Between Gaming and Microclimate Simulations: Temperature
Estimation of an Urban Area
Eva Strauss and Dimitri Bulatov
Fraunhofer Institute for Optronics, System Technologies and Image Exploitation (IOSB),
Gutleuthausstrasse 1, 76275 Ettlingen, Germany
Urban Heat Island, Thermal Simulation, Digital Twin, 3D City Model, Thermal Remote Sensing.
With the rising awareness and interest from researchers, local authorities, and industry in the urban heat island
effect, thermal remote sensing data is needed as it allows for identification, tracking, or analysis of land sur-
face temperatures. Yet, the accessibility of appropriate thermal data in both the spatial and temporal domain
states an inhibiting factor. Whilst thermal satellite data suffers from both low spatial and temporal resolution,
airborne imagery might enable adequate resolutions, however, is not acquired without time and cost consump-
tion. One way to overcome this drawback is the generation of synthetic data, which comprises the simulation
of surface temperatures. These rather simplified simulations are either quite fast, as desired in gaming applica-
tions, however, highly inaccurate, or rather complex, holistic, time-consuming and computationally intensive,
like applied in urban microclimate considerations. In this paper, we present an in-between approach towards
the estimation of urban surface temperatures that aims to fill this gap between holistic microclimate simula-
tions and climate maps.
1.1 Motiviation
In the last century, the world-wide urbanization de-
gree increased tremendously, and by 2050, the por-
tion of people living in cities or urbanized areas is
expected to be almost 70%. With the concurrent in-
crease of summer heat periods, researcher, local au-
thorities and industry became aware of the need to
maintain the city as a livable area by taking coun-
termeasures against the so-called urban heat island
(UHI) effect. This effect describes the overall higher
temperatures of urban areas compared to their rural
surroundings. Its cause is found in cityscapes, con-
struction materials and type, latent factors like popu-
lation density or traffic, and others. Therefore, many
countermeasures currently applied or under research
evolve around these causes, and interest in computer-
aided tools to quantify the actual effect of counter-
measures is growing. One such computer-aided tool
is given by urban climate simulation software. There,
heat transport and flow dynamics are usually consid-
ered, which makes the overall simulation a complex,
time-consuming task requiring interdisciplinary ex-
pert knowledge. Thus, it is not feasible for, e.g., archi-
tects or urban planners who seek rather fast and easy
to generate as well easy to interpret results. Looking
for a faster way to simulate the temperature distribu-
tion of an urban area, one might look into the area of
gaming and physics-based sensor simulations. Here,
simulation runtimes are drastically reduced up to re-
altime, however, stream dynamics are not taken into
account. In other words, the flow and temperature of
air through a city, its convective cooling and its ef-
fect on human comfort, which is generally of essence,
are not considered. Last but not least, climate maps
state another very fast option to estimate local ur-
ban climate. No differential equations need to be nu-
merically solved, instead, urban areas are segmented
by their local climate solely depending on land-use,
vertical roughness, topography, portion of water bod-
ies, and similar features. In summary, a large gap in
accuracy between near real-time climate estimations
and holistic micro-climate simulations can be iden-
tified by the urban planners. To bridge the gap, a
tool for a quick, superficial screening of a large ur-
ban scene is required allowing to detect potential ar-
eas of urban heat accumulation. For a few candidates
of (smaller) areas particularly vulnerable to UHIs, a
Strauss, E. and Bulatov, D.
Between Gaming and Microclimate Simulations: Temperature Estimation of an Urban Area.
DOI: 10.5220/0012385800003660
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2024) - Volume 1: GRAPP, HUCAPP
and IVAPP, pages 70-80
ISBN: 978-989-758-679-8; ISSN: 2184-4321
Proceedings Copyright © 2024 by SCITEPRESS Science and Technology Publications, Lda.
comprehensive micro-climate simulation can be then
launched, thus allowing to save time and computa-
tional resources. In this paper, we present an in-
between approach towards surface temperature sim-
ulation serving as previously mentioned tool. We par-
ticularly address the physical modeling of the heat
transfer. Thus in this context, the proposed methods
are more sophisticated than gaming approaches, yet
significantly simplified in direct comparison to micro-
climate simulations.
