Computers, Environment and Urban Systems 54 (2015) 181–194

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Computers, Environment and Urban Systems
journal homepage: www.elsevier.com/locate/ceus

The urban heat island effect and city contiguity
Neil Debbage ⁎, J. Marshall Shepherd
Department of Geography, University of Georgia, Athens, GA 30602, USA

a r t i c l e

i n f o

Article history:
Received 4 January 2015
Received in revised form 3 August 2015
Accepted 9 August 2015
Available online 12 September 2015
Keywords:
Urban heat island
Urban morphology
Spatial contiguity
Urban planning
PRISM
Spatial metrics

a b s t r a c t
The spatial configuration of cities can affect how urban environments alter local energy balances. Previous studies
have reached the paradoxical conclusions that both sprawling and high-density urban development can amplify
urban heat island intensities, which has prevented consensus on how best to mitigate the urban heat island effect
via urban planning. To investigate this apparent dichotomy, we estimated the urban heat island intensities of the
50 most populous cities in the United States using gridded minimum temperature datasets and quantified each
city's urban morphology with spatial metrics. The results indicated that the spatial contiguity of urban development, regardless of its density or degree of sprawl, was a critical factor that influenced the magnitude of the urban
heat island effect. A ten percentage point increase in urban spatial contiguity was predicted to enhance the
minimum temperature annual average urban heat island intensity by between 0.3 and 0.4 °C. Therefore, city contiguity should be considered when devising strategies for urban heat island mitigation, with more discontiguous
development likely to ameliorate the urban heat island effect. Unraveling how urban morphology influences
urban heat island intensity is paramount given the human health consequences associated with the continued
growth of urban populations in the future.
© 2015 Elsevier Ltd. All rights reserved.

1. Introduction
Urban areas are increasingly important, as 52% of the world population and 76% of individuals in developed countries resided in cities as of
2013 (Population Reference Bureau, 2013). Since urban population
growth is projected to continue, with approximately 67% of the world
population being urban dwellers by 2050 (United Nations, 2012), it is
imperative to work towards a better understanding of the complex
processes found at the intersection of urbanization, climate and
human health.
The enhanced anthropogenic heat emissions, reduced evaporative
cooling, increased surface roughness, lower surface albedos and narrow
urban canyon geometry associated with cities often results in the
formation of urban heat islands (UHIs), particularly at night, as urban
air temperatures are higher relative to the natural surroundings (Oke,
1982). Increasingly warm urban environments pose serious threats to
human health (Patz, Campbell-Lendrum, Holloway, & Foley, 2005;
McMichael, Woodruff, & Hales, 2006) because they amplify nearsurface ozone concentrations (Cardelino & Chameides, 1990), reduce
air quality (Sarrat, Lemonsu, Masson, & Guedalia, 2006), enhance
anthropogenic energy consumption (Rosenfeld, Akbari, Romm, &
Pomerantz, 1998) and increase heat related fatalities by magnifying
the severity of heat waves (Zhou & Shepherd, 2010; Stone, 2012; Li &

⁎ Corresponding author.
E-mail address: debbage@uga.edu (N. Debbage).

http://dx.doi.org/10.1016/j.compenvurbsys.2015.08.002
0198-9715/© 2015 Elsevier Ltd. All rights reserved.

Bou-Zeid, 2013). Partially due to the UHI effect, extreme heat events
on average are responsible for more climate-related fatalities than any
other form of severe weather (Johnson & Wilson, 2009; Stone, Hess, &
Frumkin, 2010).
While there is general agreement that cities fundamentally alter
local energy balances (Arnfield, 2003; Souch & Grimmond, 2006), how
their spatial configurations influence the UHI effect is still debated.
Traditionally, high-density urban development has been associated
with greater UHI intensities since many of the mechanisms producing
the UHI effect are often most pronounced within dense urban cores
(Oke, 1982, 1987). Oke and East (1971) provided an early example of
the linkages between city density and UHI intensity, as the UHI effect
of Montreal was generally found to be most prominent in areas of
particularly dense development.
However, more recent studies have concluded paradoxically that
both more sprawling (Stone & Rodgers, 2001; Stone, 2012) and denser
(Coutts, Beringer, & Tapper, 2007; Martilli, 2014; Schwarz & Manceur,
2014) city configurations can result in more intense UHIs. Sprawl,
typically defined as low-density, leapfrog urban expansion consisting
of segregated land uses and widespread commercial strip development
(Burchell et al., 1998), can exacerbate UHI intensities since it results in
more land clearances, impervious surfaces and excess heat generated
per capita when compared to higher density development (Stone &
Rodgers, 2001; Stone, 2012). Sprawling configurations also contribute
to the UHI intensity observed within the city center since the cooling
influence of the UHI circulation (Haeger-Eugensson & Holmer, 1999)
is impaired by the warm suburban periphery (Stone, 2012). In contrast,

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other studies have continued to document the connections between
higher densities and more intense UHIs, primarily due to the urban
canyon geometry altering heat storage release, using in-situ observations (Coutts et al., 2007), modeling (Martilli, 2014) and remote sensing
(Schwarz & Manceur, 2014).
Although some of these discrepancies are partially attributable to
the particular cities analyzed in the various studies, the specific type of
UHI evaluated and the diverse methodologies developed to quantify
UHI intensity as well as urban form, the overall lack of consensus
regarding the relationships between city configuration and the UHI
effect has implications that extend beyond the realm of urban climatology. Specifically, the conflicting findings pose a serious urban planning
dilemma: is high-density urban development a viable UHI mitigation
strategy (Emmanuel & Fernando, 2007; Stone, 2012) or will densification actually make cities less livable due to an intensification of the
UHI effect (Coutts et al., 2007; Martilli, 2014; Schwarz & Manceur,
2014)? The importance of resolving this question is highlighted by the
recent calls for additional empirical research to help clarify the ambiguous influence of city configuration on the UHI effect (Ewing & Rong,
2008; Martilli, 2014).
By examining the UHI intensities of 50 cities with various urban
morphologies, this study aims to evaluate the degree to which city
configuration influences the UHI effect and attempts to resolve the
apparent sprawl-density dichotomy concerning the most appropriate
urban form for UHI mitigation. The following section outlines the data
sources and methodologies used to investigate the relationships
between urban morphology and the UHI effect. The results of the analysis and a discussion are presented in Section 3. Finally, the broader

urban planning implications and general conclusions of the research
are summarized in Section 4.

