Session M2B – Exterior climate interaction
Building Physics 2008 - 8th Nordic Symposium
Surface Temperatures on Flat Roofs and Hygrothermal
Consequences
Christian Bludau, Dipl.-Ing.,
Department of Hygrothermics, Fraunhofer Institute for Building Physics;
christian.bludau@ibp.fraunhofer.de
Daniel Zirkelbach, Dipl.-Ing.,
Department of Hygrothermics, Fraunhofer Institute for Building Physics;
daniel.zirkelbach@ibp.fraunhofer.de
Hartwig M. Künzel, Dr.-Ing.,
Head of Department of Hygrothermics, Fraunhofer Institute for Building Physics;
hartwig.kuenzel@ibp.fraunhofer.de
KEYWORDS: temperature, long wave radiation, cold pond, flat roof.
SUMMARY:
In this paper the temperature conditions on flat roofs are discussed considering the influence of long-wave
radiation to the sky and the effect of a parapet as an important factor for the nighttime roof temperature. The
parapet leads to retention of cold air on the roof. Results of measurements on flat roofs and special
meteorological data collected at the field test site in Holzkirchen are presented.
For realistic assumptions of the boundary conditions a heat transfer coefficient depending on the ambient
conditions including the temporary insulation effects of a cold surface air pond forming between the parapet
walls is determined for flat roofs. The surface measurements on flat roofs with a parapet show a significant
decrease of the temperature below the ambient air conditions during night time. These surface temperature
recordings and meteorological data are used to validate hygrothermal simulations.
Furthermore the possibility of interstitial condensation is investigated using an adapted hygrothermal simulation
tool. The results show that the use of reflecting surfaces on flat roofs can lead to severe moisture accumulation
in colder regions of Europe. Thus the color of the roofing membrane appears to be an important factor for the
hygrothermal performance and moisture tolerance of certain constructions.
1. Introduction
For the results of hygrothermal simulations the boundary conditions play a significant role. A drop in surface
temperatures of flat roofs may result in moisture accumulation in the construction. For this reason it is important
to research the prevailing conditions. In this paper the thermal behavior of flat roofs is discussed with special
consideration of the effect of an existing parapet wall as an important factor for the nighttime roof temperature.
The parapet leads to retention of cold air on the roof. Some approaches are given to include the formation of a
cold pond of stagnant air in an existing hygrothermal simulation tool. Further calculations are performed to show
the influence of different colors of the roofing membrane on the behavior of a typical flat roof construction.
2. Fundamentals
2.1 Nighttime Cooling below ambient air temperatures
Long wave radiation is permanently emitted by all terrestrial objects and by some gases in the atmosphere. This
thermal radiation can reach several hundred W/m2 depending on the temperature of the emitting surface. The
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Building Physics 2008 - 8th Nordic Symposium
intensity of the atmospheric counter radiation strongly depends on the current amount of cloud cover. Typical
values at temperate latitudes for the counter radiation emitted by a cloudless sky range between about 180 W/m²
(cold, dry air) and about 400 W/m² (warm, humid air). With a closed opaque cloud cover, the sky behaves like a
Planckian emitter whose temperature is equal to the dew point temperature of the air. Building components
absorb long-wave radiation emitted from other objects, but they also emit this radiation themselves and are thus
in continuous radiation exchange with their surroundings. By day, this heat loss is not noticeable because of the
heat gained by incident solar radiation. By night, however, the loss is not compensated and usually causes
cooling of the surface below ambient air temperature ("overcooling"). This overcooling can lead to temperature
differences from the ambient air temperature of about 5 to 10 °C and more. Dew deposition and the risk of algae
and mold growth may result from overcooling.
2.2 Development of a cold pond on a flat roof
A typical construction for flat roofs is to surround the roof top by parapet walls. Such a wall forms a closed dam
around the roof where the cold and thus heavier air can not flow out. The accumulated cold air is cooling below
the ambient air temperature due to the long wave radiation of the roof surface and the interaction of the trapped
air with higher air layers. Further the effects of wind in the area protected by the parapet walls can be lower
reducing natural convection. Measurements show that the cold within the parapet walls lead to temperatures
clearly beneath the temperatures that can develop on an unobstructed flat roof surface. The data presented here
are recorded on a flat roof with a size of about 19 m by 6 m. The influence of the pond of cold air development
should appear on a bigger roof as well depending on the air flow conditions caused by wind. Ignoring this effect
during the design of a roof can lead to hygrothermal problems in the construction.