The rest of the paper is organized as follows: To
systematize the state of the art on available tools on
thermal simulation, we provide a concise overview of
current simulation methods and software in Section
1.2 and an introduction to the base simulation frame-
work we built up on in Section 2.1. Afterwards, we
present our methods of choice in Section 2, which
is followed by the evaluation of our methods in Sec-
tion 3. Finally, we summarize our findings and future
work in Section 4.
1.2 Related Work
While the UHI describes temperature increase of
cities in comparison to their rural surrounding, the
microclimate generally refers to the ground-level cli-
mate influenced by the physical characteristics of the
present surfaces. An alternative to laborious and
costly inner-city measurements is provided by micro-
climate simulations. They make it possible to cover
large areas, analyze the impact of city design on UHI
formation and even thermal comfort. One quite well-
known commercial software for microclimate simula-
tions is ENVI-met (Liu et al., 2021). This tool allows
for simulation of single building (yet no interior),
city quarters or whole smaller cities. Designed as a
holistic approach, each physical phenomenon influ-
encing the microclimate is modeled, including radia-
tive heat exchange, photosynthesis, and evapotranspi-
ration. Another simulation tool under ongoing devel-
opment is PALM-4U. As research project under na-
tional funding by the German Federal Ministry of Ed-
ucation and Research (BMBF), the open-source soft-
ware is designed to help in municipal adaption strate-
gies concerning the UHI and other climate-related
changes in urban areas. It offers a higher resolution in
turbulences and is highly parallelized. With PALM-
4U, it is aimed for usability in civil service and public
authority. Envi-met and PALM-4U, as usual microcli-
mate simulation tools, are based on continuous fluid
dynamics (CFD) to numerically solve for the temper-
ature and wind fields. They provide great accuracy,
yet by their CFD nature, they are time-consuming and
demanding, require expertise in the field of numerical
simulation and thus specific training.
Other simulations frameworks focus on specific
tasks or reduced scale, such as building energy tools
for single building simulation. They provide great de-
tail on an appropriate scale, yet cannot be extended to
the urban city scale without huge drawbacks in com-
putation time and cost. Thus, to overcome the gap
between precise building energy simulation (BES)
and CFD on urban areas, BES-CFD coupling tech-
niques have been researched (Rodr
Martin and Hern
erez, Iv
an and Xam
an, Je-
sus and Ch
avez, Yvonne and Gij
on-Rivera, Miguel
and Belman-Flores, Juan M., 2020; Ruijun Zhang,
2021). Bringing together the respective advantages,
high computation time and cost still remains.
Shifting the point of view from microclimate sim-
ulation tools towards scene generation and more game
oriented tools, such as the software components by
Presagis (Presagis, 2023) or Oktal-SE (Oktal-SE,
2023), a paradigm change can be observed. Instead
of expensive CFD simulation, these tools mostly rely
on highly simplified surface temperature simulation
and rather focus sophisticated camera models. Thus,
they clearly outperform microclimate simulations in
terms of runtime and computational cost, yet to the
extent of accuracy.
Motivated and inspired from the above method-
ologies to urban temperatures, our approach aims at
converging these by picking and combining respec-
tive models and thus yielding reliable results with ap-
propriate computation time, cost, and accuracy.
