently to determine green space locations in the city, balancing
various kinds of environmental benefits. Neema and Ohgai (2013)
developed a multi-objective heuristic technique for optimizing the
configuration of parks and open space with respect to air and water
quality improvement as well as noise and temperature reduction. Zhang
and Huang (2014) sought to minimize LST in the allocation of land uses
within a multi-objective heuristic, where temperature is a regressed
function of land use intensities. As yet, however, no current model has
attempted to account for the agglomeration of cooling resulting from
adjacent green spaces, which greatly affects their spatial allocation.
The above mentioned measuring and modeling gaps are addressed
in this research using an integrated framework that combines remote
sensing, GIS, spatial statistics and spatial optimization. Fine-scale
remote sensing data can greatly improve model reality, allowing better
representation of the intra-urban SUHI intensities. Incorporated with
GIS, statistical and optimization models facilitate practical location
decision making to enhance green space cooling. The study first
quantifies and predicts direct and indirect cooling benefits of the green
space using LST and land cover data, linking cooling effect with green
space locations. The exact formulation and solution for green space
allocation is developed next and explicitly accounts for agglomerationbased cooling. The multi-objective model developed here considers
both daytime and nighttime cooling impacts, enabling trade-off solutions to be identified. The framework is applied to an area in central
Phoenix.
2. Study area and data
The Phoenix metropolitan area, one of fastest growing urban
regions in the U.S., is located on the northern edge of the Sonoran
Desert. With a population approaching 1.5 million, the City of Phoenix
comprises approximately 134,200 ha of land in the center of a much
larger metropolitan area (Fig. 1). Dominated by a semi-arid climate,
this region has mild winters and hot summers. The temperature in
Phoenix commonly exceeds 38 °C on average for 110 days during the
year, and reaches 43 °C or higher for 18 days. The average annual
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Y. Zhang et al.

Fig. 1. City of Phoenix and study area.

3. Methods
Fundamentally, green space provides local heat reduction that may
contribute to region-wide benefits. Because of air movement and heat
exchange, green space moderates temperatures within and beyond its
boundaries, effectively forming neighborhood cooling (Ca,
Asaeda, & Abu, 1998; Spronken-Smith & Oke, 1998; Spronken-Smith
et al., 2000). Furthermore, the cooling effects of nearby green space
may interact, enhancing local benefits (Lin et al., 2015; SpronkenSmith & Oke, 1999). A conceptualization of this is illustrated in Fig. 4.
The thermal anisotropy of temperature is simplified, shown as a
uniform distribution of the mean value for a given area. This not only
indicates the direct benefits associated with green space, but also the
indirect benefits to neighboring areas.
These basic types of cooling benefits (Fig. 4) can be characterized
mathematically. For a given area i (or cell, parcel or land management
zone), let βi represent the temperature reduction possible if it is green
space and δik indicates the temperature reduction possible if there are k
nearby green spaces. Given the temperature for an area as it currently
exists, Ti, and the anticipated temperature if it were to be converted to
green space, Ti*, then the direct cooling benefit to area i is derived as
follows:

βi = Ti − Ti*

(1)

Similarly, indirect cooling benefits can be derived as well:

δik = Ti − Tik'
Fig. 2. Observed land surface temperature (LST) during the day and night (°C).

(2)

where Tik' denotes the anticipated temperature for area i if exactly k
green spaces are neighboring i. Eqs. (1) and (2) therefore represent
measures of potential benefit associate green space allocation and can
be used in a land use planning process once they have been derived. In
this case, Ti is estimated using the mean temperature of the local
surrounding, which reflects the temperature without the cooling effect.
Proximity corresponding to neighborhood and the local surrounding
extent can be quantified, as is done here based on distance maximums.

91.9%. For the purposes of this analysis, the 12 land cover classes were
aggregated into 6 classes: building, paved surface, soil, tree (including
shrub), grass and water (Fig. 3).

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Y. Zhang et al.

Table 1
Comparison of air temperature and land surface temperature in °C.
Weather Station (from South to North)

Air Temperature (at 11:00)

Land Surface Temperature (at 11:00)

Air Temperature (at 22:00)

Land Surface Temperature (at 22:00)

Mesa
Phoenix Sky Harbor
Phoenix Encanto
Phoenix Greenway
Desert Ridge

35.00
35.33
34.50
34.00
32.39

53.65
56.75
44.95
45.85
45.35

30.78
33.61
25.72
27.78
25.61

30.95
31.35
26.80
27.35
28.15

The bold line indicates the weather station within the study area.

