Int J Biometeorol (2010) 54:13–22
DOI 10.1007/s00484-009-0247-y

Modeling effects of urban heat island mitigation strategies
on heat-related morbidity: a case study for Phoenix,
Arizona, USA
Humberto R. Silva & Patrick E. Phelan & Jay S. Golden

Received: 4 January 2009 / Accepted: 1 July 2009 / Published online: 26 July 2009
# ISB 2009

Abstract A zero-dimensional energy balance model was
previously developed to serve as a user-friendly mitigation
tool for practitioners seeking to study the urban heat island
(UHI) effect. Accordingly, this established model is applied
here to show the relative effects of four common mitigation
strategies: increasing the overall (1) emissivity, (2) percentage
of vegetated area, (3) thermal conductivity, and (4) albedo of
the urban environment in a series of percentage increases by 5,
10, 15, and 20% from baseline values. In addition to modeling
mitigation strategies, we present how the model can be utilized to evaluate human health vulnerability from excessive
heat-related events, based on heat-related emergency service
data from 2002 to 2006. The 24-h average heat index is shown
to have the greatest correlation to heat-related emergency calls
in the Phoenix (Arizona, USA) metropolitan region. The four
modeled UHI mitigation strategies, taken in combination,
would lead to a 48% reduction in annual heat-related
emergency service calls, where increasing the albedo is the
single most effective UHI mitigation strategy.
Keywords Health vulnerability . Heat wave .
Urban heat island . Morbidity . Emergency medical dispatch .
Numerical modeling
H. R. Silva : P. E. Phelan
Department of Mechanical and Aerospace Engineering,
Arizona State University,
Tempe, AZ, USA
H. R. Silva : P. E. Phelan : J. S. Golden
National Center of Excellence on SMART Innovations,
Arizona State University,
Tempe, AZ, USA
J. S. Golden (*)
School of Sustainability, Arizona State University,
P.O. Box 875502, 800 South Cady Mall Room # 356,
Tempe, AZ 85287-5502, USA
e-mail: Jay.Golden@asu.edu

Introduction
There is indeed a dearth of simple, easy to use, inexpensive
and validated urban energy balance models. The relatively
complex urban energy models in the literature include the
Weather Research and Forecasting Model (WRF; Michalakes
et al. 1998), the fifth-generation Pennsylvania State University—National Center for Atmospheric Research Mesoscale
Model (MM5; Grossman-Clarke et al. 2005), and Envi-Met
(2008). All of these models require extensive training and/or
knowledge of atmospheric sciences, physics and computational sciences. Although these models have been shown to
be validated for many cases and have researchers continuously pushing development to more advanced capabilities,
they exist largely for usage by highly trained scientific
researchers. In an effort to create a more user-friendly model
for governmental agency officials, previous work by Silva
et al. (2008) successfully showed that one can create a
computationally inexpensive and simple-to-use model that is
validated versus a more robust model such as MM5. The
following analysis will apply this relatively simple model to
investigate how various urban heat island (UHI) mitigation
strategies reduce the number of heat-related emergency
dispatch calls for the Phoenix (Arizona, USA) metropolitan
area.

Mitigation strategies
Model recap
Beginning in the fashion of Golden et al. (2005), we can
represent the energy flows for an urban volume by six
major components. Keeping intact the surface energy
balance while simultaneously simplifying a very complex
problem, one can express the following governing equation

14

Int J Biometeorol (2010) 54:13–22

Table 1 Modeled baseline
urban thermophysical property
values for the Phoenix
metropolitan area (Bhardwaj
et al. 2006; Grossman-Clarke
et al. 2005; Taha et al. 2000;
Pomerantz et al. 1997;
Rosenfeld et al. 1995)

Classification

Baseline area share

Albedo

Emissivity

Thermal Conductivity [W m-1 K-1]