2.1 Preliminaries
The heat distribution of an urban area depends on
many factors, which makes its computation a chal-
lenging task. These factors include, but are not lim-
ited to: construction materials and geometries, cli-
mate conditions (both macro- and micro-climate), lo-
cal weather conditions and weather history over a
larger time span, as well as factors depending on the
residents, like population or traffic. Each of these
contributes to the generation or transfer of heat and
raises the need for a huge amount of information
given prior to climate simulations. A so-called dig-
ital twin, which combines 3D geometry with addi-
tional information, states a great starting point for ur-
ban temperature estimation. In this paper, we focus
on the cityscape and construction materials, and refer
to the digital twin as the 3D reconstruction of an ur-
ban area, in form of a triangle mesh, with semantic
Between Gaming and Microclimate Simulations: Temperature Estimation of an Urban Area
and material information. Since the aerial data pro-
vide the most cost-efficient method to derive the most
essential information from large scene, we followed
the procedure of (Bulatov et al., 2020) to generate the
digital twin from a high-resolution orthophoto, a nor-
malized digital surface model (ndsm), multi-spectral
imagery, and OSM data. In a nutshell, an index is
assigned by semantic segmentation and material clas-
sification to each triangle representing its semantic
type (ground, building part or vegetation), its mate-
rial type (i.e. street, grass, soil, or water for ground
triangles, roof or wall for buildings, and forest, decid-
uous tree, shrub or palm tree for vegetation), as well
as color (image-derived for visible and geo-typical for
non-visible, such as building walls, objects). These
indices are linked to a material database where physi-
cal parameters like density, heat conductivity, or spe-
cific heat capacity, needed for temperature calcula-
tion, are stored. Currently considered material classes
are street, grass, soil, water, building roof, building
wall, vegetation.
2.2 Overview of Thermal Simulation
The starting point of our proposed thermal simulation
framework is given by the 3D semantic city model,
i.e. the three-dimensional triangular mesh with dis-
tinct numeric class labels per triangle, as described
in Sec. 2.1. Environmental data needed for the sim-
ulation, including wind speed, air temperature, or
relative humidity, is considered to be available via
weather stations nearby the city to be simulated. Due
to thermal inertia, a minimum time-span of 48h has
to be simulated, such that corresponding weather data
has to be gathered. Generally, we calculate the surface
temperatures based on the well-known heat equation
applied to the full scene. To do so, a finite volume
method (FVM) is deployed by expanding each sur-
face triangle of the 3D mesh into a prism of material-
dependent depth which is sliced into several layers
following (Kottler et al., 2019). Here and in the fol-
lowing, we will refer to this as the surface volume.
For each layer, average temperatures are estimated
by modeling the net heat flux. Thus, the surface layer
is affected by convective, radiative and conductive
heat, while the inner layers only experience heat con-
duction. Due to its high complexity, latent heat is not
yet regarded in the presented work. Following (Kot-
tler et al., 2019; Bartos and Stein, 2015), the temporal
temperature evolution for each surface layer is given
= q
+ q
+ γ
+ γ
with the temperature of the surface T
, the solar short-
wave heat flux q
, the radiative long-wave heat flux
, the factors γ
[0; 1] yielding weather the sur-
face layer is exposed to sunlight and γ
[0; 1] yield-
ing the relative exposure to the sky in orthogonal di-
rection, the conductive heat flux q
, the convective
heat flux q
, the material-dependent specific heat
capacity c
and material density ρ
of the surface
layer, and finally its depth d. The inner layers, i.e.
below the surface, only experience conductive heat
transfer, yielding
= q
where i indicates the i-th layer with corresponding
heat flux q
and temperature T
, and it is i =
1...(n 1) with n being the number of layers. The
layer depths are assumed to be equal. Depending on
the present semantic class and material of the surface
element, we set the temperature of the last layer to a
constant, or assume the heat flux to be zero, i.e. some
kind of insulation being apparent in the semantic ob-
ject. In the following, details on the heat flux terms
will be outlined.
2.3 Conductive Heat
The individual layers of a given surface volume are
assumed to exchange heat by conduction following
Fourier’s law. Furthermore, we assume a lateral heat
exchange between surface volumes, in particular be-
tween neighboring layers, see Figure 1.
Thus the conductive fluxes in Eq. (1) and ((2)) are
s j
(T )
s j
s j
s j
i j
(T )
i j
s j
s j
with the area A of the surface triangle, its set of neigh-
boring triangles N
, and the length L
s j
and normaln
s j
of the corresponding edge between the surface and the
neighboring triangle indexed vy j. It is n
i j
s j
i j
= L
s j
for all sub-surface layers i. Hence, (T )
i j
denotes the derivative in direction ofn
s j
. The conduc-
tivity at layer interfaces, denoted by k
and k
i j
, are
determined as min(k
) and min(k
), respec-
tively. As previously stated, we set the boundary con-
ditions on the last layer denoted by n depending on
the surface triangles’ semantic class, i.e.