Fig. 3. Land cover data layer (1 m resolution).

3.1. Remote sensing
The thermal imagery supports green space optimization through the
extraction of surface temperature across a region. This is far more
comprehensive and complete than traditional spatial sampling approaches that rely on ground based equipment readings combined with
interpolation. The surface temperature measurements were derived
using ASTER_08 imagery, as noted previously. The data contains
surface readings in Kelvin, corrected for atmospheric transmission,
emissivity, absorption and path radiance (Gillespie, Rokugawa, Hook,
Matsunaga, & Kahle, 1999). The absolute accuracy of the measures
ranges from 1 to 4 K, with relative accuracy of 0.3 K (JPL, 2001). The
readings were then converted to Celsius. The output is observed land
surface temperature, Ti, for each of the 11,466 land units (cells) in the
study area. The 1 m land cover data layer was classified using the
object-based method based on the four bands aerial imagery, also noted
previously. The aerial imagery was first segmented into parcel sized
objects using cadastral parcel boundaries. Then, integrating spectral,
contextual, geometrical information and expert knowledge, a hierarchical classification rule set was created to further assign and segment the
image objects into detailed land cover classes (see Li et al., 2014). The
result 1 m land cover map avoids the mixed feature problem of lowresolution data. Thus, it effectively depicts small, fragmented green
space and enables examination of individual land cover effect on
cooling (Li, Zhou, & Ouyang, 2013; Myint et al., 2013).The output is
land cover, Zi, for each of the 11,466 land units (cells) in the study area.
ERDAS IMAGINE was utilized for all remote sensing processing.

Fig. 4. Simplified distribution of green space cooling effects. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of this
article.)

To address urban heat island challenges, a spatial analytic framework that incorporates remote sensing, GIS, spatial statistics, and
spatial optimization (Fig. 5) is proposed. Remote sensing provides
essential data inputs, such as land cover and surface temperature
measurements. GIS offers methods for integration and management of
spatial information, important spatial analytic functions for deriving βi
and δik, capability to structure the optimization model based on data
inputs, and support to visualize and evaluate green space planning
results. Spatial statistical analysis is used to predict cooling benefits, βi
and δik, based on observed temperature, Ti, and land cover variables
within and surrounding an area i. Spatial optimization is used for
formalizing and solving the green space planning model. Each component requires data from or contributes data to GIS. Particularly
important, however, are derived parameters and spatial information
layers that are fed back into GIS.

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Y. Zhang et al.

Fig. 5. Methodological framework.

green space areas in Phoenix enabled appropriate parameters to be
derived for temperature estimation in both day and night conditions.
SPSS and R package were utilized for all statistical analysis.

3.2. GIS
GIS is a central component in this framework, connecting remote
sensing, spatial statistical and optimization through data management,
manipulation, analysis and visualization. The study area was first
discretized into 11,466 land units (cells), with each cell of the size of
0.81 ha. Next, neighbor and local area buffers were delineated for each
area i at 90 m and 360 m, respectively, based on observed temperature
gradients around green space. Land cover variables, Vilm, were derived
using FRAGSTATS, a spatial analytical software for landscape analysis
(McGarigal & Marks, 1995). The subscripts of Vilm indicate variable type
l (e.g., percent cover, shape index, mean patch area, etc.) by zone m
(e.g., green space, neighborhood, local, etc.) for each area i. Another
proximity based attribute derived using GIS was adjacency, where
neighboring units are in the set Ni for each area i, which is associated
with the indirect cooling. This information is utilized in land cover
evaluation, statistical analysis and optimization. A final aspect of GIS is
that results from statistical analysis and spatial optimization are readily
displayed for evaluation in various ways. ArcGIS was utilized for all GIS
processing.

