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ORIGINAL PAPER
Daytime relapse of the mean radiant temperature
based on the six-directional method under unobstructed
solar radiation
Noémi Kántor &Tzu-Ping Lin &Andreas Matzarakis
Received: 7 August 2013 /Revised: 6 November 2013/ Accepted: 7 November 2013 /Published online: 27 November 2013
#ISB 2013
Abstract This study contributes to the knowledge about the
capabilities of the popular “six-directional method”describing
the radiation fields outdoors. In Taiwan, measurements were
carried out with three orthogonally placed net radiometers to
determine the mean radiant temperature (T
mrt
). The short- and
long-wave radiation flux densities from the six perpendicular
directions were recorded in the daylight hours of 12 days.
During unobstructed direct irradiation, a specific daytime re-
lapse was found in the temporal course of the T
mrt
values
referring to the reference shapes of a standing man and also
of a sphere. This relapse can be related to the short-wave fluxes
reaching the body from the lateral directions. Through deeper
analysis, an instrumental shortcoming of the six-directional
technique was discovered. The pyranometer pairs of the same
net radiometer have a 10–15-min long “blind spot”when the
sun beams are nearly perpendicular to them. The blind-spot
period is supposed to be shorter with steeper solar azimuth
curve onthe daylight period. This means that the locations with
lower geographical latitude, and the summertime measure-
ments, are affected less by this instrumental problem. A
methodological shortcoming of the six-directional technique
was also demonstrated. Namely, the sum of the short-wave
flux densities from the lateral directions is sensitive to the
orientation of the radiometers, and therefore by deviating from
the original directions, the T
mrt
decrease on clear sunny days
will occur in different times and will be different in extent.
Keywords Mean radiant temperature .Six-directional
technique .Clear sky .Daytime relapse .Lateral directions
Introduction
The mean radiant temperature (T
mrt
) combines the thermal
effect of all short- and long-wave radiation fluxes reaching
the body into one, temperature-unit value (Fanger 1972;VDI
1998). It is defined as the uniform temperature of an imaginary
black-radiant enclosure in which the body would exchange the
same energy via radiation as in the real nonuniform environ-
ment (ASHRAE 2001). In indoor conditions, without greater
radiation asymmetry, its value is close to the air temperature
(VDI 1998). In outdoors, however, the radiation environment
around the body may be complex, and the value of T
mrt
may be
much higher than the air temperature, even up to 30 °C, as
shown by studies conducted in Germany (Mayer and Höppe
1987;Ali-Toudert and Mayer 2007;Matzarakis et al. 1999,
2007,2010), Algeria (Ali-Toudert et al. 2005;Ali-Toudert
2005;Ali-Toudert and Mayer 2006), Hungary (Gulyás et al.
2006), Sri Lanka (Johansson and Emmanuel 2006), Sweden
(Thorsson et al. 2007), and Greece (Shashua-Bar et al. 2012).
In urban areas, very different radiation conditions, and
therefore, very different T
mrt
values may be developed in the
vicinity of each other due to the different shading conditions
(Mayer and Höppe 1987; Gulyás et al. 2006;Lee et al. 2013).
Several researchers have already pointed out that daytime, in
clear sky conditions, the T
mrt
is the primary factor that governs
the course of human-biometeorological indices like
Electronic supplementary material The online version of this article
(doi:10.1007/s00484-013-0765-5) contains supplementary material,
which is available to authorized users.
N. Kántor (*)
Program of Landscape and Recreation, Research Center for the
Humanities and Social Sciences, National Chung Hsing University,
250 Guoguang Road, South Dist, Taichung City 40227, Taiwan,
Republic of China
e-mail: sztyepp@gmail.com
T.<P. Lin
Department of Architecture, National Cheng Kung University, 1
University Road, Tainan 701, Taiwan, Republic of China
e-mail: lin678@gmail.com
A. Matzarakis
Chair of Meteorology and Climatology, Alberts-Ludwigs-University
Freiburg, Hebel Str. 27, D-79104 Freiburg, Germany
e-mail: andreas.matzarakis@meteo.uni-freiburg.de
Int J Biometeorol (2014) 58:1615–1625
DOI 10.1007/s00484-013-0765-5
physiologically equivalent temperature (Höppe 1999), and
this is the main parameter that results in heat stress on sunny
summer days (Jendritzky and Nübler 1981;Mayer and Höppe
1987;Mayer 1993;Gulyás et al. 2006;Ali-Toudert and
Mayer 2007;Mayer et al. 2008;Holst and Mayer 2010;
Shashua-Bar et al. 2012;Lee et al. 2013).
To calculate T
mrt
accurately, one needs to determine all the
radiation flux densities reaching the body and also the angular
factors of the surrounding radiation surfaces (Fanger 1972).
This task would require too much time and energy in such
complex environments like the urban areas (Höppe 1992;
VDI 1998). Therefore, the researchers either simulate the
radiation conditions by numerical models, like ENVI-met
(Bruse and Fleer 1998), RayMan (Matzarakis et al. 2007,
2010), and SOLWEIG (Lindberg et al. 2008;Lindberg and
Grimmond 2011), or apply field-measurement techniques
with some assumptions and simplifications. The most popular
measurement methods are the six-directional technique sug-
gested by the VDI 3787 (VDI 1998) and the globe thermom-
eter technique described in the ISO 7726 (ISO 1985,1998).
