Magnitude of urban heat islands largely explained1
by climate and population2
Gabriele Manoli
1,∗
, Simone Fatichi
1
, Markus Schl
¨
apfer
2
,
Kailiang Yu
3
, Thomas W. Crowther
3
, Naika Meili
1,2
, Paolo Burlando
1
,
Gabriel G. Katul
4
, & Elie Bou-Zeid
5
1
Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland
2
Future Cities Laboratory, Singapore-ETH Centre, ETH Zurich, 138602 Singapore
3
Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland
4
Nicholas School of the Environment, Duke University, Durham, NC 27708, USA
5
Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
∗
Corresponding author: manoli@ifu.baug.ethz.ch
3
Abstract4
Urban heat islands (UHIs) exacerbate the risk of heat-related mortality associated with global5
climate change. The intensity of UHIs is known to vary with population size and mean annual pre-6
cipitation but a unifying argument is missing, and geographically targeted guidelines for heat miti-7
gation remain elusive. Here we analyze urban-rural surface temperature differences (∆T
s
) world-8
wide and find a nonlinear increase of ∆T
s
with precipitation that is controlled by water/energy9
limitations on evapotranspiration and that modulates the scaling of ∆T
s
with city size. We in-10
troduce a coarse-grained model linking population, background climate, and UHI intensity and11
we show that urban-rural changes in evapotranspiration and convection efficiency are the main12
determinants for warming. The direct implication of these nonlinearities is that mitigation strate-13
gies aimed at increasing green cover and albedo are more efficient in dry regions, while cooling14
tropical cities is a challenge that will require innovative solutions.15
Keywords: Cities, Climate Variability, Green Cover, Population, Urban Heat Islands16
Preprint accepted in Nature
2 MANOLI ET AL.
Main17
Cities modify their surface energy balance and generally exhibit higher air and surface temperatures18
than the surrounding rural areas
1–3
. This phenomenon, known as the urban heat island (UHI) ef-19
fect, poses a threat to human health as more than half of the world population now lives in cities
4
20
and warming can increase morbidity and mortality
5,6
, especially during heat waves
7
. UHIs have21
been extensively studied in North America
2,8
, Europe
9
, China
10,11
, and globally
12,13
. A link between22
urbanization-induced warming and city size as measured by its population was first proposed in 197323
based on nighttime air temperature data
1
. With the proliferation of remotely sensed land surface24
temperature measurements, similar relations have been proposed at the global scale
13
. Local hydro-25
climatic conditions also contribute to the intensity of UHIs
2,14
, with rising mean annual precipitation26
causing an increase in urban to rural surface temperature differences (∆T
s
), a proxy for urban warm-27
ing with respect to the more efficient cooling of the surrounding rural surfaces. Given the complexity28
of urban systems, identifying and isolating the causes of UHIs remains challenging
3,15
and the factors29
contributing to the observed changes in ∆T
s
across city sizes and hydroclimatic conditions continue30
to be a subject of inquiry and debate
2,13,14,16
.31
During nighttime, the intensity of UHIs is largely controlled by urban-rural differences in surface32
geometry, thermal properties, and anthropogenic heat
3
. The causes of daytime ∆T
s
are fundamentally33
different and both changes in convection efficiency associated with surface roughness
2
and changes34
in the partitioning of latent/sensible heat fluxes associated with local climate-vegetation character-35
istics
10,14,16
have been proposed as the main drivers of warming. Some studies suggested that ∆T
s
36
increases linearly with precipitation due to changes in aerodynamic resistance, as cities in dry climates37
are more efficient than the barren surrounding in dissipating heat, while the opposite is observed in38
humid regions
2
. However, the validity of such a linear relation has been questioned. Remote sensing39
measurements from 32 cities in China hint to the existence of a precipitation threshold above which40
∆T
s
is insensitive to precipitation changes
10
. In addition, the aerodynamic explanation of UHIs is41
inconsistent with the observed power law scaling of urban warming with population as an increase in42
building height (associated with larger city sizes
17
) should enhance convection and increase cooling43
rather than warming. However, the reasoning that “rougher” cities with taller and denser buildings44
are more efficient in exchanging heat and momentum
2
is contrary to the observed decrease in rough-45
ness length with urban density
18
. Numerical simulations have confirmed possible nonlinear responses46
of ∆T
s
to precipitation
16
but, unlike previous modeling results, the variability of ∆T
s
has been ex-47