GRAPP 2024 - 19th International Conference on Computer Graphics Theory and Applications
(T )
= 0 if building roof or wall
= const. otherwise
where (T )
denotes the derivative of T along the
surface normal.
Figure 1: 3D surface volumes. Colors indicate the material
classes street (gray), gras (green), soil (brown), and user-
defined (magenta). Blue arrays indicate direction of con-
ductive heat transfer.
Gras Layer
Water Layer
Street Layer
Soil Layer
Soil Layer
Soil Layer
Soil Layer
Insulation Layer: No Heat Transfer
Core Layer: Constant Temperature
Figure 2: Schematic representation of the material compo-
sition per surface class.
Given the numeric semantic class label of the
surface triangles, material properties being needed
in above equations are deduced. Namely, these are
density, specific heat capacity, and heat conductiv-
ity. The class label serves as unique identifier refer-
encing to the material library holding these parame-
ters. However, since only the surface class is known,
sub-surface materials have to be approximated. The
authors of (Kottler et al., 2019) applied the proper-
ties of the surface triangle also on sub-surface lay-
ers, while commercial software tools such as Envi-
met (Liu et al., 2021) provide more sophisticated de-
fault compositions of material layers. Yet, case stud-
ies using microclimate simulation software often re-
veal the need for manual adaption of materials to
make them a better fit to reality. In our model, we
thus provide default as well as adaptable 1D surface
volumes. These are defined as an array of materials
each with corresponding depth boundaries. The ma-
terials are uniquely identified by a numerical value,
referencing again the given material library. By de-
fault, given the unique surface materials of a semantic
3D city model, the 1D surface volumes are automat-
ically generated and, according to the first material
in the array, i.e. the surface material, assigned to the
corresponding triangle of the 3D city model. Alter-
natively, a semi-automatic process can be employed,
where 1D surface volumes are manually defined and
automatically assigned to the 3D city model. Figure
1 illustrates the 3D surface volume with directions of
heat conduction, and Figure 2 displays the boundary
conditions and materials assigned by default to the 1D
surface volume.
2.4 Convective Heat
Convection describes the transfer of heat by a moving
fluid, such as air or water, and distinction is made be-
tween natural convection, where a fluid starts moving
due to a change in temperature, and forced convec-
tion, where a temperature change occurs due to forced
fluid motion by an external source, e.g. wind or ven-
tilators. In an outdoor scene, an example for natural
convection is the visible rising air directly above hot
streets during summer heat periods. Yet, natural con-
vection often is exceeded by forced convection due
to wind movement. Generally, the convective heat
flux is proportional to the temperature difference of
a given surface and the moving fluid. Introducing the
convective heat transfer coefficient (CHTC), the con-
vective heat flux in Eq. (1) is given by
= h(T
) (6)
with the CHTC h. Generally, the estimation of h is
a tremendously challenging task. Particularly within
a city, dependencies on cityscape, material properties
such as roughness or coating, wind speed and many
others occur. Corresponding research usually focuses
on very specific situations under well-defined condi-
tions. For this reason, we chose a CHTC model that
takes into account the 3D geometry of the city model
and is based on CFD simulations following (Awol
et al., 2020). Therein, the authors propose three new
correlations which set into relation the wind speed at
10m height above ground, the building packing den-
sity, and the flow regime. The authors differentiate be-
tween the isolated (large distance between buildings
compared to their height) and interference/skimming
(medium to low distance between buildings compared
to their height) regimes. They further assume ideal
cubic buildings uniformly spread on an orthogonal
grid. The proposed correlations from (Awol et al.,
2020) are given in the form of
h = c
· v
· (c
· λ
· λ + 1) (7)
in the isolated flow regime and
h = c
· v
· (c
· λ) (8)
in the interference/skimming flow regime, with the
wind speed at 10m height above ground v
and the
packing density λ of the buildings. The parameters c
Between Gaming and Microclimate Simulations: Temperature Estimation of an Urban Area
, c
, c
, c
, and c
depend on the relative surface ori-
entations clustered in the four categories windward,
top, lateral and leeward. To apply the proposed cor-
relation to our case, a triangle-wise estimation of the
building packing density, the flow regime, and the rel-
ative surface orientation category has to be carried
out. We hold on to the assumption of cubic buildings
and thus estimate the building packing density as
λ =
with A
the summarized planar area of all buildings
in the scene and A
the not built-up area, yet involv-
ing all ground surfaces, including streets or pavement.