Up today, the six-directional technique, introduced by
Höppe (1992), is considered the most accurate measurement
to obtain outdoor T
mrt
values. Instead of measuring the indi-
vidual radiation flux densities and determining the countless
corresponding angular factors to them, this method simplifies
the surrounding environment into six perpendicular parts: four
lateral directions and the upper- and lower-hemisphere. It
measures the radiation fluxes only from this six directions
and orders simple angular factors to them. The most reliable
way to get the necessary short- and long-wave fluxes is to
measure them simultaneously from the six directions; howev-
er, this requires the usage of six parano- and six pyrgeometers,
or three net radiometers (Ali-Toudert 2005;Ali-Toudert et al.
2005;Ali-Toudert and Mayer 2007;Thorsson et al. 2007),
which makes the measurements very expensive and rather
immobile. Other researchers apply only one rotatable net
radiometer (Streiling and Matzarakis 2003;Kántor et al.
2012a,b) or a rotatable pyrano–pyrgeometer pair (Höppe
1992;Oliveira and Andrade 2007;Andrade et al. 2011).
Because of the lighter instrumentation, the rotatable version
allows mobile measurements; however, it serves with coarser
temporal resolution of T
mrt
. In frame of the KLIMES project,
researchers used both the three net radiometer version, and
took mobile recordings with a measurement cart equipped
with a rotatable pyrano–pyrgeometer combination (Holst
and Mayer 2010,2011;Lee et al. 2013).
The six-directional method served also as an essential part
of on-site thermal comfort measurements, which were com-
pared to subjective thermal comfort assessments of visitors on
selected urban public places (Oliveira and Andrade 2007;
Andrade et al. 2011;Kántor et al. 2012a,b). The separate
measurement of the short- and long-wave fluxes make it
possible to take different absorption coefficients into account
in the short- and long-wave domain, similar to the clothed
human body. In addition, because of the directional weighting
factors, this technique allows to represent the shape and pos-
ture of the human body. Therefore, this method is treated as
the most accurate one in the field of outdoor thermal comfort
measurements (Höppe 1992;Thorsson et al. 2007).
In contrast to the models, which work with many assump-
tions, the major advantage of measurements is that they reflect
the actual thermal conditions. Therefore, six-directional field
measurements are often used to validate the results of numer-
ical simulations. For example, T
mrt
values from the RayMan
model have been compared to those derived from six-
directional measurements in Germany (Matzarakis et al.
2007,2010), Sweden (Thorsson et al. 2007), and Portugal
(Andrade and Alcoforado 2008), and the ENVI-met has been
also validated via on-site measurements in Germany (Ali-
Toudert 2005;Ali-Toudert and Mayer 2007). Lindberg et al.
(2008) compared the results of SOLWEIG model with mea-
surements in Sweden, while Lindberg and Grimmond (2011)
used measurement data from Sweden and Germany for the
validation. Moreover, the methodological basics of this simu-
lation tool are the same, i.e., modeling the radiation fluxes from
six orthogonal directions (Lindberg et al. 2008). Not only the
models but also the other popular measurement technique
(using globe thermometer) should be validated with the six-
directional method. Thorsson et al. (2007) validated the globe
technique via six-directional measurements. They used not the
standard black copper sphere (ISO 1985,1998), but a smaller,
gray-painted acrylic globe, more suitable for outdoor
measurements.
In the course of a study, which was aimed to validate the
standard black-globe with the six-directional method in
Taiwan, a special “midday-relapse”was found in the daily
course of the T
mrt
based on the six-directional technique
during clear sky conditions. The present study objects to:
&Show this special feature of the six-directional measure-
ments in Taiwan
&Compare for examples all over the world
&Identify the source of the relapse including instrumental
and methodological issues
&Discuss the potential effects of the identified shortcomings
in terms of characterizing the short-wave radiation fields.
Materials and methods
Radiation measurements in Taiwan
The six-directional radiation measurements were carried out
in the National Formosan University, Huwei, Taiwan (23.7°
N, 120.43° E, 30 m asl). One-minute averages of the short-
1616 Int J Biometeorol (2014) 58:1615–1625
and long-wave flux densities [K
i
,L
i
(W/m
2
)] from six per-
pendicular directions (i:E, East; S, South; W, West; N, North:
↓, upper hemisphere; ↑, lower hemisphere) were measured
separately with three orthogonally arranged net radiometers.
Kipp&Zonen CNR1 net radiometer was used for the two
vertical directions, and Hukseflux NR01 net radiometers were
used for the four lateral directions. In correspondence to the
gravity center of a standing man, the sensors were mounted at
1.1-m height (Mayer and Höppe 1987).
