Journal of Heat Island Institute International Vol. 9-2 (2014)

Academic Article

Modification of physiologically equivalent temperature
Yung-Chang Chen*1

Andreas Matzarakis*1*1 Chair of Meteorology and Climatology, Albert-Ludwigs-University Freiburg
Corresponding author: Yung-Chang Chen, yung-chang.chen@meteo.uni-freiburg.de
ABSTRACT
Thermal indices have been applied in the field of human-biometeorology since several decades (e.g. forenvironmental evaluations, climate assessment for tourists, as well as assessments of climate change).
Physiologically Equivalent Temperature (PET), which is based on a time-saving and two-node model, is a
widely applied thermal index. However, variations in air humidity and clothing insulation show weak influence
on PET. Other thermal indices also show limitations in their applicability. Thus, this study aims to develop a
modified PET (mPET) on thermo-physiological mechanisms and clothing factors for universal applications in
all climate zones.
Physiological thermoregulation of mPET is adapted to a simple multi-segment body model including a
blood pool element and a bio-heat transfer principle instead of the two-node human body model used in PET.
Furthermore, a multi-layer clothing model with clothing insulation and vapour resistance is established formPET. It replaces the single-layer clothing model applied in PET. Due to those two modifications, mPET canevaluate thermal conditions influenced by vapour pressure and clothing insulation.
Key Words : Physiologically Equivalent Temperature, Modified Physiologically Equivalent Temperature, Thermal index

model, which is Fiala’s thermoregulation model, and more than

1. Introduction

1000 simulations cases. The limitations of this regressionThermal indices are essential evaluating factors in the field offunction are that the air temperature is from -50 °C to 50 °C,

human-biometeorology, especially for assessments of thethe wind speed is from 0.5 m/s to 17 m/s at the height of 10 m,

thermal conditions intermediating human and environments.

the mean radiant temperature is 50 °C below than the air

Recently, Physiologically Equivalent Temperature (PET) (1) (2)temperature to 70 °C above than the air temperature, andwhich is a thermal index based on a 2-node thermoregulationrelative humidity is from 0 % to 100 % or 0 hPa to 45 hPa. Thismodel is the widest applied to evaluate thermal conditions.

limitation leads to restricted applications of the UTCI on the(4)evaluation of some extreme thermal conditions. PET and UTCIand climate changing according to the PET and the otherhave been both restricted on the evaluation of the influence onparameters. However, PET predicts weak influence of thethe some changing of biometeorological factors and also lackvariance of clothing and humidity on the assessments ofof the influence of clothing behavior. Therefore, this study aims

thermal conditions. Moreover, the Universal Thermal Comfort

to carry out a thermal index based on modifications of PET forIndex (UTCI) (5) (6) (7) is recently a further developed thermal

universal applications in all climate zones and also to reflectindex in purpose of a universal application in climatic zones.

the influence of clothing behavior.

Previous studies investigated tourist climate(3), urban climate

The UTCI is actually an operative regression function based on
a complicated 343-nodes multi-segments thermoregulation- 26 -2. YCC-thermoregulation model

In order to improve the simulation of PET on thermoregulation,
humidity

physicmulti-segments

andclothing

factors,

thermoregulation

modelamodified
combining

multi-layers clothing model is applied to replace thesemechanisms in Munich Energy-balance Model for Individuals
model (MEMI) (1) (2). This validating model has been named
YCC-thermoregulation model. Fig. 1 shows the principle ofYCC-thermoregulation model. The core of this evaluation is a16- to 26- nodes passive body model based on Pennes’ bio-heat
equation (8) applied in Fialas model and convective and radiantFig. 1 The calculating principle and flow chart ofprinciples in MEMI model. For application of this model, these

YCC-thermoregulation model

boundary conditions which are core temperature of body,operative temperature, and inner clothing temperature are

2.1 Body thermoregulation model

necessary to be given initially. To identify inner clothing

For assessment of an inhomogeneous skin temperature profile

temperature, initial skin temperature and operative temperature

due to multi-layer clothing over body, a multiple-nodes

are indeed required. The operative temperature is consisted ofthermoregulation is necessary. For this purpose, pennes’

convective and radiant heat exchanging terms. Therefore, thebio-heat equation (8) is suggested to be applied to conduct theinfluence of vapor pressure and sweating evaporation areheat exchanging fluxes for each segment in human body. The

excluding in dry process and are proposed to additionally beequation is given by the following:

considered. After given all those boundary conditions into the(Eq. 1),modified passive body model, the body temperature profile at

is conductive coefficient of tissue.