Roof
Road
Sidewalk
Parking area
Soil
Vegetation
Water
Baseline value

0.184
0.140
0.030
0.143
0.189
0.304
0.011

0.200
0.150
0.300
0.150
0.300
0.200
0.080
0.206

0.850
0.890
0.850
0.890
0.945
0.945
0.945
0.909

0.062
1.400
1.000
1.000
1.120
0.670
0.600
0.802

for the lumped urban temperature (Bhardwaj et al. 2006;
Silva et al. 2008):
mc

dT
¼ ð1 
 aÞqsol A þ qanthro A 
 qcond A 
 qevap A
dt

 qconv A 
 qrad A

ð1Þ

where m is mass, c specific heat, t time, α albedo, A area,
qsol the incident time-dependent solar heat flux, qanthro the
anthropogenic heat flux, qevap the evapotranspiration heat
flux, qcond the conductive heat loss to the deep ground,
qconv the outgoing convective heat flux, qrad the outgoing
emitted radiative heat flux, and T the characteristic
temperature. Dividing through by A and transforming the
formula to a finite difference scheme ready for numerical
implementation yields:
Δt
T nþ1 ¼ T n þ
rcd x
h
i
ð1 
 aÞqnsol þ qnanthro 
 qncond 
 qnevap 
 qnconv 
 qnrad

ð2Þ
where ρ is density, and δx the distance between the surface
and the measured 50.8-cm (20-inch) ground temperature, ∆t
the time step, the superscript n represents the present time
step, and the superscript n+1 represents the future time step.
Utilizing the same methodologies as in Silva et al.
(2008), the characteristic urban temperature T can finally be
expressed as:
h


i
kgrd
n
n
T nþ1 ¼ T n 1 
 rΔt
c dx hconv þ hrad þ dx
h
i
kgrd
n
n
n
n
ð3Þ
þ rΔt
c dx hconv TairðRuralÞ þ hrad Tsky þ dx Tgrd


n
n
þ rΔt
c dx ð1 
 aÞqSol þ qAnthro 
 Et0 rH2 0 hfg
where kgrd is the thermal conductivity of the ground,Tgrd the
ground temperature measured at a depth of 50.8 cm
(20 inches; AZMET 2008), Et0 the measured evapotranspiration (in meters) for vegetated areas, hfg the latent heat of
vaporization for water, rH2 O the density of water, Tair(Rural)
the measured rural dry-bulb air temperature, hconv the

convection heat transfer coefficient, hrad the radiation heat
transfer coefficient, and Tsky the “sky” temperature, i.e., the
effective temperature of the sky with respect to emitted
radiation (ASHRAE 2004). Note that the variables
n
qnanthro ; hnrad ; Tsky
; hnconv have embedded terms. Equation 3
is the model that will be applied to all analysis in this
manuscript. All of the meteorological data needed in Eq. 3
are taken from AZMET (2008), and the anthropogenic heat
data are taken from EIA (2008) via the formulation of Sailor
and Lu (2004). As discussed in the next section, we will
show the formulation of the radiation coefficient term below
since one of its parameters (emissivity ε) will be perturbed in
our mitigation scheme. The hrad term changes with each time
step and is given by (at a particular time step; Cengel 2003):



4
T 4 
 Tsky

hrad ¼ "s 
ð4Þ
T 
 Tsky
where σ is the Stefan-Boltzmann constant.
Perturbed values
There are four values embedded in Eq. 3 that will be explored
for UHI mitigation purposes, and to determine which
mitigation strategies lead to an overall greater percent
decrease in the calculated characteristic 24-h average temperature. The four investigated UHI mitigation strategies
increase the overall: (1) emissivity (ε embedded in the hnrad
term), (2) percentage of vegetated area (the weight of the Et0
Table 2 Corresponding changes in thermophysical property baseline
values when the percentage of vegetated area is increased by 5, 10, 15,
and 20%
Increase in
vegetated area

Emissivity Albedo Thermal
Volumetric
Conductivity
Heat Capacity
[W m-1 K-1]
[106 J m-3 K-1]

5%
10%
15%
20%

2.079
2.054
2.029
2.004

0.909
0.911
0.911
0.912

0.206
0.206
0.207
0.207

0.801
0.800
0.799
0.798

Int J Biometeorol (2010) 54:13–22

15

Table 3 Modeled baseline and increased urban thermophysical
property values for the Phoenix metropolitan area, for exploring the
four urban heat island (UHI) mitigation strategies

BASELINE
5%
10%
15%
20%

Increase
in emissivity

Increase in
fraction of
vegetated
area

Increase in
thermal
conductivity
[W m-1 K-1]

