Physiological Equivalent Temperature (PET)

The air temperature at which, in a typical indoor setting, the human energy budget is balanced with the same core and skin temperature as under the actual outdoor conditions.

Primary References:

• Höppe P (1999) "The physiological equivalent temperature - a universal index for the biometeorological assessment of the thermal environment." International Journal of Biometeorology 43:71-75.
• Mayer H, Höppe P (1987) "Thermal comfort of man in different urban environments." Theoretical and Applied Climatology 38:43-49.
• VDI 3787 Part 2 (2008) "Environmental Meteorology - Methods for the human biometeorological evaluation of climate and air quality for urban and regional planning."

MEMI Energy Balance Model

Reference: Höppe P (1984) "Die Energiebilanz des Menschen." Wiss Mitt Meteorol Inst Univ München 49.

PET is calculated using the Munich Energy Balance Model for Individuals (MEMI), a two-node model of human thermoregulation:

M + W = R + C + E_sk + E_re + S

Where:

• M = metabolic rate (W)
• W = mechanical work (W), typically ~0 for sedentary activities
• R = net radiation heat flow (W)
• C = convective heat flow (W)
• E_sk = latent heat flow from skin evaporation (W)
• E_re = respiratory heat loss (latent + sensible) (W)
• S = body heat storage (W), positive = body warming

PET Definition: The air temperature at which, in a reference indoor environment (Tmrt = Ta, v = 0.1 m/s, RH = 50%), the human body would have the same core and skin temperature as in the actual outdoor environment. The 50% RH reference condition is approximated by a fixed vapor pressure of 12 hPa.

Metabolic Rate

Reference: ISO 8996:2021 "Ergonomics of the thermal environment - Determination of metabolic rate."

Activity	Work Parameter (W)	Description
Resting	0	Lying quietly
Sitting	0	Office work
Standing relaxed	0	Standing still
Light walking	80	2 km/h (SOLWEIG default)
Normal walking	110	4 km/h
Brisk walking	150	6 km/h

The work parameter (in Watts total, not W/m²) is added directly to the whole-body basal metabolic rate, matching the upstream UMEP MEMI implementation: met = metbm + work. The default SOLWEIG value of 80 W represents light outdoor walking.

Inputs

Input	Type	Description
Ta	float or 2D array (°C)	Air temperature
Tmrt	float or 2D array (°C)	Mean radiant temperature
v	float or 2D array (m/s)	Wind speed
RH	float or 2D array (%)	Relative humidity
age	float (years)	Person's age
height	float (m)	Person's height
weight	float (kg)	Person's weight
sex	int	1=male, 2=female
activity	float (W)	Activity level added to basal metabolic rate (Watts total)
clothing	float (clo)	Clothing insulation

Outputs

Output	Type	Description
PET	float or 2D array (°C)	Physiological Equivalent Temperature

Default Human Parameters

Parameter	Default	Description
age	35 years	Middle-aged adult
height	1.75 m	Average height
weight	75 kg	Average weight
sex	1 (male)	Reference person
activity	80 W	Light walking
clothing	0.9 clo	Summer business attire

Comfort Categories

PET (°C)	Thermal Perception	Grade of Stress
> 41	Very hot	Extreme heat stress
35 to 41	Hot	Strong heat stress
29 to 35	Warm	Moderate heat stress
23 to 29	Slightly warm	Slight heat stress
18 to 23	Comfortable	No thermal stress
13 to 18	Slightly cool	Slight cold stress
8 to 13	Cool	Moderate cold stress
4 to 8	Cold	Strong cold stress
< 4	Very cold	Extreme cold stress