next time step is able to be simulated. The calculation isis temperature of tissue.

processed until achieving at energy equilibrium, the heatis radius of tissue.

transfers, mean skin temperature, and mean outer clothingis geometric coefficient of tissue. If tissue form is cylinder,

temperature are given into energy balance equation to compareis equal to 1. If tissue form is sphere,

the basically standard thermal conditions indoor and evaluate ais metabolic rate of tissue.

physiologicallyis blood density.

equivalenttemperature.

Thedifferences

between mPET and PET result from skin temperature, clothingis perfusion rate of blood.

temperature, and evaporative heat transfer. Mean skinis heat capacity of blood.

is equal to 2.

is temperature of arterial blood.

temperature and mean clothing temperatures lead to modify,sensible heat transfer in model of mPET. Changing ofis tissue density.

evaporative heat transfer adjusts sensibility of PET to variable

is time step.
Despite of the human bio heat-transfer equation, a human bodyof humidity.

model is necessary to be conducted for the parameterization of
the description of human body on physiological heat transferfrom inside body over body surfaces and clothing to theenvironments. A simple two cylinders model with variable- 27 -

multiple nodes based on clothing layers is applied hereby toCorrespond to the Fig. 2,represent a human body. The two cylinders body model isthe air temperature.

including a small cylinder occupying 8 % of total body surface

insulation from node 1 to node 6. Practically, air temperature isto present head and a small cylinder occupying 92 % of total

replaced by operative temperature. Hence, dry heat transfer

body surface to present trunk and external segments of body.

principle of this clothing model can dominate also radiant heat

Moreover, this body model is covered by a variabletransfer over clothing. Moreover, the latent heat transfers overmultiple-layers clothing model which is shown in table 1.

multiple layers clothing can be given as the Eq. 3.

Beside of two cylinders body model, each cylinder has not only,is the skin temperature and,isrepresents the total clothing(Eq. 3),shell and core segments but core, fat, and skin segments. Body

Correspond to the Fig. 2,

is the skin vapor pressure andMass Index (BMI) is applied in this model to provide theis the air vapor pressure.

,

percentage of fat segment and determines also the percentage

vapor resistance from node 1 to node 6. In summary, the totalof skin and core segments. Integrating the above principles ofheat transfers from skin over clothing to the environments can

the body model and human bio-heat equation, a bodybe given as the following equation.
,

temperature profile is able to be simulated under the influence,of environmental thermal conditions.

represents the total clothing,,(Eq. 4)

Additionally, the occurrence of the vapor condensation is able
to be considered according to this simple clothing model with

Table 1 Surface partials of the different clothing layer covered

multiple garments. The changing of latent and sensible heatand uncovered segment

transfers due to the occurrence of the vapor condensation can

1
layer
area

2
layer
area

3
layer
area

Cap
areaNudearea

be also indentified by this clothing model. (9)0.3 – 0.6

62%---38%

model with variable layers from single layer to triple layer is

0.6 – 0.9

36%

45%

--

19%

applied in YCC-thermoregulation model. The variable covered

0.9 – 1.2

42%

45%

--13%

1.2 – 1.6

30%

22%

35%

-13%

1.6 - 2.0

26%

22%

45%

-7%

2.0 – 2.5

12%

25%

55%

5%

3%

Clo

Therefore, based on this simple clothing model, one clothing

partial of clothing surface for each layer is shown in table 1.

2.2 Clothing model
A simple multiple layer clothing model is applied in
YCC-thermoregulation model. This clothing was suggested by
Wissler and Havenith in 2009 (9) and a two-layer reference
garment is able to be illustrated as Fig. 2. This figure shows theplacement with six nodes for the two-layer reference garment.
By this clothing model, two boundaries are respectively skinnode and ambient air node. While the skin temperature and air
Fig.2 Placement of six nodes for the two-layer reference

temperature are known, the total sensible heat transfer overgarment (source: Wissler and Havenith, 2009)

multiple garments is able to be represented as the Eq. 2.
,,(Eq. 2)- 28 -2.3 Vapor evaporation principle

3 Simulation results and Discussions

In MEMI model, sweating evaporation and skin diffusion areindividually calculated and the relationship between these two

The most essential modifications of YCC-thermoregulation

terms refers to the skin wettedness. In YCC-thermoregulation

model are latent heat transfers, clothing insulation, andmodel, the relationship between these two terms refers simplyphysiologicalto Eq. 5. The total latent heat transfers over body surface can be

performances of mPET on the changing of biometeorologicalregarded as sweating evaporation and skin diffusion and is able

factors and clo is important. A simple way to investigate it is

to be given by the Eq. 5.

comparing mPET to the other thermal indices, such as PET and,principles.