Increase
in albedo

0.909
0.954
0.999
—
—

0.304
0.319
0.334
0.349
0.365

0.802
0.842
0.882
0.922
0.962

0.206
0.216
0.227
0.237
0.247

term), (3) thermal conductivity of the ground (kgrd), and (4)
albedo (α) of the urban environment. The idea is to run the
model with these above four values increased from their
baseline values (Bhardwaj et al. 2006; Grossman-Clarke et
al. 2005; Taha et al. 2000; Pomerantz et al. 1997; Rosenfeld
et al. 1995) at various percentages (see Tables 1, 2, 3). The
values are increased by 5, 10, 15, and 20% (5% increments)
from their baseline values over a physically reasonable range
(up to 20%, 10% for emissivity). For the emissivity ε, note
that ε can only be increased by 10% as its value at this point
is already 0.999. This value of ε=0.999 is the maximum
value of ε applied for all UHI mitigation strategies. In
addition to examining how increases in these individual
parameters lead to reductions in urban characteristic temperature, we also examine how all of these mitigation strategies
change the temperature when implemented in unison.
For simplicity, as the percentage of vegetated area is
increased, we do not consider any corresponding increase
in the relative humidity. Our range of vegetation percentage
modifications yielded a small change in overall relative
humidity given our classification scheme (see Table 1) and
for the range of typical temperature and dew point temperatures in Phoenix. For example, a straightforward psychometric calculation involving the partial pressure of water

vapor and the saturated vapor pressure of the air in our
control volume (Phoenix urban area from the ground to the
2 m height at which air temperature is measured through
AZMET) we can achieve a maximum 5% change in relative
humidity for typical temperatures in Phoenix (AZMET
2008) year round in 2008. Also, we will treat other
alterations brought on by the thermophysical constants on
each other as negligible. However, changing the percent
vegetated area does alter the other model inputs as presented
in Table 2.
The values in Table 2 were calculated by increasing the
vegetated area to the desired value, while uniformly
reducing all the other six area classifications. Specifically,
we adopt a seven area classification scheme approach
(Bhardwaj et al. 2006; shown in Table 1) where one of the
classifications was vegetation. All seven classifications
have a percent share of the entire Phoenix urban area.
First, we increased the vegetation classification percentage
share by the desired amount (5, 10, 15, or 20%) and then
reduced the other six classifications percentage shares’
uniformly so the sum added up to 1. Then, we took this
new percentage share value for each classification and
multiplied it by its respective parameter value (albedo,
emissivity, thermal conductivity, or volumetric heat capacity) and took the weighted average over the entire Phoenix
urban area to yield the new value for each individual
parameter. To better illustrate this process, see the example
for the albedo change for a 20% increase in vegetated area
(Table 4).
Effects on average urban temperature
Figure 1 and Table 5 indicate how each UHI mitigation
strategy leads to decreases in the calculated characteristic
temperature T. It is seen from Fig. 1 that increasing the
overall albedo has the strongest influence on the 24-h average
urban characteristic temperature. This is because solar
radiation drives the energy balance. Increasing the emissivity

Table 4 Corresponding detailed change in the albedo baseline value when the percentage of vegetated area is increased (modified) by 20%
Classification Fraction of baseline
area

Albedo
value

Baseline albedo
contribution

Modified fraction of baseline
area

Modified albedo
contribution

Roof
Road
Sidewalk
Parking area

0.184
0.140
0.030
0.143

0.200
0.150
0.300
0.150

0.037
0.021
0.009
0.021

0.174
0.130
0.020
0.133

0.035
0.020
0.006
0.020

Soil
Vegetation
Water
Total sum

0.189
0.304
0.011
1.000

0.300
0.200
0.080

0.057
0.061
0.001
0.206

0.179
0.365
0.001
1.000

0.054
0.073
0.000
0.207

16

Int J Biometeorol (2010) 54:13–22
CALCULATED PERCENTAGE CHANGE IN
24−HOUR AVERAGE CHARACTERISTIC TEMPERATURE

Fig. 1 Calculated percentage
change in 24-h average characteristic urban temperature for the
listed urban heat island (UHI)
mitigation strategies for the
Phoenix metropolitan area. Each
mitigation strategy (except
emissivity) is increased by 5, 10,
15, and 20%