2. Data and methods
2.1. Study area and methodology overview
The canopy UHI intensities and spatial configurations of the fifty
most populous Metropolitan Statistical Areas (MSAs) in the contiguous
United States, according to the 2010 US Census, were analyzed (Fig. 1).
A MSA consists of at least one urban core with a population of 50,000
or greater and the adjacent counties that are socio-economically tied
to that core, as determined by commuting data. In recognition of the
methodological shortcomings associated with the urban–rural site
comparison technique traditionally used to evaluate the UHI effect,
most notably the subjective nature of selecting an urban and rural
station as well as the inability to fully capture the heterogeneity of
temperature within the urbanized area and the surrounding natural
landscape (Peng et al., 2011; Jin, 2012), this study establishes a method
for estimating UHI intensities that utilizes PRISM (Parameter-elevation
Relationships on Independent Slopes Model) climate data (Daly et al.,
2008). The spatial configurations of the cities were quantified using
several spatial metrics that evaluated shape complexity, spatial contiguity, polycentrism and fragmentation. Bivariate and multivariate statistical techniques were then employed to analyze the relationships
between urban morphology and UHI intensity. A more detailed explanation of these methodologies is provided in the following sections.

Fig. 1. Map of the MSAs included in the analysis. Approximately 54% of the United States population resided within the 50 most populous MSAs in 2010.

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2.2. Datasets and derived variables
2.2.1. Urban heat island intensity estimation
A methodology that used PRISM climate data was developed to
systematically estimate the canopy UHI intensities for each MSA (Daly
et al., 2008). PRISM is an analytical model that creates gridded estimates
by incorporating discrete measurements of climatic variables (e.g.
temperature, precipitation, etc.), expert knowledge of complex climatic
events (e.g. rain shadows, temperature inversions and coastal regimes)
and a digital elevation model into a knowledge-based system. The
gridded PRISM data has a resolution of approximately 4 km, which
allows numerous grid points to exist within the urban areas of each
MSA. Specifically, the PRISM products for annual and monthly average
minimum temperature were used. The canopy UHI is most intense at
night so minimum temperatures were analyzed rather than maximums
or averages (Oke, 1982, 1987).
The PRISM minimum temperature datasets incorporate nearly
10,000 surface observations from over ten station networks across the
United States to achieve the most comprehensive coverage possible.
The primary limitation of using PRISM, or any similar gridded climate
data product, is its dependency upon the density of the underlying
station networks. This was less of an issue since the analysis focused
on the urban environment, which is where station networks are typically denser. However, to ensure that station availability was not systematically biasing the UHI intensity estimates, the number of surface
observations within each city that were potentially used during the
PRISM interpolation process was determined. Additionally, the station
availability within different land uses and land covers (LULCs) was
analyzed to confirm that the urban areas of each city were being
sampled representatively and that any minor over or under sampling
differences between the cities were not biasing the UHI estimates.
Sample representativeness was evaluated by calculating the ratio
between the percentage of urban stations and the percentage of urban
land cover for each city, where urban was defined by the four developed
categories of the LULC dataset detailed in the following section.
The UHI intensities for each MSA were estimated by subtracting the
average rural temperature from the average urban temperature
(Eq. (1)). The average urban temperature was derived by averaging
the temperatures of all the PRISM grid cells within the 2010 Census
Urbanized Areas (UA) and Urban Clusters (UC) included in each MSA.
UA, as defined by the US Census, contain at least 50,000 people and
include one central urban core and the adjacent densely settled territory. UC are similar to UA except they must contain at least 2500 individuals. Since UA/UC are largely based on population density, some
researchers (Sutton, Goetz, Fildes, Forster, & Ghosh, 2010; Bereitschaft
& Debbage, 2013; Bereitschaft & Debbage, 2014) have used nighttime
light intensity as an alternative method to delineate urbanized areas.
However, the inclusion of non-residential urban land uses characterized
by high levels of imperviousness within the 2010 US Census definition
of UA/UC make them a more viable option since they are no longer
determined solely by population data. A rural area outside the UA/UC
included in each MSA was delineated using a buffer, and the average
rural temperature was derived by averaging the temperatures of all
the PRISM grid cells falling within this rural domain.
UHIð
 CÞ ¼ TminUrban Average –TminRural Average

ð1Þ

Potential confounding factors (Stewart, 2011) were controlled for
when defining the extent of the “rural” area for each MSA. For example,
elevation changes and neighboring urban areas could distort the UHI estimates if the buffer used to define the rural domain included mountainous terrain or overlapped neighboring MSAs. A systematic rule-based
system was developed to combat these potential biases. Firstly, a
50 km buffer around the UA/UC was created to define a preliminary
rural area (Fig. 2A). A digital elevation model was incorporated to
limit the defined rural domain to only those regions within ± 50 m

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(Imhoff, Zhang, Wolfe, & Bounoua, 2010) of the average elevation of
the UA/UC (Fig. 2B). Finally, any neighboring urban areas within the
rural buffer were systematically excluded (Fig. 2C).
The urban domain and finalized rural domain (Fig. 2C), which
controlled for elevation and neighboring urbanized areas, were used
to estimate the UHI intensities for each month in 2010, the 2010 annual
average UHI intensity and a longer-term annual average UHI intensity
calculated from 2006 to 2010. The study focuses predominately on
2010 since the urban–rural boundaries used for the UHI intensity
estimation were defined by 2010 US Census data. The longer-term
average considered 2006 to 2010, as this five-year window enabled an
appropriate comparison with the spatial metrics since they were
derived from a 2006 LULC dataset. Finally, the usage of annual and
monthly average UHI intensities, rather than daily or weekly estimates,
helped capture the influence of city configuration on the UHI effect since
urban morphologies are fairly persistent throughout a given year. Using
a finer temporal resolution would be less suitable since daily variability
in UHI intensity is more likely related to differing meteorological conditions than urban form itself.
2.2.2. Quantifying the spatial configurations of cities with spatial metrics
LULC data obtained from the US Geological Survey (USGS) MultiResolution Land Characteristics Consortium (MRLC) served as the
foundation for calculating a set of spatial metrics. The MRLC maintains
the National Land Cover Database (NLCD), which is a series of LULC
datasets based primarily on the unsupervised classification of Landsat
imagery. The NLCD 2006, which has a spatial resolution of 30 m and
an overall accuracy of 78% (Wickham et al., 2013), was used in this
study. It includes 20 LULC categories that are based on a classification
scheme modified from the Anderson Land Cover Classification System.
In order to investigate how different degrees of urbanization influence
the UHI effect, the spatial metrics were calculated individually for each
of the four urban categories included in the NLCD 2006.
Developed open space (Class 21) is the least urban of the NLCD 2006
developed land classes, as it includes pixels where impervious surfaces
account for less than 20% of the total cover. This class typically consists
of single-family homes on large parcels as well as vegetation planted
within an urban context for erosion control, esthetic purposes or recreation. The low-intensity development (Class 22) and medium-intensity
development (Class 23) categories incorporate pixels with higher levels
of imperviousness, 20–49% and 50–79% of the total cover respectively,
but both correspond predominately to single-family housing units on
smaller lots. Finally, high-intensity development (Class 24) encompasses pixels with 80–100% impervious surface coverage and includes
areas where people live or work in large quantities (Homer, Huang,
Yang, Wylie, & Coan, 2004; Fry et al., 2011). In addition to calculating
the spatial metrics for the four urban categories (Classes 21–24), the
remaining 11 LULC classes included in NLCD 2006 were also analyzed.
The LULC classes do not sum to 20 because four of the categories exist
only in Alaska and one, perennial snow, did not occur within any of
the MSAs.
Due to the focus on urban climatic processes, the LULC data were not
analyzed for entire MSAs because in some cases the MSA boundary
includes large amounts of rural land cover (Galster et al., 2001).
Overbounded metropolitan counties, those whose administrative
boundaries include not only an urban center but also contain large
rural expanses not related to the urban core, are partially responsible
for this incongruity between urban land use and MSA demarcation. In
order to analyze only the urban environments, the LULC data within
the UA/UC included in each MSA was extracted. These are the same
UA/UC used to derive the average urban temperatures for the UHI
intensity estimations. Overall, focusing on the LULC data within the
UA/UC of each MSA established a much more appropriate landscape
extent for the spatial metric calculations.
The public domain software FRAGSTATS (McGarigal, Cushman, &
Ene, 2012) was used to compute the individual spatial metrics.