3. Measurements
On the field test site in Holzkirchen many different roofing types have been build up and the hygrothermal
behaviors have been investigated over many years. An important source for data is the weather station where in
addition to the usual recordings like temperature, relative humidity and wind speed special radiation values like
the diffuse solar radiation, the radiation in west direction, atmospheric counter radiation, the vertical counter
radiation and surface temperatures of black and white surfaces in horizontal and vertical direction are measured.
Further a new measuring device was installed at one of the flat roofs in the area. This allows measuring the
thermal behavior of the surface. In Fig. 1 in the left picture the test setup is shown; in the right picture a detail of
the sensor ladder to measure the temperature in different heights in the surrounded roof is shown. Each of the
both test areas contains of four measuring fields with different colors. A black one, a white one, a gray one (this
is the typically one used for flat roof constructions in Germany) and a reflecting one. The test areas are insulated
below the surface and separated from the roof by a ventilated air gap to assure that there is no influence to the
construction below. The one in the front is free-standing to eliminate influences from the parapet walls. The
short wave absorptivity for the different surfaces is given in Table 1. The long wave emissivity is assumed to be
around 0.9. It will be determined after the final tests. The silver surface is covered with a thin plastic layer so the
emissivity should be close to the one of the other layers. It will be replaced by a uncoated metal foil in the next
test period.
TABLE. 1: Short wave absorptivity of the different surfaces..
Surface color
Absorptivity [-]
black
0.949
grey
0.849
silver
0.130
white
0.234
The test setup in the back is surrounded by parapet walls with a height of about 40 cm. The sensor ladder in the
right picture allows measuring the temperatures at 11.5 cm below the surface top of the test setup in the back (on
the roof surface) and further in heights of 0, 10, 20, 30 and 40 cm beginning on the surface top of the test setup.
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FIG. 1: Test setup for temperature recordings. The left picture shows test patches to measure the surface
temperatures; the right picture shows the sensor ladder for measuring the stratification between the parapet
walls.
The nighttime overcooling of surfaces is shown in Fig. 2. The thicker black line is the ambient air temperature
measured two meters over the ground at our weather station close to the test setup. The other lines show the
temperatures of the different colored surfaces. In the left diagram the temperature of the free-standing surfaces
are shown (Fig. 1 right picture – test setup in the front).
FIG. 2: Surface temperatures for the black, gray, silver and white surface, free-standing an d surrounded by
parapet walls.
Examining the temperatures for the displayed five days in Fig. 2 during the night one can see the cooling below
the ambient air temperatures. There is no recognizable overcooling in the morning of the 13th of Oct. due a
cloudy night. Analysis of the climatic data for the displayed days have shown that the sky most time was cloudy
during the nights from 12th to 14th Oct. and then clear for the 15th and 16th of October. In the morning of the 15th
of Oct. a overcooling of the surfaces of about 7.3 °C down to -6.7 °C was measured. The lowest temperatures
were measured at 4 a.m.. The color of the surface is not important for the overcooling only the long wave
emissivity has an influence. During the day time a high temperature develops on the surface depending on the
color (more precisely the short-wave radiation absorptivity). In the right diagram the temperatures of the test
surfaces which are surrounded by parapet walls are shown (Fig. 1 right picture – test setup in the back).
Comparing the two diagrams the test setup surrounded by the parapet walls nearly shows the same behavior like
the free standing one except for the maximum and minimum temperatures forming. For example at the 15th of
Oct. the temperature at 4 a.m. shows a difference to the ambient air temperature of 9.0 °C down to a surface
temperature of -8.4 °C. This confirms earlier measurements where temperatures down to 10 °C beneath the
ambient air temperatures where measured on the same roof but without the test setup
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Building Physics 2008 - 8th Nordic Symposium
In Fig. 3 the measured temperatures of the sensor ladder (Fig. 1 right picture) in the same time period are shown.
Again concerning the morning of the 15th of Oct. one can recognize a temperature gradient between the free
moving air and the surface in the surrounded area. The sensor at 0 cm in the diagram is not the surface level of
the roof but the surface level of the lower test setup. The sensor is situated 11.5 cm over the top of the roof
surface.
FIG. 3: Measured temperature in different heights above the roof surface in the area protected by parapet walls.
4. Calculations
All calculations were performed with the at the Fraunhofer Institute for Building Physics developed and
validated method for simultaneous calculation of heat and moisture transport in building components WUFI®
[Künzel 1994]. The simulation program allows calculating nearly any construction using measured climatic
values as boundary conditions for example. Further it includes an explicit consideration of the different
appearing radiations. Aim of the investigations is to develop more detailed models to simulate the short term
surface conditions on flat roofs and include them into simulation tools. The models are validated using the
performed measurements.