3.4. Optimization
An optimization model was structured to identify the best locations
for new green space in order to realize the greatest overall benefits
associated with day-night cooling trade-offs. The approach taken
extends the coverage location model of Church and ReVelle (1974)
(see also Church & Murray 2009; Murray, Tong, & Kim, 2010) in a
number of ways. Specially, the nature of benefits differs, where βi
accounts for direct cooling benefits. In addition, there is a need to track
indirect cooling benefits, where k explicitly notes the number of times
an area neighbors green space. In the objective, δik accounts for the
indirect cooling enhancement associated with k. The notation of the
discrete integer optimization model is defined as follows:
j = index of potential green space areas
i = index of areas
k = number of neighboring green spaces
βj = direct cooling benefit for converting area j to green space
δik =indirect cooling benefit area i received from k neighboring
green spaces
Ni = set of areas neighboring unit i
p = number of green spaces to locate in a region

3.3. Statistical analysis
As noted previously, research has established that size, shape and
land cover of green space are strong predictors of its cooling effect.
Furthermore, cooling benefit is location dependent, affected by the
surrounding land cover as well (Cheng et al., 2015). The formal
specification of cooling benefits are given in Eqs. (1) and (2). Critical
of course is the estimated temperatures associated with green space, Ti*
and Tik' , where the former is expected temperature if area i is converted
to green space and the latter is the expected temperature when exactly k
green spaces are nearby. In general, expected temperature is a function
of a variety of observed characteristics for each area (and/or neighboring areas):

⎧1 if area j converted to green space
Xj = ⎨
⎩ 0 if not
⎧1 if area i neighbors k green spaces
Yik = ⎨
⎩ 0 if not
The developed coverage is formulated as follows:

Maximize ∑ βj Xj +

∑ ∑

j

Ti* = f (Ti , Zi, Vilm, Ni )

(3)

Tik' = g(j ∈ Ni , Zj , Tj , Vjlm )

(4)

i

k

δikYik
(5)

Subject to

kYik −

∑ Xj ≤ 0

∀ j, k
(6)

j ∈ Ni

Again, Ti* and Tik' are needed for deriving benefits, βi and δik, as detailed
in Eqs. (1) and (2). Precise mathematical specification is based on
components of the spatial statistical module of the framework involving
correlation analysis, multiple linear regression, and cross-validation
methods. Model fitness was statistically significant, with no issues of
spatial autocorrelation or multi-collinearity. More than 300 observed

∑ Yik + Xi ≤ 1
k

∑
j

166

∀i
(7)

Xj = p
(8)

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Y. Zhang et al.

Xj = {0, 1}

∀j

Yik = {0, 1}

∀ i, k

(9)

The objective, (5), is to maximize the total sum of cooling benefits,
either directly or indirectly. Constraints (6) define whether indirect
cooling benefit is provided to area i. Constraints (7) ensure that at most
one of the two types of cooling benefits is provided to an area.
Constraint (8) specifies that p areas are to be converted to green space.
The value of p is predetermined base on the goals associated with the
city’s plan. Finally, binary restrictions are imposed on decision variables in Constraints (9).
Of particular note within the context of the methodological framework, the primary output that would be fed back into GIS is the decision
variable values, Xj and Yik. That is, which areas are selected for
conversion to green space and which areas benefit from indirect
cooling. Somewhat complicating things associated with this model is
that it can be applied to daytime or nighttime conditions. Viewed in this
way, trade-offs are possible when day and night are simultaneously
considered. To do this, a weighted multi-objective model can be
structured. Assume the following:

Ωday =

∑

βj Xj +

∑ ∑

j

Ωnight =

i

∑
j

βj Xj +

(10)

k

∑ ∑
i

Fig. 6. Observed cooling benefits (in °C).

δikYik
Fig. 6 demonstrates significant indirect cooling effects on neighboring
area of green space. During the daytime, when k = 1, the observed
mean value of indirect benefit (δik) is 2.04 °C. However, when k ≥ 2,
the mean value of indirect benefit increases to 3.12 °C. During the
nighttime, the observed mean value is 1.18 °C (k = 1) and increased to
1.61 °C for k ≥ 2.
Fig. 7 summarizes the predicted βi across the study area, which was
the direct cooling benefit for area i if it is converted to green space. The
daytime mean value is 6.7 °C. The nighttime mean value is 2.6 °C. We
assume the green conversion had identical land cover, which is 100%
grass. Grass cover is selected because of its simpler effects on radiation
and surface energy balance compared to trees. Unlike grass, trees affect
cooling in positive and negative ways. Shading and evapotranspiration

δikYik

k

(11)

What changes between (10) and (11) are the values of βj and δik
depending on whether it is day or night conditions. The two objectives
can be integrated using a weighting variable w as follows:

Maximize

wΩday + (1 − w )Ωnight

(12)

where w ∈ [0,1]. Thus, this model can be repeatedly solved for different
values of w, with each unique solution representing a valid and
potentially meaningful trade-off solution. Planning and decision making processes would therefore take this information into account prior
to plan implementation.
The analysis was carried out on an Intel i5 (3.10 GHz) computer
running Windows 7 64-bit with 8 GB of RAM. ArcGIS 10.2 was used to
discretize the study area and delineate the cooling coverage. Arcpy and
Gurobi python API were employed to import the location information
and constructed the mixed integer model. The model was then solved in
Gurobi using the branch-and-bound approach. The original model
contained 2,935,297 rows, 2,935,552 columns and 16,511,232 nonzero
elements. The presolve process in Gurobi first tightens the formulation,
with a reduced model size of 93,899 rows and 377,020 columns, with
1,120,292 nonzero elements. The linear relaxation is used to establish
an upper bound, with feasible integer solutions establishing valid lower
bounds. The optimality gap between the upper and lower bound
converges to zero within three minutes through the use of branch and
bound.
4. Results
4.1. Observed and predicted cooling benefits
Fig. 6 summarizes the observed cooling benefits based on green
space samples in the Phoenix area. Computation of the direct and
indirect cooling benefits are based on Eqs. (1) and (2). Ti was estimated
using the mean temperature of the local buffers (360 m). The direct
benefit, βi, is obtained by computing the temperature differences
between the green space and its local buffer. The mean observed direct
benefit for the daytime is 4.17 °C and 2.33 °C for the nighttime.
Calculation of the indirect benefit δik is more complicated, requiring
separation of the neighboring area of green space (Fig. 4). The single
and multiple coverage polygons are identified and extracted using
spatial relationship operations in ArcGIS, such as intersect and merge.

Fig. 7. Predicted direct cooling benefits (in °C, excluding existing green space and water
bodies).

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Y. Zhang et al.

Table 2
Trade-offs associated with day and night cooling benefits.
w

Ω day

Day: % of obj.
decreased

Ω night

Night: % of obj.
decreased

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

5479.80
5479.27
5476.91
5466.80
5442.68
5401.44
5328.01
5256.25
5111.26
4957.13
4738.28

0.00%
0.01%
0.05%
0.24%
0.68%
1.43%
2.77%
4.08%
6.73%
9.54%
13.53%

1908.02
1917.52
1931.42
1959.69
2002.95
2053.49
2110.58
2148.13
2194.82
2221.46
2233.94

14.59%
14.16%
13.54%
12.28%
10.34%
8.08%
5.52%
3.84%
1.75%
0.56%
0.00%

1908.02 °C in column 4. Alternatively, when w = 0, this represents the
case where nighttime cooling benefits are deemed most important, and
the objective value, Ωnight, is 2,233.94 °C. Associated with this pattern of
green space would be a total daytime cooling benefit of 4738.28 °C.
These two situations highlight that optimizing daytime benefit is not
equivalent to optimizing nighttime benefit. As such, compromise green
space selection solutions can be identified that consider both day and
night cooling benefits simultaneously by varying the value of w,
reported in Table 2.
Fig. 9 depicts the trade-off solutions of the Ωday and Ωnight columns
in Table 2 for each value of w. Included in this figure are green space
distributions of three trade-off solutions, where the w = 1 (importance
on daytime cooling benefits) green space pattern is shown closest to the
x-axis, the w = 0 (importance on nighttime cooling benefits) pattern is
shown closest to the y-axis, and the w = 0.3 pattern is in between. The
latter is a compromise between the two competing objectives. The
patterns vary spatially, which is not surprising considering the variation
reflected in predicted cooling benefits detailed in Figs. 7 and 8.
The optimal green space allocations lead to dramatic gains in local
cooling benefits. Day conditions resulted in direct and indirect benefits
of 6.68 °C and 3.74 °C on average, respectively, which is about 2 °C
higher than means for observed, existing green space cooling benefits in
the study area. Similarly, night condition local cooling benefits were
able to be increase some 1 °C–2.57 °C and 1.55 °C (direct and indirect,
respectively) on average. Beyond this, a significant drop in regional
average temperature across the study area is also observed. The mean
observed temperature in the study area is 55.60 °C and 29.85 °C for day
and night, respectively (see Fig. 2). The greatest reduction in average
temperature during the day is associated with the green space pattern
when w = 1, reducing temperature to 55.13 °C. This represents almost
0.5 °C less than the current average in the study area of 55.60 °C. The
greatest reduction in nighttime average temperature is the green space
pattern when w = 0, reducing temperature to 29.66 °C (a 0.19 °C
decrease from current average temperature). Trade-off solutions, therefore, range between these extremes. For the green space pattern when
w = 0.3, average daytime temperature is 55.15 °C and the nighttime
average temperature is 29.67 °C.
The spatial heterogeneity of cooling benefits associated with green
space allocation solution is depicted in Fig. 10 for the case when w = 0
(importance on nighttime cooling). This illustrates not only where the
green space is to be located, but also the derived direct and indirect
cooling values. The selected locations are consistent with existing
findings on nighttime SUHI, which suggest that areas of abundant
impervious cover have higher impact on cooling than vegetated area at
night (Buyantuyev & Wu, 2010; Myint et al., 2013). As demonstrated in
Fig. 10, places along the industrial corridor and nearby the airport have
the highest potential for nighttime cooling. In contrast, highly vegetated neighborhoods observe minimal new green space allocation. Of
note is the agglomeration of indirect cooling benefit captured in this
case (inset image shown in Fig. 10). The overlapped neighborhood