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Fig. 2. An example from Chicago, Illinois of the urban and rural domains used to derive the average urban temperature and average rural temperature for the UHI intensity estimates. The
2010 US Census UA/UC defined the urban domain. The UA/UC are surrounded by the initial 50 km rural domain (A), the elevation control rural domain (B) and the finalized rural domain
that controlled for elevation and did not contain any neighboring urban areas (C).

Although one specific suite of spatial metrics for analyzing urban
environments has not been established (Herold, Couclelis, & Clarke,
2005), reviewing the relevant literature helped identify some of the
most frequently utilized metrics to quantify urban form (Herold,
Scepan, & Clarke, 2002; Herold, Goldstein, & Clarke, 2003; Ji, Ma,
Twibell, & Underhill, 2006; Huang, Lu, & Sellers, 2007; Jat, Garg, &
Khare, 2008; Bereitschaft & Debbage, 2014). Since spatial metrics have
been less commonly used to analyze the specific relationship between
city configuration and the canopy UHI effect, the spatial metrics
employed by previous studies examining the linkages between urban
morphology and other urban climatological processes, such as the
surface UHI effect (Liu & Weng, 2008; Connors, Galletti, & Chow,
2013; Schwarz & Manceur, 2014) and air quality (Makido, Dhakal, &
Yamagata, 2012; Bereitschaft & Debbage, 2013), were particularly informative. The spatial metrics that were most relevant to our research
goals and therefore incorporated into the study included: areaweighted mean patch fractal dimension (AWMPFD), area-weighted
mean shape index (AWMSI), clumpiness index (CLUMPY), contagion
index (CONTAG), edge density (ED), largest patch index (LPI), patch
density (PD), percentage of like adjacencies (PLADJ) and percentage of
landscape (PLAND) (Table A.1). Each metric was calculated at the
class level (i.e. the metric values were summarized for each individual
class present in the landscape) with the exception of CONTAG, which
was calculated at the landscape level (i.e. the metric considered all the
classes present in landscape simultaneously).
AWMPFD and AWMSI both provide measures of shape complexity
based on modified perimeter-area ratios. AWMPFD values vary from 1
(simple shape) to 2 (complex shape) while AWMSI values increase
from 1 as the shape becomes more irregular. ED is another metric

commonly used to quantify urban shape complexity, but it is not
based on patch perimeter-area ratios. Instead, ED calculates the total
length of the urban edge segments, which is then divided by the total
landscape area. Within the context of urban landscapes, increasingly
irregular and complex shapes typically represent more expansive
urban morphologies.
PD and LPI are metrics used to evaluate the fragmentation/
aggregation of the urban environment. PD is the number of urban
patches divided by the entire landscape area. A larger PD proportion is
usually indicative of a more fragmented urban morphology. LPI is of
interest when analyzing cities because it quantifies the dominance of
the urban core by dividing the area of the largest urban patch, which
in most cases would be the Central Business District (CBD) if NLCD
Class 24 were being analyzed, by the total landscape area. Lower LPI
values are typically associated with increasingly polycentric and
fragmented urban environments.
PLADJ, CLUMPY and CONTAG are also measures of fragmentation/
aggregation, but they are fundamentally based on adjacency matrices.
PLADJ is calculated by dividing the number of like adjacencies involving
urban pixels by the total number of adjacencies involving urban pixels.
A higher PLADJ indicates a more contiguous urban landscape. CLUMPY
builds on the PLADJ metric by comparing the actual proportion of
urban like adjacencies to that expected from a spatially random distribution. The values for CLUMPY vary from − 1 (maximally disaggregated) to 1 (maximally aggregated) where 0 represents an essentially
random distribution. CONTAG is another aggregation metric but it
subsumes both interspersion and dispersion by analyzing the entire
landscape, not just the urban pixels. CONTAG values range from 0 to
100 with 100 occurring when the landscape is maximally aggregated.

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Although described above via an urban-centric perspective, the
same suite of spatial metrics was used to evaluate every LULC category.
For each city, the eight class level metrics were calculated for all 15 LULC
classifications while CONTAG was calculated at the landscape level. If a
LULC category was not present within a given MSA, the spatial metrics
for that class were assigned to zero.
2.2.3. Control variables
Additional control variables were derived to account for factors previously hypothesized to influence the UHI effect, such as city size, density and climatological conditions (Oke, 1982). City area was defined
as the combined area of all the UA/UC included in each MSA. Population
density was calculated using 2010 US Census data by summing the populations of the UA/UC within a given MSA and dividing that total population by the derived city area variable.
With regard to the climatological conditions, aridity was estimated
using the PRISM datasets for monthly average precipitation and maximum temperature during 2010. Specifically, the monthly average precipitation and maximum temperature for each city were derived by
averaging the pixel values within the same UA/UC employed during
the UHI estimations. Although fairly simplistic, De Martonne's (1926)
aridity index was used (Eq. (2)).
IAR ¼ P=ðT þ 10Þ