4.1 Heat Transfer Coefficient
4.1.1 Flat roofs
For the use of the hygrothermal simulation tool WUFI a heat transfer coefficient was determined by comparing
calculated profiles with measured profiles of certain flat roofs at Holzkirchen. Only the convective part was
determined because WUFI can calculate an explicit part for radiation [Kehrer and Schmidt 2006]. The
convective part for flat roofs was determined to α = 12.8 W/m2K. This value is close to the coefficient used in
WUFI to calculate roofs α = 12.5 W/m2K which was determined for measured values below the roof tiles for an
inclined roof [Kaufmann 1995]. Fig. 4 shows the comparison of the measurement and the calculation using the
determined heat transfer coefficient for flat roofs. The determination of the coefficient for flat roofs is not
completely exact at the moment. The influence of the wind is not included yet.
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Building Physics 2008 - 8th Nordic Symposium
FIG. 4: Comparison of measurement and calculation using the determined heat transfer coefficient for flat roofs.
4.1.2 Simulation of the cold pond influence
The behavior of cold air which can not flow out though the surrounded walls is not totally investigated yet.
There are a few possibilities on how to include the factor of the insulating air layers into the used calculation
model. One possibility is to simulate it by adapting the heat transfer coefficient as well as the radiation
absorptivity and emissivity of the surface. Another possibility is to simulate the pond of cold air as one or more
air layers which insulate the surface of the roof from the ambient air. The investigations are running and are not
finished at the moment.
4.1.3 Snow and wind
Free-standing surfaces like the here discussed flat roofs offer a large contact surface for the wind. The model for
the wind dependent heat transfer coefficient used in the current version of the software was developed for
vertical construction parts. This model only uses fixed parameters and seems not to be accurate enough for the
explicit calculation of the short term variation of surface temperatures.
FIG. 5: Insulation effect of a snow layer on a flat roof. .
Snow is hard to include in simulation tools, because the appearance like the layer thickness strongly depends on
the exhibition of the researched surface like angle, wind, construction (e.g. parapet walls). A snow layer leads to
an insulation layer which keeps the temperature of the surface constant at about 0 °C. Fig. 5 shows the insulating
effect of a snow layer. The thickness of the layer is not very important. This effect can be observed at very thin
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Building Physics 2008 - 8th Nordic Symposium
layer thicknesses. Considering thin layers of snow there is a translucency so there may be a small energy
increase by absorption of solar radiation of the roof surface leading to a faster melting of the layer.
Including the snow in a hygrothermal simulation tool would not be very complicated. It is enough just to set the
temperature and the heat transfer coefficient to zero during the snow is laying on the surface. The problem is
getting the data of the snow periods. Most stations do not measure this value and it is not included in the
available climatic data files.
Not including snow layers leads to an underestimation of the prevailing temperature. This leads to a calculation
on the unfavorable side most of the time. If the mean temperatures are higher than the snow temperature during
the covered time the temperatures is more moderate than the ambient air temperature. This can lead to a lower
accumulation of condensation water than calculated.
4.2 Investigation of interstitional condensation
For determining the interstitional condensation in a typical flat roof the construction displayed in Fig. 6 was
chosen and simulated with a dark (short wave radiation absorption factor 0,9) and a bright (absorption factor 0,2)
surface at for different climatic locations.
FIG. 6: Flat roof construction.
From inside to outside the construction consists of a gypsum board, a vapor retarder with a sd-value of 20 m, a
mineral wool insulation layer with a thickness of 20 cm. On the top there is an oriented strand board and the
construction is sealed with a bituminous felt. Helsinki (Finland) is used as cold location, Holzkirchen (Germany)
and Copenhagen (Denmark) are used as moderate location and Dubai (United Arab Emirates) is used as warm
location. From this locations hourly given climatic data were used as boundary conditions for the simulation.
Table 1 shows the minimum, mean and maximum temperatures for the used climatic data.
For the investigations the indoor conditions according to the [WTA-Guideline 2004] are used. The temperature
moves in the yearly course between 20 and 22 degree Celsius while the relative humidity show values between
40 and 60 % RH. The calculations were performed for three years, starting in October.
TABLE. 2: Minimum, mean and maximum temperatures at the climatic locations.