Fig. 8. Predicted indirect cooling benefits (k = 1 case, in °C, excluding existing green
space and water bodies).

facilitate cooling. Trees also lower wind speed and reduce advection,
however, which may decrease the cooling effect. In addition, during
nighttime, tree canopies inhibit long-wave radiative cooling by blocking part of the skyview, while excess moisture increases the thermal
capacity of the soil and slows down surface cooling (Erell et al., 2012).
When area i is converted to green space, it also distributes indirect
cooling benefits to neighboring land, eight areas in this case. The
predicted indirect cooling benefit estimations are summarized in Fig. 8
for the case of a single neighboring green space (k = 1, so δi1). The
mean daytime and nighttime δi1 are 2.7 °C and 1 °C, respectively.
Spatially, Fig. 8 is much patchier compared to Fig. 7. The patchy
pattern (steep values changes within short distance) highlights potential cooling centers in the study area. For example, during the daytime,
the local cooling centers are places that have a high percent of
vegetation cover or complex shaped buildings within their neighborhood, and low percent of vegetation cover beyond. At nighttime,
however, local cooling centers change to places that have high contrast
between the percent cover and shape of the paved surface within and
beyond their neighborhood. While not shown here, multiple neighboring green spaces will enhance local cooling. This is reflected in the cases
when k ≥ 2 for δik.
4.2. Day-night cooling trade-offs
The optimization model allows for any level of green space
allocation to be evaluated, but the results presented here are necessarily
focused on the city’s plan objective. Consequently, in this analysis it is
assumed that 150 land units will undergo conversion to green space,
thus p = 150. This equates to 121.5 ha of new green space (1.3% of the
study area). Table 2 summarizes the trade-off solutions identified when
the importance weight for day and night cooling benefits is varied.
When w = 1, daytime cooling benefits are considered to be the most
important. The result, Ωday, corresponds to 5,479.80 °C in total
temperature reduction across all cells in the study area. Associated
with this allocation of green space, the nighttime cooling benefit is
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Fig. 9. Day-night trade-off solutions (in °C).

green spaces accounting for diurnal UHI variations, creating an
information lacuna for decision makers confronting the negative
impacts of excessive urban temperatures (e.g., Hondula,
Vanos, & Gosling, 2014). Our framework effectively addresses this issue
by integrating GIS, remote sensing and spatial statistics with optimization modeling. The model links green space allocation with local
landscape context and enables identification of trade-off solutions that
balance diurnal cooling benefits.

received 0.6 °C higher cooling than the single coverage neighborhood.
It proves beneficial to ensure in this case that indirect local benefit is
enhanced. That is, capturing the contribution of local benefits (k ≥ 2) is
favored. The model is able to strategically account for this in order to
maximize regional cooling benefits
5. Discussion
It is well known that increasing green spaces in urban areas helps to
ameliorate the extremes of UHI and SUHI effects. The research
dedicated to this relationship has largely focused on the amount or
area of green spaces, although increasing attention has focused on the
broader characteristics of the pattern of green spaces such as concentration or dispersion (Myint et al., 2015). To our knowledge, however,
no attempts have been made to determine the optimal locations for

5.1. General implications of UHI reduction
The results suggest that optimal green space siting may lead to
1–2 °C local LST reduction and nearly 0.5 °C regional LST reduction, on
average, throughout the Phoenix study area. This is remarkable given
that the new green space was limited to only 1.3% of the study area.