ð2Þ

In Eq. (2), P is precipitation measured in millimeters and T is temperature measured in degrees Celsius. The index approaches zero as the environment becomes more arid. Annual average aridity was calculated
for each city from the individual monthly index values. Since ecological
context is largely governed by precipitation and temperature climatology, the aridity variable served as a proxy that accounted for the general
character of the various natural environments surrounding the cities. Finally, the monthly and annual average wind speed for each city was calculated using NCEP/NCAR reanalysis data. The reanalysis data were resampled to a 0.10 by 0.10 degree grid to ensure that numerous pixels
fell within the UA/UC of each MSA, which again served as the averaging
domain.
2.3. Statistical methods
Both bivariate and multivariate statistical techniques were used to
evaluate the degree to which city configuration influences UHI intensity.
Pearson's correlation coefficient (r) was calculated to analyze the
relationships between each of the spatial metrics and the UHI effect.
These bivariate relationships were examined for the monthly UHI intensities in 2010, the 2010 annual average UHI intensity and the longerterm average UHI intensity from 2006 to 2010. Comparing the results
in 2010 to the longer-term average helped determine if the relationships in 2010 were atypical or fairly consistent with recent history
while the monthly analysis enabled an exploration of any seasonality
present in the relationships. In addition to evaluating the degree of
association between the spatial metrics and UHI intensity, correlation
coefficients were also calculated between the UHI effect and each of
the control variables.
For the multivariate models, the independent variables that were
considered for inclusion encompassed the various components of
urban morphology as well as potential confounding factors in order to
reduce the likelihood of over-estimating the influence of city configuration on the UHI effect. Specifically, the potential independent variables
included all the derived spatial metrics in addition to controls for city
area, population density, aridity and wind speed. The independent
variables actually incorporated into the multivariate models were manually selected based on a consideration of existing theory, the bivariate
correlations and the overarching research goals. The spatial contiguity
of low-intensity urban development (PLADJ_22) and the spatial contiguity of high-intensity urban development (PLADJ_24) were included

185

in each model to evaluate the different influences of sprawling and
high-density urban development on the UHI effect. The remaining independent variables, the percentage of barren land (PLAND_31), the shape
complexity of deciduous forest (AWMPFD_41), the percentage of shrub
land (PLAND_52) and the annual average aridity in 2010 (Aridity),
accounted for influential confounding factors. All six independent
variables were included in each of the regression models. Several multivariate regression models were estimated to evaluate the relationships
at both seasonal and annual timeframes. Specifically, there were six
dependent variables of interest: the four 2010 seasonal UHI intensity
averages, the 2010 annual average UHI intensity and the 2006 to 2010
annual average UHI intensity.
Despite the advantages of multivariate techniques, namely the ability to analyze the partial effects of multiple variables while controlling
for potential confounding factors, Ordinary Least Squares (OLS) regression models are built on a set of assumptions (Hamilton, 1992).
Although in actual research these assumptions are seldom, if ever, literally met (Hamilton, 1992), a series of diagnostics can be used to discern
the severity of the violations, help evaluate the overall robustness of the
results and determine if any corrective measures should be pursued.
Firstly, OLS regression fits the best linear relationship between the
dependent and independent variables, which is inappropriate if the
functional form is fundamentally non-linear. To determine if the relationships between urban morphology and UHI intensities were linear,
the functional form of the bivariate scatter plots and the addedvariable plots created during the regression analysis were examined.
For the estimated parameters to be unbiased, all relevant independent variables must be included in the model. Determining if all pertinent variables are incorporated is difficult, due to the infinite number
of potential independent variables, and typically relies heavily on theoretical justification. Generally, a certain degree of specification bias is
unavoidable in regression analysis since all relevant independent
variables often cannot be included due to data limitations. To soundly
conduct inferential tests on regression model coefficients, the error
terms must be: homoskedastic (have constant variance across all values
of X), uncorrelated with each other (no autocorrelation) and normally
distributed. The error terms of all the models were checked for
heteroskedasticity (unequal variance across the values of X) using
White's Test (White, 1980), and normalcy was evaluated using histograms. Finally, regression models are sensitive to overly influential observations and multicollinearity (correlation between the independent
variables). Overly influential observations were tested for using Cook's
D (Cook & Weisberg, 1982) and DFBETAS (Belsley, Kuh, & Welsch,
1980) while the presence of multicollinearity was determined by calculating the correlation coefficients of the independent variables as well as
their respective variable inflation factors (VIFs).
3. Results and discussion
3.1. Suitability of PRISM for UHI intensity estimation
On average, roughly 18 stations were considered for the computation of the PRISM grids within each city, with a minimum of approximately 6 and a maximum upwards of 50. The statistically insignificant
(p = 0.66) correlation between the number of surface observations
within each city that were potentially considered by PRISM and the
UHI intensity estimates indicates that station availability did not bias
the UHI intensity calculations. The ratio calculated between the percentage of urban stations and the percentage of urban land cover had a mean
near one (1.14) and a low standard deviation (0.24), implying that the
surface observations potentially used in the PRISM interpolation
process provided a relatively representative sample of the urban land
cover within each city. Importantly, the ratio was insignificantly (p =
0.33) correlated with the UHI intensities, which suggests any slight
over or under sampling was not substantial enough to systematically
bias the UHI estimates.

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The insignificant correlations combined with a qualitative visual
inspection of the station distributions within each city collectively indicated that PRISM provided an adequately representative depiction of
urban temperatures for the cities included in this study. An example
of how PRISM successfully resolved the UHI effect of Louisville,
Kentucky is provided in Fig. 3. PRISM (Torres-Valcárcel, Harbor,
Torres-Valcárcel, & González-Avilés, 2014) and DAYMET (Gallo & Xian,
2014), a similar gridded climate data product, have been used previously to evaluate the UHI effect since they, “potentially provide more

detailed information related to the factors that are relevant to urban
heat island analyses” (Gallo & Xian, 2014, p. 9).
3.2. UHI intensities in 2010
In 2010, the minimum temperatures of the fifty cities were on average 0.37 °C warmer than their surrounding natural environments
(Fig. 4). Since these are annual average UHI effects, which incorporate
both those nights that are optimally and poorly suited for UHI

Fig. 3. A) PRISM annual average minimum temperature grid revealing the UHI of Louisville, Kentucky overlaid with the surface observation stations potentially used during the PRISM
interpolation process. B) Corresponding NLCD 2006 data for Louisville, Kentucky.

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187

Fig. 4. Map of the annual average UHI intensity (°C) in 2010 for the 50 most populous MSAs in the United States.

formation, the magnitudes were never expected to approach the maximum thermal modification under ideal conditions of approximately
12 °C (Oke, 1987). Averaging the minimum temperatures throughout
the entire UA/UC also contributed to the reduced magnitude relative
to the potential maximum UHI effect, which is typically obtained by
comparing the temperature within the urban core of a city to its rural
surroundings. Although minimum temperatures were analyzed in this
study, the annual average UHI intensities were more comparable to
the 1–3 °C amplification of the annual mean air temperature identified
by Oke (1997) for large mid-latitude cities.
Salt Lake City exhibited the most intense UHI effect (1.49 °C), which
is partially due to the high prevalence of temperature inversions in that
region (Pope et al., 2006) since inversions typically produce calm, clear
and stable conditions ideal for UHI formation (Hu et al., 2013). The
January peak of the Salt Lake City UHI (Fig. 5) supports this theory
since inversions most commonly occur during the colder months
(Pope et al., 2006). Salt Lake City has also previously been identified as
the most intense UHI amongst numerous American cities (Gallo et al.,
1993), although this prior estimate was derived from a weekly instead
of annual average and contained less stringent controls for elevation
biases. The second most intense UHI of 1.34 °C occurred in Miami and
is potentially attributable to the tall skyscrapers along the coastline
creating a wall effect (Wong, Nichol, To, & Wang, 2010), which would
impede sea breezes from ventilating the city. Ecological context is also
important to consider (Imhoff et al., 2010), as the wetlands surrounding
Miami provided a relatively cool rural temperature that contributed to
the UHI intensity. The Louisville UHI (1.12 °C) finalized the top three
likely because it was one of very few major American cities without a
comprehensive tree ordinance in 2010 (Partnership for a Green City,
2009). The absence of seasonality in the Louisville UHI also suggests
that a lack of tree canopy coverage is contributing to the UHI effect
since the natural life cycle of vegetation typically enhances seasonal
UHI variability (Fig. 5).