0

−5
−10
−15
−20
−25
5%
10%
15%
20%

−30
−35

Emissivity

has the smallest effect overall. This makes sense since the
emissivity of the Phoenix urban fabric is already high (0.91),
thus limiting any further increases. Also, increasing the
thermal conductivity has a greater effect than increasing
the percentage of vegetated area. This is due to the fact that
the percentage of vegetated areas (~0.3–0.37) is outweighed
by the rest of the urban environment, so we can conclude that
the thermal conductivity strategy should have a greater effect
than increasing the vegetated area strategy as most of the
urban area is not covered by vegetation.
The combined mitigation strategy effect (All four strategies included; Table 5), where we increase all of the four
respective parameters by the maximum 20% over their
baseline values, can reduce the overall temperature by almost
32% as predicted by the model. This is a theoretical finding
as increasing these values may be difficult to implement due
to financial and time constraints (even though the increases
yield physically reasonable values). It is better to concentrate
merely on albedo, because the share of albedo in the
reduction of 24-h average urban characteristic is highest.
Implementation of these mitigation strategies may be

Vegetated Area % Thermal Cond.

Albedo

Total

achieved by changing the material of urban roads to yield
higher albedo by e.g., increased use of concrete pavements
or whitetopping of existing pavements (Golden and Kaloush
2006). Surface treatments and paints can provide positive
adjustments of material emissivity values. A thermal
conductivity strategy can include the inclusion of metallic
or ceramic particles to the pavement/sidewalk material mix,
thus yielding higher thermal conductance (Mityakin and
Pivinskii 1980). Rooftop mitigation strategies include white
rooftops and/or green rooftops that incorporate membrane
separation of the roof with the topmost layer incorporating
vegetation and soil. A common mitigation strategy is the
deployment of an urban forestation program, which
increases the percentage of vegetated area in the urban
environment by adding more trees, grass, succulents, etc.
(EPA 2001, 2008). Figure 2 recasts the data of Fig. 1 to
highlight the relative contributions of each mitigation
strategy to the reduction in the predicted 24-h average urban
characteristic temperature.

Correlation with heat-related morbidity
Table 5 Percentage decrease in calculated 24-h average characteristic
temperature resulting from the four UHI mitigation strategies
Increase in Increase in
Increase
Increase in All four
emissivity fraction of
in thermal
albedo
strategies
vegetated area conductivity
included
5%

-1.66%

-1.68%

-2.60%

-4.97%

-10.55%

10% -3.25%

-3.55%

-5.11%

-9.48%

-19.32%

15% —

-5.38%

-7.54%

-13.59%

-25.81%

20% —

-7.18%

-9.88%

-17.36%

-31.48%

Correlation analysis and extended validation
We have taken into consideration nine different sets of
meteorological data for correlation to heat-related emergency calls between 2002 and 2006 in the greater
Phoenix AZ region (Golden et al. 2008). They include:
(1) 24-h average heat index (relates temperature and
relative humidity to give a true felt outside temperature),
(2) 24-h average relative humidity, (3) 24-h average temperature, (4) 24-h maximum heat index, (5) 24-h maximum

Int J Biometeorol (2010) 54:13–22

17

Fig. 2 Pie graph describing the
relative contributions of the four
UHI mitigation strategies to the
reduction in 24-h average urban
characteristic temperature

Increase of 5 %

Increase of 10 %

15%

15%

15%

17%

24%

24%
46%

44%

Increase of 15 %

Increase of 20 %

20%
28%

21%

29%

51%
Emissivity



Amn 
 A Bmn 
 B
m n
r ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi


2
2
PP
PP
Amn 
 A
Bmn 
 B
m

0
20

30

40

20

0

50

70

20

0

90

50

15

30

AVG TEMP ( °C )

45

110

20

0

50

MIN TEMP ( °C )

50

80

110

MAX RH ( % )

40

0

80

20

0
20

100

NO. OF CALLS

NO. OF CALLS

20

50

40

MIN RH ( % )

40

0

20

MAX HI ( °C )

40

AVG RH ( % )

0

40

0
20

200

NO. OF CALLS

NO. OF CALLS

NO. OF CALLS

20

30

100

ð5Þ

n

MIN HI ( °C )

40

0
10

m

40

0

50

n

NO. OF CALLS

20

Vegetated Area %

PP

NO. OF CALLS

40

Albedo

We use the classic correlation analysis as presented by
Kreyszig (1999), which can be used for matrices or vectors
of the same size:

AVG HI ( °C )

NO. OF CALLS

Fig. 3 Scatter plots of nine
different meteorological data
sets against the number of
heat-related emergency calls for
the city of Phoenix spanning
2002–2006. AVG 24-h average,
MIN 24-h minimum, MAX 2
4-h maximum, HI heat index,
RH relative humidity, TEMP
Temperature, # OF CALLS
number of heat-related emergency calls

NO. OF CALLS

relative humidity, (6) 24-h maximum temperature, (7)
24-h minimum heat index, (8) 24-h minimum relative
humidity, and (9) 24-h minimum temperature as shown in
Fig. 3. Statistically, as presented by Golden et al. (2008)
these indicate that either 24-h maximum temperature or
24-h average heat index has the strongest correlation to calls
for service during this time frame.

50%
Thermal Cond.

40

20

0

0

20

40

MAX TEMP ( °C )

60

18

Int J Biometeorol (2010) 54:13–22

Table 6 Correlation values between Phoenix heat-related emergency
calls (2002—2006) and meteorological data
Correlation value
24-h
24-h
24-h
24-h
24-h
24-h
24-h
24-h
24-h

average heat index
average temperature
minimum temperature
maximum heat index
maximum temperature
minimum heat index
maximum relative humidity
average relative humidity
minimum relative humidity

0.56
0.51
0.50
0.47
0.46
0.34
-0.17
-0.11
-0.01

where A and B are the two sets of data that are being
compared, where A and B are the means (averages) of their
respective data set.
2

1

6
6T
HI ¼ 6
6 T2
4
T3

These meteorological data sets (except for ones involving the heat index) were all obtained from AZMET (2008)
and were extracted in accordance with the day of the year
that the call occurred. The data sets were taken from the
AZMET measurements at their Phoenix Encanto (urban)
and Queen Creek (rural) stations for this study. Also, these
data sets would have been extracted in accordance with the
time of day the call occurred and would have allowed for
more meteorological data sets to be considered (including
temperature at time of call, heat index at time of call,
relative humidity at time of call, etc.) but the data provided
for the heat-related emergency calls did not provide such
detail. The heat index was calculated with the measured air
temperature and relative humidity data via the following
equation (Stull 1999):

32
16:92
5:38
7:29ð10Þ
3 2:92ð10Þ
5
6
76
76 1:85ð10Þ
1 
1:00ð10Þ
1 
8:15ð10Þ
4 1:97ð10Þ
7
76
76

3
3:45ð10Þ
4
1:02ð10Þ
5
8:43ð10Þ
10
54 9:42ð10Þ

3:86ð10Þ
5
1:43ð10Þ
6 
2:18ð10Þ
8 
4:82ð10Þ
11

Fig. 4 Scatter plot of the actual
24-h average heat index and the
modeled 24-h average heat
index with their associated
occurrences of the number of
heat-related emergency calls
for the city of Phoenix spanning
2002–2006

NUMBER OF HEAT−RELATED EMERGENCY CALLS

where HI is the heat index, T the temperature (in degrees
Fahrenheit), and R the relative humidity (in percentage). To
solve for all the data points, Eq. 6 needs to be repeated for the
entire data set and can be solved symbolically with a linear

35

3
7
7

7
7 1 R R2 R3
7
5

ð6Þ



algebra solver or by matrix multiplication HI ¼ Ti Aij Rj if
implemented numerically.
After all of our calculations were completed for the
entire set of emergency calls, we found that the highest

Real Data
Model Calculation

30

r = 0.99
25
20
15
10
5

20

25

30
35
40
24−HOUR AVERAGE HEAT INDEX (°C)

45

50

Int J Biometeorol (2010) 54:13–22

19

Fig. 5 Exponential fit curve of
the actual 24-h average heat
index and associated occurrences of the number of heat-related
emergency calls for the city of
Phoenix spanning 2002-2006
with a1 =12.20, a2 =-−2.04,
and a3 =0.13, where x is the
24-h average heat index in °C

NUMBER OF HEAT−RELATED EMERGENCY CALLS

60
Real Data [ x ]
Exponential Fit Curve [ f(x) ]
50

f(x) = a exp(a2 + a3 x)