The individual radiation flux densities were weighted and
summed to get the total radiation flux density absorbed by the
human body [S
rad
(W/m
2
)] from which the T
mrt
was
expressed:
Srad ¼X
i¼1
6
WiakKiþalLi
ð1Þ
Tmrt ¼ffiffiffiffiffiffiffiffi
Srad
alσ
4
r−273:2¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
i¼1
6
WiakKiþalLi
ðÞ
alσ
4
v
u
u
u
t−273:2ð2Þ
For short- and long-wave absorption coefficients (a
k
and
a
l
), the commonly used 0.7 and 0.97 values were adopted, as
these represent the average absorptive capacity of the clothed
human body (Höppe 1992;VDI 1998). Selecting different
values for the W
i
directional weighting factors allows to
consider different reference shapes, e.g., a standing man and
a sphere. In the latter case, all fluxes were weighted identically
with 0.167, while in the “standing man”case, the role of the
lateral fluxes became relatively greater than the vertical ones
according to the W
i
of 0.22 and 0.06, respectively.
The investigations were carried out in the daylight hours of
12 days, mainly on the top of the university without consid-
erable horizon limiting objects, i.e., with a Sky View Factor
(SVF) near to 1. To show the special characteristics in the
temporal course of the T
mrt
and the radiation flux densities
observable during clear sky conditions, this study uses the
data measured on 2011–01–27 between 0644 and 1708 hours
(Chinese Standard Time).
Model calculations
To increase the knowledge about the six-directional technique,
with special emphasis on the probable shortcomings we found
in clear sky conditions, additional short-wave radiation calcu-
lations were made. Without horizon limiting objects and
clouds, the model calculations have the advantage over the
measurements that they offer clear picture about the behavior
of the radiation flux densities reaching the body. The calcula-
tions were completed for the location of the measurements
(Huwei, Taiwan, 23.7° N, 120.43° E, 30 m asl). To simply
represent the annual variability of the radiation conditions, we
choose four specific days: Spring Equinox (2011–03–20),
Summer Solstice (2011–06–21), Autumn Equinox (2011–
09–23) and Winter Solstice (2011–12–22).
Sun elevation (elev.) and azimuth (azim.) data were obtain-
ed from the RayMan model (Matzarakis et al. 2007,2010)in
1-min resolution together with the data of global (G), diffuse
(D), and direct (I) radiation. The simulated Gvalues corre-
spond to the short-wave radiation flux densities from the
upper hemisphere: K↓=G. The reflected radiation, i.e., the
short-wave flux densities from the lower hemisphere was
calculated as K↑=albedo K ↓by assuming a mean surface
albedo of 0.2. The direct radiation flux densities on a perpen-
dicular surface (I
⊥
) were calculated according to:
I⊥¼I=sin elev:ðÞ ð3Þ
The lateral short-wave flux densities (K
→
)fromanarbi-
trary lateral direction were calculated according to the follow-
ing general equations (based on Lindberg et al. 2008;simpli-
fied for SVF=1 condition):
K→¼DþI⊥cos elev:ðÞsin azim:→
ðÞif 0<azim:→<180
ð4Þ
K→¼Dif 180<azim:→<360ð5Þ
The azim.
→
means the modified azimuth angles—modified
according to the specific →lateral direction what we are talking
about. In the case of the Eastern direction, there is no need for
modification: azim.E=azim. However, in the case of any other
lateral direction, there is a need for adjustment: azim.S =azim.–
90°, azim.W=azim.–180°, and azim.N= azim.–270° for the
Southern, Western, and Northern directions, respectively.
Theoretically, the six-directional technique should not be
sensitive to the exact orientation of the lateral radiometers as
long as the criterion of perpendicularity satisfies. This means
that the (absorbed) sum of the short-wave flux densities
reaching the body from N–E–S–Wdirectionsshouldbeequal
to the sum of them from any other four perpendicular lateral
directions. To verify this assumption, we have analyzed these
sums not only for the original N–E–S–W orientation (0°
deviation), but for the NNE–ESE–SSW–WNW (22.5° devia-
tion) and NE–SE–SW–NW (45° deviation) orientations, too.
Results and discussion
Radiation conditions on a clear day in Taiwan
The 1-min data of 2011–01–27, a clear-weather measurement
day, were used in order to show the temporal characteristics of
the radiation environment influenced by the apparent path of
the sun, i.e., elevation and azimuth angles. The sun elevation
and azimuth angles were calculated with the RayMan model
(Matzarakis et al. 2007,2010).
Int J Biometeorol (2014) 58:1615–1625 1617
Corresponding to the wintertime measurement on 2011–
01–27, the daylight period was somewhat shorter than the half
of the day, but because Huwei locates on the Tropic of Cancer,
it is still relatively long, ca. 11 h. The highest daily sun
elevation angle at the solar noon (1211 hours) was 47.8°,
and the corresponding maximal value of the simulated global
radiation (G)was830W/m
2
(Fig. 1a). Despite the totally clear
sky conditions on the sample day, the measured values of the
global radiation (K↓; measured by the upper pyranometer)
were consistently somewhat lower than the simulated G
values. This can be attributed to that we have not changed
the RayMan's default turbidity value, which depends only on
the date but not on the geographical location. For 2011–01–
27, it was 1.5, which was probably somewhat lower (resulting
higher simulated global radiation values) than the real turbid-
ity in Huwei.