In contrast to the intense UHIs of Salt Lake City, Miami and Louisville,
the negative values in Fig. 4 indicate that a city was actually cooler than
its natural surroundings. Riverside and Las Vegas exhibited the strongest urban cool islands (UCIs) of − 1.37 and − 0.76 °C, respectively.
This “oasis effect” is largely due to the increased presence of moisture

Fig. 5. Monthly UHI Intensities for each MSA in 2010. Gray lines depict values near the
consenus while more extreme UHIs and UCIs are highlighted in red and blue, respectively.

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and heightened potential for evaporative cooling within the cities
relative to the surrounding desert landscapes (Brazel, Selover, Vose, &
Heisler, 2000). The Riverside UCI was a particularly extreme case that
was partially influenced by the seasonality of aridity (Fig. 5), as the summertime UCI peak occurred during a phase of extremely arid conditions
according to the De Martonne index.
Although the lack of comparability between UHI studies that utilize
different methodologies prevented a more extensive validation of the
UHI intensities, the reasonable magnitudes and the agreement between
the reported estimates and mechanisms outlined in the existing literature suggest that the PRISM methodology is suitable for UHI analysis.

Additionally, using a fundamentally areal-based technique to estimate
the canopy UHI intensity provides a useful alternative to the traditional
urban–rural site comparison approach because it holds the potential to
better capture the heterogeneity of temperature within the entire city
and its surroundings (Jin, 2012).
3.3. Previously hypothesized factors influencing UHI intensity
While it is somewhat challenging to draw direct comparisons across
UHI studies that employ different methodologies, it is still useful to
consider the factors previously hypothesized to influence the UHI effect

Fig. 6. Relationships between 2010 annual average UHI intensities and previously hypothesized influential factors.

N. Debbage, J.M. Shepherd / Computers, Environment and Urban Systems 54 (2015) 181–194

prior to exploring the relationships between UHI intensity and city configuration (Fig. 6). Larger cities in terms of area are thought to produce
more intense canopy UHIs (Oke, 1982), although studies focusing on
the surface UHI have provided the most empirical evidence for this
relationship (Imhoff et al., 2010; Zhou, Rybski, & Kropp, 2013). The
annual average canopy UHI intensities of the 50 MSAs were not significantly correlated with city area (p = 0.58). This result lends some
support to the hypothesis that city area has a minimal influence on
UHI intensity and that other factors, which are usually strongly correlated with increases in city area, are actually responsible for this ostensible
relationship (Atkinson, 2003). The potential cooling influence of water
bodies was also not observed (Park, 1986) since annual average UHI
intensity and water area within a city exhibited an insignificant correlation (p = 0.20).
Despite the relationship being well documented (Oke, 1973; Park,
1986), there was an insignificant (p = 0.27) correlation between UHI
intensity and city population. Logarithmic transformations of the population variable were performed but they did not substantially improve
the correlations. It appears that the relationship between population
size and UHI intensity deteriorates when analyzing exclusively very
large cities, since the sample included only the fifty most populous
MSAs. The relationship was likely further weakened because the annual
average included days where the conditions for UHI formation were not

189

ideal, unlike the approximate maximum UHI considered by Oke (1973).
UHI intensity and population density were also not significantly correlated (p = 0.30), which contrasts with previous studies that found
population density, rather than total population, to be influential in
governing the magnitude of the UHI effect (Steeneveld, Koopmans,
Heusinkveld, van Hove, & Holtslag, 2011; Elsayed, 2012; Wolters &
Brandsma, 2012). Climatological factors, such as wind speed and aridity,
are also known to influence UHI intensities (Oke, 1982), but insignificant relationships were exhibited for the annual averages, with pvalues of 0.97 and 0.79, respectively. However, when the monthly UHI
intensities in 2010 were compared to the corresponding monthly
wind speed and aridity values for each city individually, several significant correlations were discovered.
3.4. City configuration and UHI intensity — bivariate relationships
Of the spatial metrics calculated for the four urban land use classes,
the percentage of like adjacencies (PLADJ) had the strongest correlations with UHI intensity. The amount of urban land cover (PLAND)
across all four intensity levels was not as strongly correlated with
the UHI effect, which indicates that the spatial configuration of urban
development, not merely its abundance, is of importance. The PLADJ
for developed open space (PLADJ_21), low-intensity development

Fig. 7. Correlations between annual average UHI intensity in 2010 and the percentage of like adjacencies (PLADJ) for developed open space (21), low-intensity development (22), mediumintensity development (23) and high-intensity development (24).

190

N. Debbage, J.M. Shepherd / Computers, Environment and Urban Systems 54 (2015) 181–194

(PLADJ_22) and high-intensity development (PLADJ_24) all had significant (p b 0.05) positive correlations with UHI intensity (Fig. 7). Therefore, increasing the spatial contiguity of urban development across a
wide spectrum of intensity levels appears to enhance the UHI effect
amongst large US cities. One caveat was the contiguity of mediumintensity development (PLADJ_23), which did not have a positive
correlation with UHI intensity. The correlation coefficient was negative,
albeit insignificant (p = 0.20), in part because the arid cities of the
Southwest, particularly Riverside and Las Vegas, were characterized by
strong UCIs and high PLADJ_23 values. When Riverside and Las Vegas
were omitted, the correlation coefficient was positive but still not
significantly different from zero (p = 0.84), which makes it challenging
to draw any robust conclusions.
Finding that UHIs are generally magnified by more contiguous urban
development, across a variety of urban intensity levels, potentially
elucidates the false dichotomy implied by previous research that either
sprawling (Stone & Rodgers, 2001; Stone, 2012) or high-density (Coutts
et al., 2007; Martilli, 2014) city configurations amplify UHI intensities.
Instead, our results suggest that sprawling and high-density city configurations both have the propensity to increase UHI intensities if the
urban development is highly contiguous.
The correlations between the spatial contiguity of urban development and UHI intensity varied throughout the year due to the seasonality of the UHI effect (Table 1). The relationships exhibited clear seasonal
trends, as the PLADJ for high-intensity urban development (PLADJ_24)
was most strongly correlated with UHI intensity during the summer
months of June, July and August. The spatial contiguity of developed
open space (PLADJ_21) and low-intensity development (PLADJ_22),
in contrast, displayed stronger relationships with UHI intensity during
the late fall and winter. Finally, the contiguity of medium-intensity
urban development (PLADJ_23) was again an exception since it was
insignificantly (p N 0.05) correlated with UHI intensity throughout
the year.
The bottom portion of Table 1 compared the relationships between
urban spatial contiguity and the annual average UHI intensity in 2010
with the correlations estimated for the longer-term 2006 to 2010
annual average UHI intensity. Relative to the 2010 correlation coefficients, the contiguity of high-intensity urban development (PLADJ_24)
had a marginally stronger relationship with UHI intensity when analyzing the longer-term annual average whereas the correlations for the
contiguity of low-intensity development (PLADJ_22) and developed
open space (PLADJ_21) were marginally weaker. However, the overall
differences between the correlation coefficients for the 2010 annual
average and the longer-term average were minimal, suggesting that