Fig. 10. Green space allocation pattern (w = 0). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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of the quality of estimates but also in terms of green space selection
impact. For example, the non-linear relationship between cooling
benefit and the size of green space has been reported in several studies
(Cao et al., 2010; Chang et al., 2007). On the modeling side, parameter
value changes and sensitivities could also be explored. As noted
previously, more new green space could be considered, which would
involve increasing the parameter p and re-running the optimization
models. The relationship between green space allocation and regional
temperature response certainly is an area for more research.

There may well be increased benefits if more green space is considered.
Other research beyond Phoenix indicates that a similar reduction in air
temperature, to which LST contributes, leads to a decrease of up to 10%
in peak energy demand (Fung, Lam, Hung, Pang, & Lee, 2006;
Meier & Taha, 2000). The consequences for water use are more complex, however. Green spaces, such as the turf grass assumed in this
study, require substantial water in desert cities. All turf grass and nonnative vegetation in Phoenix is irrigated, and outdoor water application
currently accounts for a majority of residential and neighborhood water
use in the metropolitan area (Balling, Gober, & Jones, 2008; Gober
et al., 2009; Wentz et al., 2016). As a result, adding more green space
may increase water demand, but the rate of use might be lowered by
incorporating mixed vegetation. Research in the Negev Desert in Israel,
for example, found that a combination of grass covered by shade trees
or mesh shading created a synergy with greater cooling and led to a
50% reduction in water use (Shashua-Bar, Pearlmutter, & Erell, 2009).
Finally, ameliorating temperature extremes is known to have positive
health impacts (e.g., Hondula et al., 2012).

6. Conclusions
Our integrated framework demonstrates significant cooling potentials can be gained through optimal green space placement in Phoenix,
Arizona. Daytime and nighttime cooling trade-offs are examined
because of their combined impacts on human wellbeing, energy and
water use, and environmental performance. In addition to size, land
cover, and shape, green space optimization also depends on the
surrounding land cover context, agglomeration of cooling resulting
from adjacent green spaces and diurnal heat island variations. The
selected optimal locations enhance landscape heterogeneity at the local
scale, which would increase the surface temperature gradients and
potentially accelerate air flow, preventing daytime heat storage and
facilitating nighttime cooling. The developed model can be further
applied to assess different land arrangements for various cooling
considerations. Our findings help to address the growing environmental
problem of extreme temperatures confronting urban areas worldwide.

5.2. Trade-offs of green space cooling
Beyond temperature reduction, this study also provides valuable
insights on green space patterning in relation to cooling trade-offs. Our
finding is consistent with existing research that the concentration of
green spaces enhances local cooling (Chang et al., 2007; SpronkenSmith & Oke, 1999). Such observations, however, do not consider the
trade-offs between local and regional cooling benefits. Our model
demonstrated that, although clustered pattern enhances local cooling,
their overall regional cooling benefit is lower than the spatially
dispersed pattern (see Fig. 9). This is because the dispersed pattern
ultimately influences a larger area through the local cooling provided to
adjacent parcels of land. In addition, other studies in the Phoenix area
have observed the varied diurnal role of different land covers on SUHI
(Buyantuyev & Wu, 2010; Myint et al., 2013). As of yet, however,
minimal attention has been given to the evaluation of trade-offs
between day and night relative to an established pattern of land cover
(Turner, Janetos, Verburg, & Murray, 2013). Our modeling approach
addresses this, indicating that maximized daytime cooling of green
spaces results in an approximately 15% reduction in nighttime cooling
and vice versa. Optimizing for both day and night simultaneously, it is
possible to achieve some 96% of the potential cooling benefits.

Acknowledgements
This research was supported by the Central Arizona-Phoenix LongTerm Ecological Research program (NSF Grant No. BCS-1026865), the
Decision Center for a Desert City (NSF Grant No. SES-0951366),
National Science Foundation (NSF) under Grant No. SES-0951366,
NSF DNS Grant No. 1419593 and USDA NIFA Grant No. 2015-6700323508, the Julie Ann Wrigley Global Institute of Sustainability. The
research was undertaken in the Environmental Remote Sensing and
Geoinformatics Lab, Arizona State University. We thank for the valuable inputs from Dr. Anthony Brazel and our reviewers.
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