Location
Min. Temperature [°C]
Mean Temperature [°C]
Max. Temperature [°C]
Helsinki
-30.0
4.3
28.5
Holzkirchen
-20.1
6.6
31.1
Copenhagen
-9.6
8.3
26.8
Dubai
10.9
27.0
43.1
Fig. 7 shows in the left diagram the water content in mass percent in the OSB layer and in the right diagram the
total water content of the construction. Many standards do not accept moisture contents in wooden materials
above 20 M.-% to avoid damage by rot or mould growth. The value of the total water content is not significant
but the tendency shows if there is water accumulating in the construction or if the construction has enough
potential to dry out.
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Building Physics 2008 - 8th Nordic Symposium
In Helsinki the winters are quite cold and the summers only show moderate high temperatures. In this climate
using the discussed construction the water content in the OSB layer as well as the total water content is
increasing over the years (black lines). At this location the color only show a low influence on the hygrothermal
behavior of the construction. This construction will fail after some years and is not useable at this location.
For Holzkirchen the graph for the roof with the dark roofing membrane (red solid line) shows a moisture content
in the OSB layer between 12 and 19 M.-% which is not increasing over the calculated years. The course of the
total water content is decreasing. This shows that the roof has enough potential to dry out. Concerning the
courses of the roof with the bright surface the results change. The water accumulates in the OSB layer (red
broken line). The temperatures in the construction during summer and day time are too low. The total water
content is increasing during the calculated three years. The construction has no potential to dry out. Already in
the first winter the OSB board reaches critical moisture values.
The construction in Copenhagen shows the same behavior (blue lines). Analogical to the courses of the
calculations with the climate in Holzkirchen the dark surface color leads to high enough temperatures to dry out
the construction during the summer periods. The water content in the OSB layer oscillates between about 13 M.% in summer and about 19 M.-% in winter. The course of the total water content again decreases. This
construction can be build at locations with similar climatic behavior without restrictions. On the other hand the
bright construction again shows moisture problems. The water content in the OSB layer exceed the limit of
20 M.-% during the first winter. The total water content is steady increasing. This construction can fail after a
view years only by using a bright surface color instead of a dark one.
In Dubai the construction is unproblematic. The water contents (green graphs) stay very low at this location.
During the year there is nearly no change of water content in the OSB layer (swinging between about 10 and
13 M.-%). The total water content is decreasing very fast which points to a drying of the build up water content.
In Dubai this construction can be engineered with any color of the surface. There are no restrictions due to the
hygrothermal behavior. For saving cooling energy a bright roof can be useful.
FIG. 7: Water content in the OSB layer and in the complete construction calculated with two surface colors for
four different climatic locations.
5. Summary and conclusions
In this paper measurements and a test setup are presented dealing with temperature conditions of flat roofs. The
measurements clarify the overcooling effect due to long wave radiation and due to this the building of a cold
pond on surfaces that are surrounded by parapet walls. The temperatures of the surfaces within the parapet walls
are even lower than of the unobstructed. Surface temperatures about 10 °C lower than the ambient air
temperature were measured. For unobstructed flat roofs a heat transfer coefficient is determined, not yet
including the factor wind.
Possibilities are suggested to include the formation of a pond of cold air into simulation models as well as the
influence of wind or snow. Further investigations are needed on flat roofs surrounded with parapet walls. Here
especially the air flow pattern due to wind have to be determined.
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Building Physics 2008 - 8th Nordic Symposium
The effect of the surface color by simulating a dark and a bright roof are discussed on the interstitional
condensation of a typical flat roof construction at four different locations. The calculations show that
accumulation of water occurs in the construction using a bright surface in moderate climate zones. In these
locations the bright surface reaches not very high temperatures during the day and low temperatures below the
ambient temperature during the night. The construction can not dry out. In warm regions the color does not show
a high influence on the hygrothermal behavior of the used construction. In very cold regions the roof considered
here will fail.
6. References
Kaufmann, A. (1995). Untersuchungen zur Auswahl geeigneter Materialien für den Einsatz als feuchteabhängige
Dampfbremse bei vollgedämmten Dachkonstruktionen und rechnerische Abschätzung ihrer praktischen
Feuchtewirkung. Diplomarbeit Technische Physik, Fachhochschule München, Germany
Kehrer M., Schmidt Th. (2006).Temperaturverhältnisse an Aussenoberflächen unter Strahlungseinflüssen,
Proceedings BauSIM2006, 9.-11. Okt., TU München, Germany
Künzel, H.M. (1994). Simultaneous Heat and Moisture Transport in Building Components. One- and twodimensional calculation using simple parameters. Dissertation Universität Stuttgart
WTA-Guideline (2004). WTA Merkblatt 6-2-01/ E: Simulation of heat and moisture transfer. Fraunhofer IRB
Verlag, ISBN 978-3-8167-6827-2
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