Table 1
Correlation coefficients between the average UHI intensity for various time periods and
the PLADJ metrics for each urban intensity level.–
Time period

PLADJ_21

PLADJ_22

PLADJ_23

January average
February average
March average
April average
May average
June average
July average
August average
September average
October average
November average
December average

0.34⁎
0.35⁎
0.22
0.28–
0.24–
0.23
0.22
0.32⁎
0.29⁎
0.40⁎⁎
0.42⁎⁎
0.46⁎⁎⁎

0.43⁎⁎
0.40⁎⁎
0.23
0.22
0.11
0.09
0.17
0.22
0.23
0.45⁎⁎
0.44⁎⁎
0.43⁎⁎

−0.23
−0.13
0.03
−0.13
−0.07
−0.16
−0.19
−0.19
−0.07
−0.23
−0.23
−0.24–

2010 annual average
2006–2010 annual average

0.36⁎⁎
0.36⁎

0.33⁎
0.32⁎

−0.18
−0.15

–
Sig. level p b 0.10.
⁎ Sig. level p b 0.05.
⁎⁎ Sig. level p b 0.01.
⁎⁎⁎ Sig. level p ~ 0.000.

PLADJ_24
0.06
0.22
0.21
0.20
0.20
0.33⁎
0.42⁎⁎
0.43⁎⁎
0.32⁎
0.25−
0.12
−0.02
0.28⁎
0.30⁎

the relationships between urban spatial contiguity and UHI intensity
observed in 2010 were fairly typical and consistent with recent history.
3.5. City configuration and UHI intensity — multivariate models
OLS regression models were used to further disentangle the
influences of sprawling and high-density urban development on UHI
intensities. The original no-omission regression model, which included
all the cities, violated the diagnostic tests for Cook's D and DFBETAS,
indicating that the sample included extreme and overly influential
values (Table S1). The no-omission model also suffered from
heteroskedasticity as it failed to meet the criteria of White's Test,
which can partially be attributed to the difficulty of predicting the
extreme values. In order to better meet the assumptions of multivariate
regression modeling, the overly influential cities were omitted from the
remaining models. Firstly, Miami and Tampa were omitted because
they did not contain any deciduous forest, which meant their respective
values for AWMPFD_41 were assigned to zero and therefore fairly
extreme. Secondly, Las Vegas, Phoenix and Riverside were omitted
because the lack of other arid cities within the sample made them
overly influential, particularly during the summer.
Excluding the five cities mentioned above from the remaining
regression models provided much more robust estimates, as indicated
by the model diagnostics. Overly influential observations were not
present, as Cook's D never exceeded 0.32 (Cook's D values greater
than 1 are considered to be overly influential). Multicollinearity was
also minimal since the VIFs were less than 1.6 (VIFs greater than 4 are
typically indicative of problematic levels of multicollinearity). Finally,
heteroskedasticity was negligible as the p-values for White's Test
were never below 0.07 (p-values less 0.05 would result in a rejection
of the null hypothesis of homoskedasticity). A full output table is only
provided for the model estimated with the 2010 annual average UHI
intensity as the dependent variable, but complete details for the noomission (Table S1), long-term average (Table S2) and seasonal
(Tables S3–S6) models are all provided in the supplementary
information.
Overall, the model performed well when analyzing the 2010 annual
average, as it explained almost half of the variability in UHI intensity
(Table 2). There was very little reduction in the adjusted R-Squared
value, which suggests that the model was not overly complex. The
partial slope coefficients indicated that the spatial contiguity of highintensity urban development (PLADJ_24) had a statistically significant
(p b 0.05) relationship with UHI intensity. Specifically, a ten percentage
point increase in the spatial contiguity of high-intensity urban development, the equivalent of shifting roughly from Orlando (PLADJ_24 =
69.8%) to Seattle (PLADJ_24 = 79.3%), was predicted to enhance a city's
annual average UHI intensity by 0.4 °C. This is quite a substantial UHI
amplification, especially considering that the annual average UHI effects
had a fairly modest mean value of 0.37 °C. The partial slope coefficient
for the spatial contiguity of low-intensity urban development
(PLADJ_22) was also significant, as a ten percentage point increase
was predicted to enhance a city's annual average UHI intensity by
0.3 °C. Therefore, as suggested by the bivariate analysis, both low and
high-density urban land uses appear to amplify the UHI effect if they
are highly contiguous.
The remaining variables included in the model accounted for the
influences of non-urban land covers and aridity on the annual average
UHI intensity. The partial slope coefficient for the proportion of barren
land (PLAND_31) was significant and positive, as the overall dearth of
vegetation present within the barren class was likely partially responsible for increased UHI intensities. However, the heterogeneity of the
LULCs included in the NLCD barren category complicates this interpretation slightly. Deciduous forest shape complexity (AWMPFD_41) also
had a significant influence on UHI intensity, as increasingly complex
forest shapes were predicted to enhance the UHI effect. Since increased
deciduous forest shape complexity is likely due to the fragmentation

N. Debbage, J.M. Shepherd / Computers, Environment and Urban Systems 54 (2015) 181–194
Table 2
2010 annual average regression model. Annual average UHI intensity in 2010 is the dependent variable. The anomalous cities of Miami, Tampa, Phoenix, Las Vegas and Riverside
were omitted (N = 45).
Independent variable

Coefficient

Std. coefficient

p-Value

Sig. level

Constant
PLADJ_22
PLADJ_24
PLAND_31
AWMPFD_41
PLAND_52
Aridity

−9.857
0.028
0.039
0.380
5.161
−0.028
−0.020

0.33
0.30
0.28
0.42
−0.16
−0.49

0.00
0.02
0.03
0.03
0.00
0.28
0.00

***
*
*
*
**
**

0.00

***

R-Squared
Adjusted R-Squared
F-statistic

0.46
0.38
5.46

Sig. levels: – = p b 0.10; * = p b 0.05; ** = p b 0.01; *** = p ~ 0.000.