40

1

30

20

10

0

22

correlation to the heat-related emergency calls was that of
the 24-h average heat index, at a value of r=0.56 as shown
in Table 6. Next, we show that the model predicts a
relatively similar 24-h average heat index as compared to
the measured 24-h average heat index at the time of the
heat-related call. In order to do this we run the model for
the entire 5-year period, then extract the temperature as
predicted by the model in accordance with the day of the
year for each year with each emergency call and then
calculate the 24-h average heat index via Eq. 6. Figure 4
demonstrates graphically that the model is in strong
agreement with the actual raw data at the occurrence of
their respective heat-related call. In fact, the two data sets
(the actual 24-h average heat index and the calculated 24h average heat index from the model) have nearly a perfect
correlation, with r=0.99 via Eq. 5.

Table 7 Predicted average annual reduction in Phoenix heat-related
emergency calls, where the total annual average number of heatrelated emergency calls is 637
Increase in
emissivity

Increase in
percent
vegetated
areas

Increase
in thermal
conductivity

Increase in
albedo

All four
strategies
included

16

17

25

48

103

10% 32

35

50

92

188

15% —

53

73

132

251

20% —

70

96

169

306

5%

24

26
28
30
32
34
24−HOUR AVERAGE HEAT INDEX (°C)

36

38

Exponential fit curve analysis
After validating our model with highest correlated meteorological data sets to heat-related emergency calls in the
city of Phoenix region, we developed a methodology for
using the model to predict reductions in the number of these
calls as a result of implementing UHI mitigation strategies.
We use the raw data in conjunction with model predictions
to bring this analysis together. Given a discrete and raw
data set (24-h average heat index) we can create a
continuous curve that accurately portrays the typical
behavior for this discrete data set. From the previous plots
it is observed that the raw data behave nonlinearly in an
exponential fashion. Thus, we utilize an exponential
function that behaves similarly to the raw data set. Many
different types of exponential functions were experimented
with but the one with the highest correlation will be
discussed below. There are many factors and anomalies that
can disrupt the correlation with such a raw data set,
especially similar to the discrete jumps in Fig. 5. However,
the correlation for the chosen exponential function was still
0.60, showing a strong relationship between the two data
sets. The chosen exponential function was the following:
f ðxÞ ¼ a1 expða2 þa3 xÞ

ð7Þ

where a1 =12.20, a2 =−12.04, and a3 =0.13 as shown in
Fig. 5 superimposed on top of the raw data. We utilized this
function in combination with the model to predict the
decrease in heat-related emergency calls when UHI
mitigation strategies are put into effect.

20
350

CALCULATED REDUCTION IN
HEAT−RELATED EMERGENCY CALLS

Fig. 6 Predicted annual reduction in heat-related emergency
calls for the city of Phoenix
resulting from the four investigated UHI mitigation strategies

Int J Biometeorol (2010) 54:13–22

5%
10%
15%
20%

300

250

200

150

100

50

0

Emissivity

Conclusions with mitigation strategies
The model was run for the 5-year period 2002—2006, for
the Phoenix metropolitan region. We extracted only the
calculations needed for this analysis, which are the
occurrences where there was a heat-related emergency
dispatched by the Phoenix Fire Department Regional
Dispatch Center. There are 19 extracted calculation sets—
2 for the increased emissivity strategy, 4 for the increased
albedo strategy, 4 for the increased thermal conductivity
strategy, 4 for the increased percentage in vegetated area

Albedo

Total

strategy, 4 for all the strategies in unison, and 1 for the
baseline values. Every 24-h average heat index value that
occurred when a call was made was inserted into the
exponential function (Eq. 7) and given a new predicted
heat-related emergency call number. After all occurrences
were accounted for, a new total number of predicted
emergency calls was recorded for all 19 calculation sets,
which is simply the sum of all the predicted heat-related
emergency calls for a specific strategy. In order to calculate
the actual effect on the decrease in total calls we constructed
a percent change (reduction) equation in concert with the

90

CALCULATED REDUCTION IN
HEAT−RELATED EMERGENCY CALLS

Fig. 7 Predicted calculated reduction in heat-related emergency calls versus calculated
reduction in 24-h average heat
index in degrees Centigrade for
the city of Phoenix spanning
2002–2006 resulting from all
the run sets with c1 =9.54, c2 =
−3.59, and c3 =1.14

Vegetated Area % Thermal Cond.