Therefore,

toestimate

the(Eq. 5)

UTCI. Fig. 3 shows the comparison between PET, mPET andIn the left term of this equation, the total latent heat transfers

UTCI in different air temperature above -50 °C to 50 °C underover body surface are definitely evaluated by the actual skinvariance of wind speed from 0.5 m/s to 17 m/s, relative

vapor pressure, air vapor pressure and water vapor resistance ofhumidity at 50 % and the mean radiant temperature equal to thethe clothing or skin vapor resistance. The left term represents

air temperature. The x-axis represents the variable of air

the actual latent heat transfer limited by water vapor resistancetemperature and the y-axis represents the variable of air thermalof the clothing or skin vapor resistance. In the right terms ofindices. The bar plots in Fig. 3 mean the variance of thermal

this equation, there are the sweating evaporation and skinindices due to changing of the wind speed under different airdiffusion. Hereby, the skin diffusion is represented as thetemperature and the line in these bar plots represent mediandifference between statured skin vapor pressure and actual skinvalue. The mPET is different to the other two thermal indicesvapor pressure dividing the skin vapor resistance. The only

according to the changing of the air temperature under cold

unknown term in Eq. 5 isand can be solved by Eq. 5

thermal conditions due to the effect of the modified clothing

without an assumed actual skin vapor pressure. However,model. The influence of the variance of the wind speed on

MEMI model assumed that the skin vapor pressure keeps at themPET is smaller than UTCI but greater than PET. Fig. 4 shows

statured situation and evaporates at the uncovered segments, if

the comparison between PET, mPET and UTCI in different air

no sweating occurs. The statured skin vapor pressure is given

temperature above -50 °C to 50 °C under wind speed at 0.5 m/s,

by the following equation.

relative humidity at 50 % and the mean radiant temperature∙,

100,,.

18.956

according to the simulation of global radiation from 0 W/m2 to(Eq. 6),

800 W/m2 at 1th July. The influence of the variance of the mean

Another right term of Eq. 5 describes the energy exchanging ofradiant temperature on mPET is smaller than PET but greater

sweating evaporation. The sweating rate is able to given by Eq.

than UTCI. Fig. 5 shows the comparison between PET, mPET

7 in YCC-thermoregulation model.

and UTCI in different air temperature above -50 °C to 50 °C

6.92 ∙ 10∙35.8 ∙is calculated by mean skin temperaturetemperature(Eq. 7)

under wind speed at 0.5 m/s, the variance of relative humidity

and corefrom 0 % to 100 % and the mean radiant temperature equal tothe air temperature. The influence of the variance of the relative

given by0.2 ∙0.8 ∙(Eq. 8)

humidity on mPET is smaller than UTCI but greater than PET.

Using these above equations, the total latent heat transfers overFig. 6 shows the comparison between PET, mPET and UTCI inclothing

different air temperature above -50 °C to 50 °C under variancecoveredanduncovered

segments

ofYCC-thermoregulation model can be considered.

of wind speed from 0.5 m/s, relative humidity at 50 %, themean radiant temperature equal to the air temperature andvariance of clo from 0.3 to 2.4. The influence of the variance of- 29 -the clo on mPET works very well, while changing of clo cannot

condition for human being. The mPET was evident to bevary the other two thermal indices.

regarded as a useful und realistic thermal index for universal

For the assessment of the sensible heat transfer over human, theapplications.

mPET performs weak variance due to the changing of the airtemperature and the mean radiant temperature to compare toReference

PET. Otherwise, the mPET refers to a strong variance due to(1) P. Höppe , Die Energiebilanz des Menschen, Wiss. Mitt.

the changing of the latent heat transfer over human to compare

Meteorol. Inst. Uni München, 49 (1984)

to PET. The simulating result of the mPET is more realistic(2) P.Höppe, The physiological equivalent temperature - aperformance corresponding to subjective experiences than PET.

universal index for the biometeorological assessment of theFurthermore, the changing of clothing insulation results more

thermal environment, Int. J. Biometeorol., 43, 71-75 (1999)

variance of mPET than PET especially under cold conditions.