caused by urban expansion, it is logical that more complexly shaped forests were indicative of more intense UHIs. Unlike barren land and forest
shape complexity, the presence of vegetative shrub land (PLAND_52)
actually had a mitigating effect on UHI intensities, albeit insignificant
(p N 0.10). Finally, the model predicted that cities located in relatively
more arid environments would have stronger UHIs, but this was
perhaps due to the omission of the overly influential arid cities.
To summarize the seasonality of the relationships, the regression
coefficients for the contiguity of low-intensity (PLADJ_22) and highintensity urban development (PLADJ_24) in the models estimated
with the seasonal average UHI intensities as dependent variables were
graphed by vertical bars in the left panel of Fig. 8. During the winter,
the overall predictive power of the model was comparable to the results
for the annual average as its R-Squared value was 0.47 (Table S3). The
spatial contiguity of high-intensity urban development (PLADJ_24)
was less influential in governing UHI intensities during the winter.
However, the partial slope coefficient for the spatial contiguity of
low-intensity urban development (PLADJ_22) was highly significant
(p b 0.01), as a ten percentage point increase was predicted to enhance the winter UHI effect by almost 0.4 °C. The model performed

Fig. 8. The vertical bars represent the regression coefficients for the spatial contiguity of
low (PLADJ_22) and high-intensity (PLADJ_24) urban development. The left panel
displays the coefficients from the seasonal models (Tables S3–S6) while the right panel
displays the coefficients for the 2010 annual average model (Table 2) and the longerterm 2006–2010 annual average model (Table S2). Sig. levels: – = p b 0.10; * =
p b 0.05; ** = p b 0.01; *** = p ~ 0.000.

191

poorest during the spring since it explained roughly one third of
the variability in the average spring UHI intensity (Table S4). The spatial
contiguity of low-intensity urban development did not significantly
(p = 0.39) influence the spring UHI effect while the spatial contiguity
of high-intensity urban development (PLADJ_24) had only a marginally
significant (p = 0.09) partial effect. However, the magnitude of this
partial slope coefficient was still relevant, as a ten percentage point increase in the contiguity of high-intensity development was predicted
to enhance the spring UHI effect by roughly 0.3 °C. With regard to the
summer months, the model explained just over 45% of the variability
in the average summer UHI intensity (Table S5). The spatial contiguity
of high-intensity urban development (PLADJ_24) was significant
(p b 0.05) during the summer whereas the spatial contiguity of lowintensity urban development (PLADJ_22) was of only marginal significance (p = 0.10). Finally, the partial slope coefficients for the spatial
contiguity of low and high-intensity urban development were both
significant (p b 0.05) during the fall, as the model explained almost
half of the variability in the average fall UHI intensity (Table S6). A ten
percentage point increase in the spatial contiguity of either low or
high-intensity urban development was predicted to enhance the fall
UHI effect by slightly more than 0.4 °C.
The right panel of Fig. 8 compared the regression coefficients for the
spatial contiguity of high (PLADJ_24) and low-intensity (PLADJ_22)
urban development when the longer-term annual average UHI intensity
was the dependent variable with the results from 2010. This helped
ensure that the relationships between city contiguity and the UHI effect
observed in 2010 were not anomalous. When analyzing the longer-term
annual average, the model explained roughly half of the variability in
UHI intensity (Table S2). The spatial contiguity of high-intensity urban
development (PLADJ_24) had a significant (p b 0.05) influence on
both the 2006 to 2010 and 2010 average UHI effects but exhibited a
slightly larger magnitude when analyzing the longer-term average
(0.043 versus 0.039). The partial slope coefficient for the spatial contiguity of low-intensity urban development (PLADJ_21), in contrast,
was only marginally significant (p = 0. 05) and exhibited a slightly
reduced magnitude (0.024 versus 0.028) when the longer-term average
was the dependent variable. However, the general similarities suggest
that the relationships in 2010 were fairly consistent with recent history.
Although the nature of the data, particularly the commonality of
extreme outliers, created modeling difficulties and resulted in the omission of five cities from the majority of the analysis, the regression
models collectively provided a compelling diagnosis of the UHI effect.
The results suggest that more contiguous urban development across a
spectrum of intensity levels can amplify the annual average and seasonal average UHI effects (Fig. 8). This partially reconciles the false dichotomy implied by previous research that either sprawling (Stone &
Rodgers, 2001; Stone, 2012) or high-density (Coutts et al., 2007;
Martilli, 2014) city configurations enhance the UHI effect. Instead, at
least amongst large American cities, both sprawling and high-density
configurations appear to magnify UHI intensities if the urban development is highly contiguous. Increasing the spatial contiguity of low or
high-intensity urban development ten percentage points was predicted
to enhance the UHI effect by a minimum of 0.1 °C in the spring and a
maximum of almost 0.5 °C in the fall (Fig. 8). Additionally, during the
summer when the overly influential cities were not omitted from the
model, the UHI amplification resulting from a ten percentage point increase in the spatial contiguity of high-intensity urban development
reached almost 1 °C. Therefore, the results presented in Table 2 and
Tables S2–S6 provide inherently conservative estimates of how urban
spatial contiguity influences UHI intensities.
4. Urban planning implications and conclusions
By developing a methodology to estimate UHI intensities from
PRISM climate data and utilizing spatial metrics to quantify urban
morphology, this study has found that the spatial contiguity of urban

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N. Debbage, J.M. Shepherd / Computers, Environment and Urban Systems 54 (2015) 181–194