plained by changes in rural temperature
16
rather than convection efficiency
2
. In short, the causal links48
Preprint accepted in Nature
GLOBAL URBAN WARMING 3
between ∆T
s
, population, city texture, and climate appear to be complicated by hidden thresholds49
and remain uncertain. As a consequence, identifying general guidelines for heat mitigation remains50
a daunting task
15
and a fundamental knowledge gap persists in understanding how cooling effects of51
urban vegetation
19
and albedo management
2
vary across cities and climatic conditions. A case in52
point is the Italian city of Matera which, despite its dense urban fabric and the lowest green cover in53
Europe (only 0.1% of the total area
20
), exhibits a negative UHI
21
while Singapore, with more than54
50% of green spaces
22
, shows a daytime ∆T
s
of +1.9
◦
C (ref.21). Hence, the efficiency of heat miti-55
gation strategies cannot be direclty inferred from studies on a few selected cities because an adequate56
basis for generalization is missing. More broadly, such global issues need to be tackled with a holis-57
tic perspective to put existing results into geographic context and transfer knowledge across climatic58
gradients, which frames the scope of this work.59
Here, surface temperature anomalies in more than 30000 cities
21
are analyzed and used to de-60
velop a mechanistic coarse-grained model that links ∆T
s
to population (N) and mean annual pre-61
cipitation (P ), where N is an aggregate measure for urban infrastructure size and P is a proxy for62
time-integrated surface-atmosphere exchanges and climatic patterns. The model is based on the fact63
that, as a city grows, its structure and functioning are predictably modified
23
. Different building ma-64
terials are employed, heat storage and evapotranspiration fluxes are altered, and human activity and65
energy consumption increase. The urban fabric (e.g. area, materials, mean building height, height-to-66
width ratio of street canyons) also changes, thus altering reflectivity and emissivity of the city surface67
as well as its roughness and convection efficiency relative to the surrounding (often vegetated) areas.68
Despite the diversity and complexity of urban systems, universal scaling laws linking urban popula-69
tion to infrastructure size and socio-economic metrics exist and have been confirmed when combining70
data from cities across the entire globe
23
. How can links between such established scaling laws, ∆T
s
,71
and climate-vegetation characteristics be beneficially used to globally address urban-induced warm-72
ing motivates the work here. When coupled to energy and radiative transfer principles, it is shown73
that the aforementioned scaling laws provide logical bases to coarse-grained representations of UHIs.74
This approach constitutes a major departure from empirical analysis that lump different mechanisms75
into statistical correlations, e.g. between ∆T
s
and population or urban texture
1,12
. Likewise, it differs76
from the current state-of-the-science being employed in climate simulations that resolve the physics77
of energy exchanges and atmospheric flows at the street-canyon and building level but cannot cap-78
ture emergent large scale phenomena associated with population and infrastructure dynamics. Our79
findings explain the global variability of UHIs, they complement exisiting micro-scale urban climate80
studies
24
and provide guidance for the increasing efforts aimed at greening and cooling world cities,81
Preprint accepted in Nature
4 MANOLI ET AL.
especially to the large number of metropolises that have not benefitted from intensive observational or82
modelling studies. Also, the approach here offers guidance on where detailed observational and sim-83
ulation studies can be more effective so as to address UHIs across climatic gradients and city sizes.84
The main novelty of the proposed approach is the inclusion of emergent behaviors of urban-biosphere85
systems in a coarse-grained model that explains the observed global patterns of ∆T
s
. These patterns86
are then translated to general guidelines for planning and retrofitting of cities
5,25
.87
Global patterns of urban warming88
The focus of our analysis is on mean daily urban-rural surface temperature differences ∆T
s
during89
summertime when the intensity of UHIs and the risk of heat-related mortality are expected to be the90
highest
8,13
. Also, any links to precipitation are likely to be more evident during summer beacuse91
vegetation is active
16
. Consistent with prior results
10,16
derived from a smaller data set, a nonlinear92
relation between ∆T
s
and mean annual precipitation is found (Fig. 1a). The reported linear increase
2
93
holds for low precipitation regimes but ∆T
s
saturates at high precipitation values exceeding around94
P =1500 mm yr
−1
. A nonlinear response between ∆T
s