The air temperature ranged from 13 to 20 °C, meaning 7 °C
daily amplitude. The T
mrt
values calculated from the measured
radiation flux densities showed much greater temporal vari-
ability (Fig. 1b). Even though they were around 10 °C at
sunrise, they quickly exceed the 30 °C and remained above
this from ca. 0730 to1650 hours. The highest values occurred
during the midday period and were around 60 °C, which
means that the T
mrt
values were up to 40 °C higher than the
air temperature. This result corresponds to the findings of
other studies conducted in clear weather conditions
(Matzarakis et al. 1999;Ali-Toudert et al. 2005;Gulyás
et al. 2006; Johansson and Emmanuel 2006; Ali-Toudert and
Mayer 2007;Thorsson et al. 2007;Mayer et al. 2008;
Shashua-Bar et al. 2012).
There are some remarkable differences between the T
mrt
values characterizing the radiation load of a spherical body
(T
mrt-sp.
) and a standing man (T
mrt-st.
). The latter was clearly
higher before 1030 and after 1400 hours, while around mid-
day, the spherical shape had greater values (Fig. 1b). This can
be attributed to the different weighting factors: in the case of
the standing shape, the role of the lateral fluxes became
considerably greater than the vertical ones, which results in
T
mrt-st.
values higher than T
mrt-sp.
during the time of lower sun
elevation.
In the cases of both reference shapes, there is a very clear
decrease around 1240 hours; this is however more pro-
nounced in T
mrt-st.
(Fig. 1b). Similar T
mrt
decreases were
found also on other measurement days (6 from the 12 days),
which could be also characterized by free (or relatively free)
horizon and clear sky conditions.
Individual radiation flux densities on a clear day in Taiwan
To reveal the background of this daytime T
mrt
relapse, Fig. 2
illustrates all of the individual short- and long-wave radiation
flux densities on 2011–01–27. Keep in mind, that according to
real orientation of the instrument on this day, the lateral flux
densities indexed with E, S, W, and N are meaning the
radiation flux densities measured by the radiometers facing
to 101.5, 191.5, 281.5, and 11.5°, respectively. This 11.5°
deviation angle explains that the daily maximum of K
s
oc-
curred around 1300 hours, i.e., after the daily maximum of the
global radiation K↓at local solar noon (Fig. 2a). It explains
also that the “E-faced”pyranometer got direct radiation for
longer period than the “W-faced”one, and measured higher
values. Due to the lower sun elevation angles in winter, the
maximal K
s
values exceeded slightly the maximum of K↓
(Fig. 2a).
As the measurements were conducted on a roof without
significant horizon limitations, the long-wave flux densities
from the four lateral directions (L
E
,L
S
,L
W
,andL
N
)were
absolutely similar to each other, and did not show remarkable
temporal fluctuations (Fig. 2b). The atmospheric counter ra-
diation L↓(measured by the upper pyrgeometer) was clearly
lower. As the surface of the roof was warmed up by the
absorbed short-wave radiation during the day, it caused
Fig. 1 a Sun path properties on 2011–01–27 in Huwei together with the simulated (G)andmeasured(K↓) global radiation values. bThe six-directional
technique-based mean radiant temperature for a spherical shape (T
mrt-sp.
) and for a standing man (T
mrt-st.
), as well as their differences (delta T
mrt
=T
mrt-sp.
−T
mrt-st.
)
1618 Int J Biometeorol (2014) 58:1615–1625
gradually higher amount of emitted long-wave radiation L↑
(measured by the lower pyrgeometer). Contrary to the short-
wave flux densities, which were quite different and could be
characterized with spectacular temporal patterns (Fig. 2a), the
long-wave flux densities showed relatively constant values
during the day, as well as they were more similar to each other
(Fig. 2b).
In the course of the T
mrt
calculation, using different ab-
sorption coefficients (0.7 for the short- and 0.97 for the long-
wave domain), the role of the long-wave flux densities be-
came relatively greater than the short-wave flux densities.
Additionally, due to the directional weighting factors (W
i
)
all flux densities became lower in magnitude. There are,
however, remarkable differences between the two reference
shapes. Using the W
i
=0.167 for all directions in the spherical
reference shape, the resulted absorbed radiation flux densities
showed similar temporal tendencies as the originally mea-
sured ones. However, by representing a standing person the
relative importance of the lateral flux densities grows signif-
icantly to the detriment of the vertical ones.
Combined radiation flux densities on a clear day in Taiwan
To clearly illustrate the overall effect of the different W
i
factors on the resulted T
mrt
values, Fig. 3displays the total
absorbed short- and long-wave flux densities separated ac-
cording the vertical and lateral directions. The sum of the
absorbed flux densities from the four lateral directions is
higher than the sum of them from the two vertical directions
in every cases of wavelength or reference shape. Additionally,
the order of importance is also the same in the short- (Fig. 3a)
and long-wave (Fig. 3b) domain; in ascending importance:
vertical standing, vertical spherical, lateral spherical, and
lateral standing. That is, the sums of the absorbed radiation
flux densities from vertical and lateral directions are
closer to each other in the cases of a spherical reference
shape, while in the “standing man case”the sum of the
lateral fluxes is more important.