Actual Calculation [ x ]
Exponential Fit Curve [ f(x) ]

80
70
60

f(x) = c1exp(c2 + c3 x)

50
40
30
20
10
0

0

1

2
3
4
CALCULATED REDUCTION IN
24−HOUR AVERAGE HEAT INDEX ( °C )

5

6

Int J Biometeorol (2010) 54:13–22

21

baseline values calculation set (predicted 3,538 total calls),
since the baseline calculation will serve as the predicted total
number of calls as calculated by the exponential function.
The formulation for the resulting reduction in calls for a
particular strategy was taken as follows:
RIC ¼

BVP 
 MSP
BVP

ð8Þ

where RIC is the reduction in heat-related emergency calls,
BVP is the baseline value prediction and MSP is the
mitigation strategy prediction.
Table 7 presents the approximate values for each mitigation strategy’s average annual reduction in heat-related
emergency calls, and Fig. 6 shows a bar graph of the relative
impacts of the different strategies. Increasing albedo results in
the highest reduction in heat-related dispatches, while
increasing emissivity had the lowest reduction, which is in
line with previous results for 24-h average temperatures. The
increased thermal conductivity strategy had a larger effect
than increasing the percentage of vegetated area strategy, and
when we apply all of the strategies together we achieve the
largest reduction in calls, which is in qualitative agreement
with our earlier analysis.
The model predicts that we can reduce the total of
number of calls from 3,186 (over the 5-year period) by
1,530 if we implement the 20% increase for the combined
UHI mitigation strategies. Thus, the model showed that the
total number of calls can be reduced by almost half if the
most aggressive mitigation strategies were deployed in
unison. Additionally, by implementing the most passive
strategies in unison (all strategies at the 5% increase), the
number of calls can be reduced by 515, which is still
approximately a 16% from the 3,186 total. These findings
show that any strategy listed can have impacts on the
number of heat-related emergency calls, which has various
sustainable development implications. Furthermore, of the
four discussed UHI mitigation strategies, increasing the
albedo will lead to the greatest reduction in heat-related
emergency calls, increasing the thermal conductivity comes
in second, increasing the vegetated area comes in third, and
increasing the emissivity comes in last. Concluding our
analysis, we would like to show a relationship between the
calculated reduction in 24-h average heat index and the
calculated reduction in heat-related emergency calls for
the entire run set. Figure 7 shows a sound relationship
between these two data sets, where their correlation coefficient is r=0.78 and best fit was found to be:
f ðxÞ ¼ c1 expðc2 þc3 xÞ

ð9Þ

where c1 =9.54, c2 =−3.59, and c3 =1.14. Equations 7, 8, 9
show the full functional relationship of the model with heat-

related calls, which affords policy makers the flexibility of
planning with either metric (24-h average heat index or
reduction in 24-h average heat index). Lastly, these findings
show promise when embarking on these strategies to
facilitate the well-being of those impacted by the extreme
heat.
In order to be able to run the model for another arid
climate such as the urban area of Las Vegas, Nevada, or
other regions, practitioners would need to obtain measured
data for certain thermophysical constants and dynamic
meteorological parameters. These would include the following five thermophysical constants: (1) emissivity (%), (2)
albedo (%), (3) volumetric heat capacity (J m-3 K-1), (4)
thermal conductivity (W m-1 K-1), and (5) the land-cover
distribution, like that shown in Table 1. Second, the following seven regional specific dynamic meteorological data
would have to be obtained and incorporated into the model:
(1) air temperature (K), (2) relative humidity (%), (3) solar
irradiation (W m-2), (4) wind velocity (m s-1), (5) evapotranspiration rate (m s-1), and ground/soil temperature (K) at
a depth where the temperature does not vary greatly with
time. Once the user has the above data they can run the
model and/or analyze various mitigation strategies.
Acknowledgments This work was supported by the National Center
for Environmental Health at the US Centers for Disease Control and
Prevention (Contract 30-07184-03 CDC / Task Order 0078), and the
National Center of Excellence on SMART Innovations (www.
ASUsmart.com) at Arizona State University. H.R.S. gratefully
acknowledges the partial support of this work by the National
Consortium for Graduate Degrees for Minorities in Engineering and
Science, Inc. in the form of a GEM Doctoral Fellowship.

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