The planar areas A
and A
are yielded by the orthog-
onal projection of the 3D city model with its semantic
class labels. We further estimate the flow regime by
the percentage of the built-up area with respect to the
full scene and neglect differences in building heights.
Given the LOD1 buildings, each roof triangle is as-
signed the category top of the relative surface orien-
tation. By taking the dot product of surface normals
and wind direction, which is assumed to be constant
in space and time, wall triangles are assigned the cor-
responding categories windward, lateral, or leeward.
Since the correlations given by Eq. (7) and (8) are
only valid for buildings, another CHTC model has to
be used for ground and vegetation. At ground, par-
allel laminar flow is assumed, and from (Energie und
Umwelttechnik, 2009), we formally set the CHTC to
h =
, if v
> 5 m/s
1.8 + 4.1v
, otherwise
depending on the wind speed, i.e. whether forced con-
vection outperforms natural convection or not.
The CHTC model above is valid for building tri-
angles, yet ground and vegetation triangles have to be
considered separately. Vegetation further raises the
challenge in thermal modeling due to their active na-
ture, as it actively regulates its temperature via evapo-
transpiration to a certain degree (Kibler et al., 2023).
In our approach, we assume the temperature of vege-
tation to be equal to air temperature. Thus, latent heat
accounting for the effect of transpiration and evapo-
ration from vegetation as well as moist ground is not
included in our model for the sake of simplicity.
2.5 Radiative Heat
Radiative heat exchange in an urban area can be sepa-
rated in heating due to solar exposure, heat exchange
between objects, and exchange between surfaces and
the surrounding atmosphere. While the first partic-
ularly occurs due to the short-wave infrared radia-
tion within the solar spectrum, the latter two occur
in the long-wave infrared spectrum, which is also
known as thermal radiation and strongly depends on
the scenery, namely the surface materials, surface ar-
eas and their mutual exposure.
We formally follow (Kottler et al., 2019; Bulatov
et al., 2020) to model both radiative heat fluxes. Thus,
the solar heat flux q
on an exposed surface oriented
by the angle φ in direction of the incoming sunlight is
given by
= (1 a)E
cos(φ) (11)
with the color-dependent solar albedo a, i.e. the so-
lar reflectance of the surface, and the solar irradia-
tion E
at the surface, i.e. damped by the atmosphere.
The sky is mathematically assumed as infinite surface
with a corresponding sky temperature T
the long-wave radiative heat flux
= σε(T
) (12)
with the emissivity ε of the surface material and the
Stefan-Boltzmann constant σ.
2.6 Initial Condition
The numerical estimation of temperatures in transient
heat transfer states an initial value problem and due
to thermal inertia, the initial temperature distribution
is crucial and affects the temporal temperature evolu-
tion. This is why the simulation of temperatures of
a 3D city model at a given point in time should al-
ways include the simulation of temperatures for a pre-
ceding time span, from a few hours up to a few days
depending on the chosen initial temperatures. When
measured temperature distributions are given, the pre-
ceding simulation time can be minimized. Our over-
all simulation framework was thus designed to allow
for aerial thermal imagery to be used as initial data,
whereas unseen structures are interpolated. For ex-
ample, these might be walls, windows, or tree trunks.