There are two other interesting characteristics on this fig-
ure. Firstly, the magnitude of the absorbed long-wave flux
densities (Fig. 3b) overcomes to the corresponding absorbed
short-wave flux densities (Fig. 3a) in every case. Secondly,
while the former (Fig. 3b) are more stable with time, the latter
(Fig. 3a) showed clear time dependence during the day. The
most interesting temporal variability can be seen in the cases
of the lateral short-wave sums (K
lat
*
): a clear decrease around
1240 hours (Fig. 3a), which coincides exactly the time of the
formerly discovered T
mrt
relapse (Fig. 1b), and as the T
mrt-st.
relapse was more pronounced than the T
mrt-sp.
(Fig. 1b), the
K
lat
*
decrease is also more obvious in the case of the standing
shape (Fig. 3a).
Through the analysis of the total absorbed short- (K*) and
long-wave (L*) flux densities (Fig. 4a), we can realize that, in
the long-wave domain, there is a slight and almost constant
difference between the two shapes. Delta L*isaround−5W/
m
2
, indicating that the standing human body absorbs all day
long higher amount of long-wave radiation than the spherical
shape (Fig. 4b). On the contrary, the difference between the
two shapes from the point of view of K*ismuchbiggerin
absolute values, and it shows remarkable time dependence;
delta K*rangesbetween−17.3 and 22.6 W/m
2
(Fig. 4b). This
is because the standing shape absorbs more short-wave radi-
ation during lower sun elevations and less during higher sun
elevations. In our sample day, the change points (delta K*=0)
occurred at 1001 hours (elevation= 37.2°) and at 1426 hours
(elevation=36.5°). The greatest negative differences (delta
K*≤−16.5 W/m
2
; standing shape absorbed more radiation)
were found between 0752 and 0826 hours and between 1559
and 1628 hours. The greatest positive differences (delta K*≥
22 W/m
2
; spherical shape absorbed more radiation) occurred
around 1234–1244 hours, after the local solar noon.
The difference between the total absorbed all-wave radia-
tion flux densities (delta S
rad
) shows similar temporal patterns
Fig. 2 The measured original ashort- and blong-wave flux densities on 2011–01–27 in Huwei
Int J Biometeorol (2014) 58:1615–1625 1619
than the delta K*, with the same time intervals of the positive
and negative extremes (Fig. 4b). However, because of the
nearly constant negative delta L* values, the time period when
the spherical shape absorbed more all-wave radiation (positive
delta S
rad
) is shorter than the corresponding time interval for
the positive delta K*.
As a consequence of the former findings, despite the fact
that the long-wave flux densities are primarily responsible for
the magnitude of the daytime T
mrt
values, the specific tempo-
ral characteristics of T
mrt
are governed by the short-wave flux
densities (see also by Holst and Mayer 2010), and these are
responsible mainly for the differences between the T
mrt-st.
and
T
mrt.sp.
(Fig. 1b). The interesting T
mrt
relapse around 1240
hours (Fig. 1b) can be explained by the decrease of the
absorbed short-wave radiation (K*) at that time (Fig. 4a),
which in turn is attributable to the local minimum of the
short-wave flux densities absorbed from the lateral directions
(K
lat
*
;Fig.3a). More specifically, this special shape can be
traced to the short-wave flux densities measured by the East-
and West-faced pyranometers (K
E
and K
W
; Fig. 2a).
T
mrt
relapse in other studies
Besides 2011–01–27, T
mrt
relapses were found on every
measurement days, which could be characterized with free
(or relatively free) horizon and clear sky conditions (Table 1).
By reviewing the literature, similar T
mrt
decreases were found
in Swedish (Thorsson et al. 2007) and German (Ali-Toudert
and Mayer 2007;Mayer et al. 2008) studies, which were
based also on six-directional measurements during clear-
weather conditions (Table 1). The T
mrt
relapses in the
Swedish study (Thorsson et al. 2007) are as obvious as the
presented one in Taiwan because both analyzes were based on
1-min data. However, due to the hourly mean values, the
midday T
mrt
relapses are not so clear in the German studies
Fig. 3 Sum of the absorbed ashort-wave (K
…
*) and blong-wave (L
…
*) radiation flux densities from vertical (vert) and lateral (lat) directions for a
spherical shape (sp.) and a standing man (st.) on 2011–01–27 in Huwei
Fig. 4 a Sum of the totally absorbed short- (K*) and long-wave (L*)
radiation flux densities for a spherical shape (sp.) and a standing man (st.).
bThe differences between the reference shapes (delta=sp.−st.) in terms
of the totally absorbed short-wave (delta K*), long-wave (delta L*), and
all-wave (delta S
rad
) radiation on 2011–01–27 in Huwei
1620 Int J Biometeorol (2014) 58:1615–1625
and look more like break points in the temporal courses of the
T
mrt
(Ali-Toudert and Mayer 2007; Mayer et al. 2008).