(3) T.-P. Lin and A. Matzarakis, Tourism climate information

The mPET has solved the weak variance of the PET due to thebased on human thermal perception in Taiwan and Easternchanging of the relative humidity and the clothing insulation.

China, Tourism Management, 32(3), 492–500 (2011)

To compare to the UTCI, mPET performs a weak variance on(4) D. Fröhlich and A. Matzarakis, Modeling of changes in

the changing of humidity but realistic sensibility. Moreover,thermal bioclimate: examples based on urban spaces inmPET has considered the influence of specific clothing

Freiburg, Germany Theoretical and Applied Climatology,insulation on human thermal sensation. At the same time, UTCI111(3-4), 547–558 (2012)

has ignored specific clothing behavior instead of a standard(5) D. Fiala, K. J. Lomas, and M. Stohrer, A computer model ofclothing behavior according to an empirical investigation based

human thermoregulation for a wide range of environmental

on the changing of the air temperature.

conditions: the passive system, Journal of Applied Physiology,

In summary, mPET has modified the weakness of PET on the87(5), 1957–1972 (1999)

performance of clothing and humidity and kept the well(6) D. Fiala, K. J. Lomas, and M. Stohrer. Computer prediction

performance on air temperature, mean radiant temperature, andof human thermoregulatory and temperature responses to awind speed. The other index, UTCI, changes violently due towide range of environmental conditions. International Journal

the variance of wind speed and slightly according to theof Biometeorology, 45(3), 143–159 (2001)

variance of mean radiant temperature. Besides, there is almost(7) G. Jendritzky, R. de Dear, and G. Havenith, UTCI--Whyno difference between PET and UTCI, if clo was given in 0.9

another thermal index? Int J Biometeorol, 56, 421-428 (2012)

to calculate PET. This means the auto changing clothing model(8) H. H. Pennes, Analysis of tissue and arterial bloodin UTCI doesn’t work.

temperature in the resting human forearm, J. Appl. Physiol. 1,
93–122 (1948)(9) E. H. Wissler and G. Havenith, A simple theoretical model

4. Conclusionof heat and moisture transport in multi-layer garments in cool
A new thermal index, mPET, was delivered by this study andambient air, European Journal of Applied Physiology, 105(5),based on YCC-thermoregulation model which has applied

797–808. (2009)

physical factors of sensible heat transfers by MEMI model (1) (2),a simple multi-layer garment-model (9) and simplified human(Received Dec. 3, 2014, Accepted Dec. 27, 2014)

thermoregulation-model by Fiala (6) (7) to evaluate the thermal- 30 -Fig. 3 The box plot graphic of PET, mPET, and UTCI, which were simulated with input variables of the air temperature from -50 °C
to 50 °C, the wind speed from 0.5 m/s to 17 m/s, the mean radiant temperature equal to the air temperature, the relative humidity at50 %, and clo auto changing for calculation of mPET. The variance of these box plots were caused by the changing of the windspeed.

Fig. 4 The box plot graphic of PET, mPET, and UTCI, which were simulated with input variables of the air temperature from -50 °C
to 50 °C, the wind speed at 0.5 m/s, the mean radiant temperature varied by global radiation from 0 w/m2 to 1000 w/m2 on 1th July,
the relative humidity at 50 %, and clo auto changing for calculation of mPET. The variance of these box plots were caused by thechanging of the mean radiant temperature.
- 31 -Fig. 5 The box plot graphic of PET, mPET, and UTCI, which were simulated with input variables of the air temperature from -50 °C
to 50 °C, the wind speed from 0.5 m/s, the mean radiant temperature equal to the air temperature, the relative humidity from 10 % to90 %, and clo auto changing for calculation of mPET. The variance of these box plots were caused by the changing of the relativehumidity.

Fig. 6 The box plot graphic of PET, mPET, and UTCI, which were simulated with input variables of the air temperature from -50 °C
to 50 °C, the wind speed from 0.5 m/s, the mean radiant temperature equal to the air temperature, the relative humidity at 50 %, andclo changing from 0.3 to 2.4. The variance of these box plots were caused by the changing of clo.
- 32 -