If no measured data is available, a 1D precalculation,
i.e. no lateral heat conduction, of material-wise tem-
peratures is performed. In other words, the 1D tem-
perature distribution of each unique surface volume is
independently simulated. Each surface volume is as-
sumed to represent a flat triangle with no elevation nor
shadowing, the environmental conditions are given by
the first 24 hours of the overall timespan to be simu-
lated, and the first air temperature entry serves as ini-
tial temperature.
2.7 Thermal Radiance for
Image-to-Image Comparison
Generally, when an aerial thermal image is provided,
measured surface temperatures need to be deduced.
GRAPP 2024 - 19th International Conference on Computer Graphics Theory and Applications
Since any thermal camera generally measures heat
radiance instead of actual temperatures, the cameras
sensor output is translated into temperature values by
some approximations either within the camera or by
camera-specific tools. Yet, the underlying correla-
tions, applied approximations and specifications are
usually company property, thus not publicly available
and often not provided. To compare the simulated sur-
face temperatures against thermal imagery, we thus
consider not only the simulated surface temperatures
themselves but also the simulated heat radiance for
better image-to-image comparability. Given the simu-
lated surface temperatures T
, this radiance is approx-
imated by
L = ε
)dλ whereby
(λ,T ) =
λ · T
with the material-wise thermal emissivity ε, integra-
tion over the long-wave infrared spectrum with λ
8µm and λ
= 14µm, and the spectral radiance fol-
lowing Planck’s law with constants c
and c
. The in-
tegral can be solved numerically by transforming into
a fast converging series, yielding (Wallrabe, 2001)
L = ε
) S(x
)] whereby
) =
+ 3(ix
+ 6ix
+ 6
with x
for n = 1, 2.
To keep the radiance model as simple as possible,
atmospheric or sensor-specific effects are not mod-
eled. With simulated temperature and radiance values
per triangle, a simple OpenGL rendering is performed
in order to generate simulated images of the area in
correspondence to the measured thermal image.
The simulation approach has been carried out for an
urban area in the City of Melville, Western Australia.
The reconstructed area of size 2 km × 1 km is shown
in Figure 3. The reconstruction as discussed in Sec.
2.1 is a triangle mesh with semantics and materi-
als assigned. This mesh consists of 1648685 trian-
gles. Hereby, buildings are given with level-of-detail
(LOD) 1 while the vegetation is represented either
as a standard tree model for isolated single trees and
shrubs or as forest boxes for larger tree regions. En-
vironmental conditions for the simulation are drawn
from a nearby weather server.
Figure 4 shows an excerpts of the simulation re-
sults. As the temperature is calculated per triangle,
the triangle mesh with the corresponding tempera-
tures given at 8pm is shown (top image). The two
bottom images show the results of the urban area at
8pm from different viewpoints, showing the impact of
the 3D characteristics taken into account, i.e. the wall
temperatures differ according to their relative orienta-
tion (north/south, east/west).
3.1 Qualitive Evaluation of the Initial
An aerial thermal image of the considered area was
provided, such that both initial condition implementa-
tions are tested. Figure 5 displays the initial tempera-
tures set from the aerial image, and by precalculation,
i.e. material-wise approximations. As described in
Sec. 2, the precalculation starts with uniform tem-
perature all over the scene equal to air temperature,
and the calculated initial temperatures already reveal
the diverse material characteristics in the urban area.
Street and ground becomes distinguishable from veg-
etation and buildings. Furthermore, while street and
soil are comparable to the thermal image tempera-
tures, gras temperatures appear overestimated, and
vegetation and building temperatures tend to under-
estimation. The precalculated values still suffer from
said starting values, i.e. air temperature, and more
detailed evaluation will be considered from the final
simulation results in the following.
3.2 Evaluation of Simulation Results
The evaluation is based on two components. First, im-
age similarity measures are considered since an aerial
image is given as ground truth data. To quantify im-
age similarity from both human perception and from
a computer vision point of view, the metrics of mutual
information (MI) and structural similarity index mea-
sure (SSIM) are employed. MI originally stems from
information theory and quantifies the statistical cor-
relation between two variables. SSIM quantifies the
similarities of two images by their luminance, con-
trast and structure. Second, given the measured sur-
face temperatures from the thermal image and simu-
lated surface temperatures, the root-mean square error
(RMSE) and mean absolute error (MAE) of the sim-
ulation are considered as well. Besides taking into
account the fully rendered area, RMSE and MAE are
also evaluated in a class-wise manner to assess the
class-specific modeling of heat conduction.