Based on our findings, the T
mrt
relapse can be connected to
the absorbed short-wave flux densities (K*), which have a
daytime local minimum at the same time (Fig. 4a). A study
from Germany explained this midday minimum in K*with
the smaller irradiated body surface at the time of the highest
sun elevation (Ali-Toudert 2005;Ali-Toudert and Mayer
2007). However, if this explanation would be absolutely suf-
ficient, then the daytime relapse would be occurred only in the
case of the “standing man”reference shape and not in the case
of the spherical. On the other hand, according to this explana-
tion, the T
mrt
relapses (or breakpoints) should have occurred
only at the time of the local solar noon.
In fact, the T
mrt
relapses occurred sometimes before the
solar noon and sometimes after that, in relation to the devia-
tion angles of the instruments compared to the original N–E–
S–Wdirections(Table1). When the instruments' deviation
angle was positive (eastwards compared to N), then the
breakpoints occurred after the solar noon; in the other case,
before that. It should be noted that this pattern is not so
unequivocal in the case of the German studies with 1-h reso-
lution and without information about the orientation.
Moreover, on two of the summertime measurements (2006–
07–26, Sweden; 2007–06–19, Germany), additional
breakpoints have been found in the daytime courses of the
T
mrt
(Table 1).
Instrumental explanation of the relapse
According to Thorsson et al. (2007), these T
mrt
patterns on
clear days are attributable to the orthogonal instrument setup,
i.e., the increased mean instrumental error with high angles of
incidence. This explanation seems to be closer to the reality,
but it requires further clarification. Therefore, we investigated
the short-wave fluxes more closely, taking special care on the
instrumentation’s physical characteristics. So far, based on the
time course of the T
mrt
on clear days, we can find the
following:
&The interesting T
mrt
relapses/breakpoints are attributable
to the local minimum of the short-wave flux densities
absorbed from the lateral directions (K
lat
*
; Fig. 3a). More
specifically, they seem to be connected with the short-
wave flux densities measured by the East- and West-
faced pyranometers (K
E
and K
W
;Fig.2a).
&The time of T
mrt
decreases appear to be connected to the
exact orientation of the instruments, i.e., the deviation
angles from the original N–E–S–W directions (Table 1).
Tabl e 1 List of six-directional
measurementdayswithobserv-
able daytime T
mrt
relapse: present
study in Taiwan and earlier stud-
ies in Sweden and Germany
a
Based on Figs. 4 and 10 of
Thorsson et al. 2007
b
BasedonFig.10ofAli-Toudert
and Mayer 2007
c
Based on Fig. 4 of Mayer et al.
2008
Location Measurement place Date Solar
noon
hours
Instrument's
deviation (°)
Time of the
daytime T
mrt
relapse (hours)
Taiwan, Huwei
(23.7 °N)
Roof 2010–12–07 1151 16 1250
2010–12–29 1201 −3 1145
2011–01–27 1211 11.5 1240
2011–02–09 1213 9.5 1235
2011–03–03 1211 20 1235
Open space 2011–04–09 1200 0 1200
Sweden, Göteborg
(57.7 °N)
largeopensquare
a
2005–10–11 1158 −20 0900
2006–07–26 1218 −20 1130 (1620)
Germany, Freiburg
(48 °N)
E-W oriented street,
S-oriented sidewalk
b
2003–07–14 1234 0 (?) 1300
2003–07–15 1234 0 (?) 1300
NW-SE oriented street,
SW-oriented sidewalk
c
2007–06–19 1230 0 (?) 1300 (1700)
Fig. 5 Explanatory figure for the daytime minimum of the sum of the
lateral short-wave fluxes from E (K
E
)andW(K
W
):Thereareacoupleof
minutes when neither of the pyranometers—facing away from each
other—gets direct solar radiation. The exact time interval of this
“pyranometer blind spot”corresponds to the time when the corrected
azimuth angle is 180°±2.5°, i.e., when the sun shines from the direction
of the axis of the net radiometer
Int J Biometeorol (2014) 58:1615–1625 1621
We try to find a possible instrumental explanation for these
results, taking the 2011–01–27 measurement day as an exam-
ple. The Fig. 5illustrates in detail the time period of the day
when the T
mrt
relapse occurred. There are a couple of minutes
around 1240 hours when both of the K
E
and K
W
curves are
quite flat, meaning that neither of the E- nor the W-facing
pyranometers got direct solar radiation that time. The figure
displays also the original azimuth angles and the so-called
corrected azimuth angles. The latter were calculated by
subtracting the instrument's deviation angle from the original
azimuth angles.
The specific time interval, when both K
E
and K
W
were
without direct radiation, can be concluded based on the time
when the corrected azimuth angle was between 177.5 and
182.5° (Fig. 5). That is, instead of the 2×180° angular view
of the pyranometers facing in opposite directions, there is a 5°-
wide “blind-spot”. By analyzing the other clear-sky measure-
ment days, the findings verified this explanation. The time of
the day when the “critical time interval”(both K
E
and K
W
are
without direct radiation) occurred is affected by the instru-
ment's actual orientation: at positive (Eastwards) deviation
angle, this interval occurred after the solar noon, and at neg-
ative deviation, before noon. Moreover, in the cases when the
(corrected) azimuth curve was steeper around 180°, the critical
time interval was shorter, as the sun went through quickly on
the “pyranometer blind spot”. This finding means that because
of this instrumental shortcoming, the winter-time measure-
ments have bigger failure than the summer-time measure-
ments, as the winter-time azimuth curves are flatter during
the day (Appendix 1(a) series). Moreover, in the cases of
geographical locations closer to the Poles like Göteborg, with
flatter daytime azimuth curves (Appendix 2(a) series), the
problem of the equipment may be more serious all year long.