development makes a statistically significant contribution to the UHI
effect. The shape complexity, polycentrism and relative abundance of
urban development were all less influential, which emphasizes the
potential for contiguous, uninterrupted urban footprints to enhance
urban temperatures. An ulterior motive of this research was to examine
the urban planning implications of this central finding and potentially
clarify if increasing urban densities is a viable UHI mitigation strategy.
Based on the correlations and multiple regression models, more contiguous urban development across a range of intensity levels magnifies the
UHI effect. Therefore, simply increasing urban densities, which would
presumably also increase the contiguity of high-intensity urban
development (PLADJ_24), is not likely a viable UHI mitigation strategy.
Additionally, policies encouraging infill development also appear potentially detrimental from an UHI perspective since they would increase
city contiguity further.
Advocating for urban densification as a UHI mitigation plan is particularly troubling given the seasonality exhibited by the correlations
(Table 1) and regression coefficients (Fig. 8). Increasing the contiguity
of high-intensity urban development was predicted to enhance UHI
intensities most significantly during the summer and fall months,
which is precisely when cities are most vulnerable to heat waves. At
the opposite end of the urban development intensity spectrum, increasing the contiguity of low-intensity urban development and developed
open space also magnified the UHI effect. However, since these relationships were strongest during the winter months, highly contiguous lowintensity urban development and developed open space could
potentially be beneficial by reducing the amount of energy used to
heat buildings.
Interpreting the statistical models very literally, any city configuration that reduces the contiguity of urban development would potentially mitigate the UHI effect. However, in reality certain LULC types would
more successfully accomplish this goal. The inclusion of urban green
spaces and parks would decrease the contiguity of urban development
and simultaneously provide an additional cooling influence via evapotranspiration. If the total green space area were held constant, interspersing several smaller green spaces throughout the urban fabric
would provide a more substantial reduction in urban contiguity than a
singular park of greater size. Therefore, networks of smaller urban
green spaces seem to hold considerable potential for UHI mitigation.
While increasing urban densities alone appears somewhat problematic,
UHI intensities may be more successfully alleviated if densification was
accompanied by networks of smaller urban parks that would substantially reduce the contiguity of high-intensity urban development. Additionally, white and green roof mitigation techniques could be
incorporated in such a scenario since they become more economically
feasible at higher density levels (Stone, 2012).
Overall, planning to reduce UHI intensities is very complex and the
policies will likely need to be tailored to individual cities. This is partic-

ularly true given that the seasonality of the UHI effect, an important
component when evaluating the benefits of a warmer winter versus
the detriments of a warmer summer, was very localized to each city
(Fig. 5). Additionally, policies have to comprehensively address the entire urban system and not simply focus on the UHI effect in isolation.
While high urban densities have traditionally been considered detrimental from an urban climatological perspective (Oke, 1982; Coutts
et al., 2001), they can provide benefits, such as improving air quality, increasing the feasibility for public transit, decreasing energy consumption and promoting more active lifestyles, when compared to more
sprawling morphologies (Ewing, Pendall, & Chen, 2002). Therefore,
the success of any UHI mitigation strategy hinges largely on its ability
to reduce the temperatures observed within cities without disrupting
the complex array of feedbacks associated with the greater urban
metabolism (Kennedy, Cuddihy, & Engel-Yan, 2007). When the urban
system is considered in its entirety, discontiguous high-intensity
urban development may emerge as a useful compromise since such a
configuration would likely preserve the broader benefits of higher
densities while simultaneously moderating UHI intensity. The historic
downtown district of Savannah, Georgia provides a more concrete
example of the rather abstract discontiguous high-intensity city configuration concept, as its network of over twenty heavily vegetated
squares reduces the contiguity of the high-intensity urban development
substantially.
Admittedly, future work will be needed to help further elucidate
the influence of city contiguity on the UHI effect and more fully evaluate
the potential of discontiguous high-intensity urban development as a
viable UHI mitigation strategy. Since this study was based on statistical
modeling, one promising avenue for future research is the usage of
physically-based models to analyze how city contiguity impacts specific
components of the urban energy balance. Physically-based modeling
approaches, which more explicitly account for the three dimensionality
of the urban environment, may also be able to further clarify the caveat
discovered for medium-intensity development.
The results also must be generalized with caution since the study focuses solely on large American cities. Future research will analyze if and
how the relationships between city configuration and UHI intensity
vary for cities of different sizes and for those located in other portions
of the world. Despite these qualifications, the current findings demonstrate that the spatial contiguity of urban development is an important
and previously unidentified contributing factor to the UHI effect,
which deserves consideration when devising strategies for UHI
mitigation.
Acknowledgments
We would like to thank the three anonymous reviewers and
J. A. Knox for providing constructive feedback on the manuscript.

Appendix A
Table A.1
Equations and descriptions of the spatial metrics used to quantify the urban morphologies of the MSAs. Adapted from McGarigal et al. (2012).
Spatial metric
Area-weighted mean patch
fractal dimension
(AWMPFD)
Area-weighted mean shape
index (AWMSI)
Clumpiness index (CLUMPY)

Equation

Description



n

AWMPFD ¼ ∑ j¼1

n




AWMSI ¼ ∑ j¼1

2 lnð0:25pij Þ
lnaij

0:25pij
pffiffiffiffi
aij


Given Gi ¼

CLUMPY ¼

"





aij
n

∑ j¼1 aij

aij
n
∑ j¼1 aij




gii
m

∑k¼1 gik
Gi −Pi
1−Pi
Gi −Pi
1−Pi
Pi −Gi
−Pi

for Gi ≥Pi
for Gi bPi &Pi ≥0:5
for Gi bPi &Pi b0:5

#



Where pij is the perimeter of patch ij and aij is the area of patch
ij (i = number of patch types, j = number of patches)

Where pij is the perimeter of patch ij and aij is the area of patch
ij (i = number of patch types, j = number of patches)
Where gii is the number of like adjacencies between pixels of
patch type i based on the double count method, gik is the
number of adjacencies between pixels of patch types i and
k based on the double-count method, and Pi is the proportion
of the landscape occupied by patch type i

N. Debbage, J.M. Shepherd / Computers, Environment and Urban Systems 54 (2015) 181–194

193

Table A.1 (continued)
Spatial metric

Equation

"

Contagion Index (CONTAG)




CONTAG ¼ 1 þ

Edge density (ED)

 

gik

m

∑k¼1 gik



lnðPi Þ

2 lnðmÞ

∑k¼1 eik
A

 10; 000

LPI ¼
ni
A

 100

 10; 000  100

Patch density (PD)

PD ¼

Percentage of like adjacencies
(PLADJ)

PLADJ ¼




gii
m
∑k¼1 gik

 100

n

∑ aij
PLAND ¼

j¼1
A

gik

m

∑k¼1 gik

 100

Where Pi is the proportion of the landscape occupied by patch
type i, gik is the number of adjacencies between pixels of patch
types i and k based on the double-count method, and m is the
number of patch types present in the landscape
Where eik is the total edge length (m) of class i in the
landscape and A is the total landscape area; the result is
multiplied by 10,000 to convert to hectares
Where max (aij) is the area (m2) of the largest patch of the
corresponding class and A is the total landscape area (m2);
the result is multiplied by 100 to convert to a percentage

n

maxðaij Þ
j¼1
A

Description

 #



m

ED ¼

Largest patch index (LPI)

Percentage of landscape
(PLAND)



m
m
∑i¼1 ∑k¼1 ðPi Þ

 100

Where ni is the number of patches in the landscape of patch
type i and A is the total landscape area (m2)
Where gii is the number of like adjacencies between pixels of
patch type i and gik is the number of adjacencies between
pixels of patch types i and k
Where aij is the area (m2) of patch ij and A is the total
landscape area (m2); the result is multiplied by 100 to
convert to a percentage

Appendix B. Supplementary data
Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.compenvurbsys.2015.08.002.

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