As described in Sec. 2.7, an orthogonal projec-
tion of the 3D triangle mesh with surface temperatures
Between Gaming and Microclimate Simulations: Temperature Estimation of an Urban Area
Figure 3: Reconstructed area as triangle mesh with respective class labels.
Figure 4: Qualitative results of the heat simulation on the LOD1 reconstruction of the urban area at 8pm. Top: simulated
surface temperatures displayed together with the triangle mesh. Bottom: simulated surface temperatures displayed without
triangle mesh. Left: view from the west. Right: view from the east.
GRAPP 2024 - 19th International Conference on Computer Graphics Theory and Applications
Table 1: Image similarity by mutual information (MI) and structural similarity index measure (SSIM).
Initial Condition Rendered Value MI SSIM
Precalculated Temperature 0.61 0.50
Long-Wave IR Radiance 0.60 0.63
Thermal Image Temperature 1.19 0.67
Long-Wave IR Radiance 1.00 0.67
Figure 5: Initial temperatures from precalculation (left), i.e.
material-dependent temperature value, and initial tempera-
tures from a given thermal image (right).
Table 2: Root-Mean-Square-Error (RMSE) and Mean Av-
erage Error (MAE) of simulated temperature values over all
classes, i.e. considering the full scene, and class-wise only.
All 8.56 6.96
Street 4.31 0.62
Soil 3.96 1.12
Gras 10.23 1.25
Buildings 13.58 12.96
Vegetation 5.52 5.40
Thermal Image
All 8.28 6.64
Street 4.34 0.73
Soil 2.98 0.89
Gras 7.85 0.97
Buildings 13.97 13.26
Vegetation 5.52 5.40
and radiances is applied. The resulting images, to-
gether with the measured aerial image, are displayed
in Figure 6. There, the effect of emissivity, i.e. the
material-dependent ability of surfaces to radiate heat,
can clearly be seen in the simulated long-wave in-
frared image. Simulation of the surface temperatures
took approximately 2 hours (application of initial
temperatures excluded) on a personal computer (In-
tel(R) Core(TM) i9-10900K, CPU@3.70GHz, 32GB
RAM, Nvidia GeForce RTX 2080 Super) and the
Matlab Parallelization Toolbox was used for GPU us-
age. Please note that the implementation of the math-
ematical model was conducted under the premise
of prototyping a simulation framework in an object-
orienting programming (OOP) matter in MATLAB
2021 and is not runtime-optimized. Therefore, ab-
solute run-times of the overall simulation are not rep-
resentative since OOP does not perform fast in MAT-
LAB, however, the final coding structure of our im-
plementation is easily transferable to other program-
ming languages, allowing the fast implementation of
plugins for software in the field of 3D graphics or vir-
tual environments.
As first part of the evaluation, image similarity is
considered, and MI and SSIM are summarized in Ta-
ble 1. By determining the initial temperatures by the
given thermal image, MI is strongly increased. This is
expected and likely caused by the inner-class temper-
ature variations introduced by the initial temperatures.