It should be noted that these results were found in the case
of Hukseflux net radiometers. It would be worthwhile to
examine the existence and measure of these “pyranometer
blind spots”in the cases of other constructions, e.g.,
Kipp&Zonen CNR-1 and CNR-2 net radiometers, as well as
single rotatable pyranometer–pyrgeometer pairs.
The illustrated instrumental problemmay occur not only in
the cases of K
E
–K
W
, but K
S
–K
N
pairs, too. Assuming 0°
instrumental deviation, the latter situation is possible only in
the summer half of the year, i.e., when the sun rises Northeast
and sets Northwest, and therefore the North-facing
pyranometer also get some direct radiation. This offers an
explanation also for the finding that in the German and
Swedish studies there was another, second T
mrt
breakpoint
on the summertime measurement days (Table 1).
Methodological explanation of the relapse
In spite of that the pyranometer-related instrumental short-
coming of the six-directional technique seems to elucidate
well the daytime T
mrt
relapse on clear days, it is not a
completely satisfactory explanation. Namely, if problems
would exist only from instrumental point of view, than the
model simulations based on the six-directional philosophy
would be free from that. Indeed, by reviewing the literature,
we can discover the daytime T
mrt
decrease also on the figures
of Swedish researchers (Lindberg et al. 2008;Thorsson et al.
2007), who modeled the radiation conditions by SOLWEIG.
The model simulates the radiation flux densities on the theo-
retical basis of Höppe 1992, i.e., from six perpendicular
directions. In spite of that the equations for short-wave flux
densities are not affected by the pyranometer problem, the
T
mrt
relapses are clearly noticeable, and the time of those are
related to the orientation of the simulations. Therefore, we can
conclude that the problem is rather methodologically and may
be associated with the restricted number of sides from which
the radiation components are considered (measured or
modeled).
To verify the former assumption, radiation calculations
were carried out for four special days of a year (Spring
Equinox, Summer Solstice, Autumn Equinox, and Winter
Solstice) with three different orientations. The aim was to
identify the differences between the absorbed short-wave flux
densities (K*) modeled in the case of the original N–E–S–W
orientation (0° deviation) and in the cases of the lateral direc-
tions, which deviate with 22.5 and 45° from that (Fig. 6). In all
three cases, the vertical flux densities were the same. The
calculations were performed not only for Huwei (23.7° N)
but also for the location of Göteborg (57.7° N), in order to
ensure the representativeness in spatial manner, and taking
into account quite different sun path and radiation conditions
(Appendices 1and 2).
As the hourly temporal resolution of the SOLWEIG model
is too rough, we performed the 1-min short-wave radiation
calculations manually according to the published equations of
Lindberg et al. (2008). The necessary data of sun elevation
and azimuth,as well as global, diffuse, and direct radiation for
the selected four days and two geographical locations were
obtained from the RayMan model. Figure 6illustrates
the final results in terms of the short-wave flux densities
absorbed by a standing man (K
st.
*
) on the four special
days in Huwei, while Appendix 1displays the details
(vertical and lateral sums) also for the standing human
and for the spherical shape. Appendix 2illustrates the
same series for Göteborg.
The different orientation have resulted in dissimilar time
courses of K
st.
*
(Fig. 6), and even K
sp.
*
, which in turn are
derived from the absorbed lateral short-wave flux densities
(K
lat
*
;Appendices1and 2). The maximal values of K
st.
*
may be
similar sometimes (Table 2); nevertheless, the most obvious
differences are between the shapes of the K
st.
*
curves, namely,
the number and timing of daytime minimums or breakpoints
(Fig. 6, Appendices 1and 2). In absolute values, the greatest
1622 Int J Biometeorol (2014) 58:1615–1625
discrepancies were found between the 0 and 45° K
st.
*
,
exceeding even 50 W/m
2
during the Winter Solstice in
Huwei and during the Spring Equinox in Göteborg
(Table 2). However, if we analyze the delta K
st.
*
values relative
to the actual values of the 0° K
st.
*
, we can notice the greatest
differences at the Equinox days in the cases of both cities;
meaning more than 40 % differences between the 0 and 45°
cases (Table 2).
Tabl e 2 Differences between the short-wave radiationflux densitiesabsorbed by a standing man (K
st.
*
) in the cases of different orientation (N–E–W–S:
0° deviation, NNE–ESE–SSW–WNW: 22.5° deviation, NE–SE–SW–NW: 45° deviation) at different days of the year in Huwei and Göteborg
Location Day Maximal K
st.
*
(W/m
2
) Maximal delta K
st.
*
(W/m
2
) Maximal delta K
st.