and background temperature T
s
is also ob-95
served (Fig. 1b) with peak warming occurring at T
s
≈ 22
◦
C and decreasing UHI intensities for warmer96
climates. A positive correlation between daytime surface UHI intensity and mean air temperature (T
a
97
between -10 and 30
◦
C) have been reported
10
suggesting a possible intensification of urban warm-98
ing under future climate change scenarios
26
. However, an opposite correlation was observed during99
nighttime
10
and during the day in 54 US cities
27
. The global results here show that ∆T
s
decreases100
for T
s
higher than ≈25
◦
C. Unlike previous results suggesting that the scaling ∆T
s
∼ N
δ
is invariant101
with climate
2
, precipitation is shown to introduce appreciable corrections to the observed exponent δ102
with a weakening of such scaling under wet conditions (Fig. 1c). Specifically, δ is 0.21 globally but103
it varies between 0.15 and 0.34 under wet and dry conditions, respectively. These results agree with104
early work on the impact of soil moisture on the relation between UHI intensity and population
28
and105
the values of δ are in agreement with prior scaling exponents reported in the literature
13
.106
The observed global variability of ∆T
s
with mean annual precipitation P and urban population N107
can be expressed mathematically as (see derivation in the Supporting Information, SI):108
∆T
s
(P, N) =
1
f
s
(P ) −
γ
a
T
f
a
(P )
∆S(P, N); (1)
where f
−1
s
and f
−1
a
[K W
−1
m
2
] represent the surface and air temperature sensitivities to 1 W m
−2
109
Preprint accepted in Nature
GLOBAL URBAN WARMING 5
energy forcing, γ and a
T
are phenomenological parameters that account for the coupling between T
s
110
and T
a
, and ∆S [W m
−2
] is the energy forcing perturbation due to urban-induced changes in surface111
albedo (∆α), emissivity (∆ε
s
), evapotranspiration (∆ET ), convection efficiency (∆r
a
), and anthro-112
pogenic heat (∆Q
ah
). Eq. 1 provides a parsimonious description of the coupled urban-biosphere113
system (Supplementary Fig. S1) based on general scaling laws for urban form/function and global cli-114
mate relations (see Methods and SI for details). The proposed approach is deemed “coarse-grained”115
because “fine-grained” properties of cities and rural areas are smoothed over in space and time to116
focus on collective phenomena and climatic patterns rather than microscopic (i.e., building to block117
scale) processes. The validity of the model for the purposes of this study can be evaluated by its ability118
to recover the observed patterns of ∆T
s
changes with simultaneous changes in background climate119
and population (Fig. 1a-c and Supplementary Fig. S2). The model has a good fit and accuracy when120
predicting the observed trend of global UHIs across precipitation gradients, closely matching the 1:1121
line and accounting for 74% of the variation (inset in Fig. 1a). The agreement between observed and122
modeled ET (Supplementary Fig. S3) and the modeled impact of background temperature and wind123
speed on urban warming (Fig. 1b and Supplementary Fig. S4, respectively) are also acceptable, thus124
confirming the robustness of the approach here. A conceptual analysis of ∆T
s
variability using Eq. 1125
suggests that the observed nonlinear responses of UHIs to background climate (Fig. 1) arise from126
distinct mechanisms, the relative contribution of which vary with precipitation
2,29
as now discussed127
using the combined data-model results.128
The shape of the P − ∆T
s
relation is largely controlled by changes in evapotranspiration (ET). In129
wet climates, energy limitations define an upper bound to ET differences between urban and rural en-130
vironments while, in arid regions, water limitations reduce the magnitude of rural ET thus limiting the131
contribution of ∆ET to ∆T
s
(Fig. 1a,d). In dry climates, when the water budget of urban vegetation132
is supplemented by irrigation, ∆T
s
becomes negative creating an “oasis” effect
30–32
. The amount of133
urban vegetation also plays a role as estimates of urban green cover fractions (g
c,u
) from Europe (EU)134
and South East Asia (SEA) reveal a significant larger green area in cities located in high precipitation135
regimes (see Methods). This dependence of urban greenery on hydroclimate, together with changes136
in air specific humidity with precipitation gradients (see results in the SI), explaisn the concavity of137
the P − ∆T
s
relation in Fig. 1a.138
As proposed elsewhere
2,7
, urban-rural changes in convection efficiency also contribute to city139
cooling in dry and warm climates. Given that the height of natural vegetation increases logistically140
with precipitation
33
, cities in dry regions are aerodynamically rougher than the surrounding rural141
surfaces characterized by deserts or short vegetation and heat dissipation by convection could be more142
Preprint accepted in Nature