Yet, MI is reduced when long-wave infrared radiance
is compared to the measured thermal image. Two po-
tential causes occur: first, the radiance model might
be oversimplified. Second, the processing of the ther-
mal image before delivery causes unexpected and un-
documented deviations. The SSIM shows generally
good agreement between measurement and simula-
tion, yet, usage of long-wave infrared radiance instead
of surface temperatures shows none or only minor im-
provement, presumably for the same reasons as stated
As second part of the evaluation, RMSE and MAE
of the simulated surface temperatures are determined
against the measured temperatures from the thermal
image, as previously outlined, and summarized in Ta-
ble 2. With an MAE of 6.96 for precalculated initial
values and 6.64 when the thermal image is applied
as initial condition, the need for a class-wise consid-
eration is raised. There, ground classes (street, soil,
gras) show good agreement with the measurements,
however, buildings and vegetation deviate, increasing
the comprehensive MAE. With vegetation being chal-
lenging to model due to its active nature, and given the
applied simplified model, a larger deviation than other
classes was expected. The high MAE value on build-
ings lies in an overestimation of roof temperatures,
cp. Figure 6, originating most likely from an underes-
timation of weather conditions and heavy generaliza-
Between Gaming and Microclimate Simulations: Temperature Estimation of an Urban Area
Figure 6: Measured and simulated thermal images. From left to right: measured temperatures from aerial thermal image,
simulated surface temperatures with initial temperatures from precalculation (top) with corresponding simulated long-wave
infrared radiance image (bottom), and simulated temperatures with initial temperatures from thermal image (top) with corre-
sponding simulated long-wave infrared radiance image (bottom).
GRAPP 2024 - 19th International Conference on Computer Graphics Theory and Applications
tions in roof construction. The underlying roof model
including insulation is generalized to most cities, yet
in our test area, i.e. the City of Melville, insulation is
often missing. Indeed, many buildings even allow for
air circulation between building walls and roof.
Comparing the initial conditions, only slightly
better results are found when the thermal image is
used. The precalculation is supposed to overcome the
thermal inertia rendering the initial condition crucial,
thus this minor improvement aligns with expected be-
havior. From the class-wise approach, ground sur-
faces suffer from outliers with large deviations be-
tween simulation and measurement. A reasonable ex-
planation are the neglected variations in moist, soil
composition, and street types (e.g. asphalt, concrete,
In summary, the simulation shows good agree-
ment with the measured temperatures for most
classes, yet buildings and vegetation will need further
improvement in future work.
We presented a tool for temperature computation of
urban areas being more precise in thermal modeling
than game-oriented software yet less computation-
ally heavy than microclimate simulations. Starting at
meshes derived from multi-source sensor data, we are
driven by the motivation to create realistic tempera-
ture values which will allows for faster decisions in
urban planning.
We realized that the path from raw multi-source
sensor data to thermal image of an urban area is chal-
lenging and complex. The geo-referenced 3D para-
metric model, enriched with the weather data, makes
it possible to derive the temperatures of the scene
elements at any moment of time, and from there,
the radiance (infrared) image can be generated. The
negative consequence of a complex procedure is al-
ways that an inaccuracy at a very early stage re-
sults in barely inexplicable deviation from the refer-
ence data in the final output. Providing a better co-
registration of sensor data; more robust procedures for
land cover and material classification; higher levels of
details for buildings and trees; consideration of fur-
ther terms for infrared image synthesis out of surface
temperatures: all this influences the quantitative result
greatly. In this work, we concentrated on the under-
lying physics-based thermal models. Semantic- and
material-dependent models for conductive and con-
vective heat were presented. There, the convective
model by (Awol et al., 2020) has been adapted to real
urban areas. To handle the thermal inertia and the
challenging initial temperature conditions, material-
wise precalculation and usage of thermal imagery
were introduced, and the precalculation show promis-
ing results which is of importance as acquisition of
thermal imagery can be challenging.
In summary, our approach yielded promising re-
sults for a quick, superficial screening of a large ur-
ban scene. Such a quick screening can assist in urban
planning. Yet, the simplified vegetation model of the
simulator at its current stage is a major drawback. Im-
proving this model, by integrating latent heat, is one
important direction of future work. Furthermore, we
strive for the inclusion of a simplified CFD simula-
tion, i.e. replacing the global wind velocity and direc-
tion by triangle-wise values. Naturally, as the current
implementation is in form of a prototype, we further-
more strive for a final implementation and compari-
son of absolute runtimes to microclimate simulation
and gaming approaches.
Many thanks for providing the multi-source data of
the test site, City of Melville, particularly to Dr. Petra
Helmholtz from Curtin University, Australia.
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GRAPP 2024 - 19th International Conference on Computer Graphics Theory and Applications