*
(%)
0°
deviation
22.5°
deviation
45°
deviation
022.5°
deviation
045°
deviation
022.5°
deviation
045°
deviation
Taiwan, Huwei (23.7° N) Spring Eq. 211 231 226 −26; 36 −30; 36 −31; 17 −42; 21
Summer St. 213 231 231 −19; 13 −20; 0 −9; 23 −10; 4
Autumn Eq. 223 234 227 −20; 30 −24; 31 −32; 13 −43; 15
Winter St. 238 227 211 −30; 41 −53; 59 −25; 21 −33; 25
Sweden, Göteborg (57.7° N) Spring Eq. 229 232 231 −38; 38 −51; 50 −38; 18 −40; 22
Summer St. 230 233 228 −25; 26 −34; 33 −14; 13 −19; 30
Autumn Eq. 221 229 231 −30; 30 −41; 38 −31; 14 −41; 18
Winter St. 149 172 179 −33; 30 −45; 14 −25; 21 −31; 25
Fig. 6 Absorbed short-wave flux densities by a standing man (K
st.
*
)inthe
cases of three orientations (N–E–W–S: 0° deviation, NNE–ESE–SSW–
WNW: 22.5° deviation, NE–SE–SW–NW: 45° deviation), as well as the
delta K
st.
*
between the 0 and 22.5° and the 0 and 45° cases. The calcula-
tions were carried out for aSpring Equinox, bSummer Solstice, c
Autumn Equinox, and dWinter Solstice
Int J Biometeorol (2014) 58:1615–1625 1623
Based on our recent findings, in contrast to the previous
assumptions, the six-directional technique (measurements and
modeling too) is quite sensitive to the lateral orientation; i.e.,
we get different results when we taking the investigations with
different orientations. This is because the “standing man”
reference shape is in fact a rectangular column and not a
rotationally symmetric cylinder. As well as, the spherical
reference shape is actually a cube, according to the six-
directional technique. Because of the edges of the reference
shapes, we cannot expect identical results in the cases of
different orientations.
There is a theoretical solution for the discovered problem,
which could be useful in the cases of the model simulations.
By solving the equations for the lateral flux densities consid-
ering 90 different orientation cases (0–89° deviation) and by
averaging the resulted K* values, we could achieve the values
represent really a rotationally symmetric cylinder, which is a
closer approximation to the standing human body.
Conclusions
In the frame of a survey series in Huwei (Taiwan), radiation
measurements were carried out from the six perpendicular
directions of a space to determine the T
mrt
. A specific relapse
was found in the temporal course of the T
mrt
values around
midday, but not exactly at the time of the local solar noon.
This decrease was noticeably both in the cases of a standing
man (T
mrt-st.
)andaspherical(T
mrt-sp.
) reference shape. We
find instrumental and methodological shortcomings.
The detailed analysis for 2011–01–27 corresponded with
already existing studies about the daytime T
mrt
relapse and
that it can be related to the short-wave radiation fluxes
reaching the body from the lateral directions. The time period
about the occurrence of the T
mrt
decrease can be partly ex-
plained by an instrumental shortcoming of the six-directional
technique (pyranometer blind spot).When the sun shines from
the direction which is nearly perpendicular for both
pyranometers of the same net radiometer, there are a couple
of minutes (5–15 min) when neither of the pyranometers gets
direct radiation. Assuming 0° deviation angle form North (i.e.,
N–E–S–W–facing lateral pyranometers) and free horizon (at
least free Southern hemisphere), the problem will occur every
clear-sky time in the case of the E–W facing pyranometer
pairs. In summer time, the relapse will occur also in the caseof
the N–S facing pyranometer pairs, provided the direct sun
beams are not obstructed by the surrounding objects. The time
of the “pyranometer blind spot”period is supposed to be
shorter when the solar azimuth curve is steeper during the
daylight period. In the case of Huwei, this means that the
summertime measurements are more accurate. On the other
hand, the problem gets bigger in wintertime and in the case of
locations with higher geographical latitude.
In addition, a methodological problem of the six-
directional technique was also discovered, which explains
the patterns that have been seen also in earlier studies.
Namely, the (absorbed) sum of the short-wave flux densities
from the four lateral directions (K
lat
*
) is very sensitive to the
orientation of the radiometers, and therefore, by deviating
from the original four cardinal directions, the K* and the
T
mrt
relapse on clear sunny days will occur in different times
and will be different in extent. In terms of absorbed short-
wave flux densities (K*), the biggest differences were found
between the original instrument orientation and the case when
the instruments deviate 45° from that. On the days of the
Equinoxes, the K* difference may be up to 40 %.
Both the instrumental and the methodological shortcom-
ings of the six-directional technique need further and deeper
research (measurements and simulations, too) in order to
quantify the magnitude of the effects of these specific prob-
lems on the resulted T
mrt
. The importance of this research
topic can be confirmed by that the six-directional technique is
treated as the most accurate outdoor method to determine the
T
mrt
, and it is used to validate the other measurement tech-
niques (e.g., with globe thermometers) and the outcomes of
model simulations. The validation is necessary as, during clear
weather conditions, the T
mrt
is the main influencing factor of
state-of-the-art thermal indices for the quantification of ther-
mal comfort and heat stress issues.
Acknowledgments The authors would express a special thank for the
sponsorship of the Research Center for the Humanities and Social Sci-
ences at the National Chung Hsing University.
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