Properties

Fundamental Properties

1. PET is person-specific
2. Varies with age, sex, fitness level

3. Same environment can have different PET for different people

4. PET reference is indoor

5. Reference: Tmrt=Ta, v=0.1m/s, RH=50%
6. PET=21°C is comfortable indoors

Radiation Properties

1. Higher Tmrt → higher PET
2. Radiation increases heat load

3. Sun to shade: ΔPET ≈ 5-15°C

4. PET more sensitive to radiation than UTCI

5. Direct sun has larger effect on PET
6. Better captures radiant heat stress

Personal Factor Properties

1. Activity increases PET
2. Higher metabolic rate → more heat generated

3. Running vs standing: ΔPET ≈ 5-10°C

4. Clothing affects PET bidirectionally

5. In heat: more clothing → higher PET

6. In cold: more clothing → lower PET (better insulated)

7. Age affects thermoregulation

8. Elderly have reduced sweating capacity
9. Children have higher surface-to-mass ratio

Wind Properties

1. Wind generally reduces PET
2. Convective heat loss increases
3. Less effective at high humidity

Comparison: PET vs UTCI

Aspect	PET	UTCI
Reference	Indoor environment	Outdoor walking
Personal factors	Yes (age, sex, etc.)	No (fixed person)
Clothing	Variable input	Fixed (adaptive)
Activity	Variable input	Fixed (walking 4 km/h)
Computation	Iterative solver	Polynomial
Speed	Slower	Faster

Typical Values

Condition	Ta	Tmrt	PET	Perception
Hot sunny	35	65	48	Very hot
Hot shaded	35	40	38	Hot
Pleasant	22	25	22	Comfortable
Cool shade	18	18	17	Slightly cool
Cold	5	5	5	Cold

Implementation Notes

Iterative Solution

PET requires solving the energy balance iteratively to find the equivalent temperature. The algorithm:

1. Compute skin and core temperatures for actual outdoor conditions using a 6-mode thermoregulation loop (j = 1..6), each mode representing different physiological states (sweating, vasoconstriction, etc.). Note: 7 core temperature formulas exist (tcore[1]..tcore[7]), but only 6 modes are tried as convergence candidates (the loop guard j < 7 prevents mode 7 from executing).
2. Within each mode, a 4-pass bracketing scheme finds the clothing temperature (tcl) with decreasing step sizes: 1.0 → 0.1 → 0.01 → 0.001°C. Each pass runs up to 200 iterations, searching for a sign change in the energy balance.
3. Once outdoor skin/core temperatures converge, repeat the same 4-pass bracketing for the PET reference indoor conditions (Tmrt = Ta, v = 0.1 m/s, vapor pressure = 12 hPa) to find the equivalent temperature.
4. Effective precision: 0.001°C.

Body Surface Area (DuBois Formula)

Reference: DuBois D, DuBois EF (1916) "A formula to estimate the approximate surface area if height and weight be known." Archives of Internal Medicine 17:863-871.

The body surface area A_body (m²) is calculated from height (m) and weight (kg):

A_body = 0.203 × height^0.725 × weight^0.425

This empirical formula, derived from direct body surface measurements, remains the standard for thermoregulation calculations. For the default person (1.75m, 75kg):

A_body = 0.203 × 1.75^0.725 × 75^0.425 ≈ 1.90 m²

Clothing Insulation

Reference: ISO 9920:2007 "Ergonomics of the thermal environment - Estimation of thermal insulation and water vapour resistance of a clothing ensemble."

Clothing insulation is measured in clo units (1 clo = 0.155 m²K/W):

Ensemble	Insulation (clo)	Description
Shorts only	0.1	Minimal
Light summer	0.5	T-shirt, shorts
Summer business	0.9	Shirt, trousers (SOLWEIG default)
Winter indoor	1.0	Sweater, trousers
Winter outdoor	1.5-2.0	Coat, layers

Two clothing-related factors are computed:

Clothing area factor (linear, from ISO 9920):

fcl = 1 + 0.15 × Icl

Fraction of body covered by clothing (cubic polynomial, from Hoeppe MEMI):

facl = (-2.36 + 173.51×Icl - 100.76×Icl² + 19.28×Icl³) / 100

These serve different roles: fcl scales the total clothing surface area for heat transfer calculations, while facl determines the fraction of skin covered for radiation absorption.

Convective Heat Transfer

Reference: Höppe P (1999) "The physiological equivalent temperature." International Journal of Biometeorology 43:71-75.

Convective heat transfer coefficient (W/m²K), from the Hoeppe MEMI formulation:

h_c = 2.67 + 6.5 × v^0.67
h_c = h_c × (P / P₀)^0.55

Where:

• v = wind speed (m/s)
• P = local barometric pressure (hPa)
• P₀ = standard sea-level pressure (1013.25 hPa)

The pressure correction accounts for altitude effects on air density. During the PET reference phase (indoor conditions), v = 0.1 m/s is used.

References

Primary UMEP Citation:

• Lindberg F, Grimmond CSB, Gabey A, Huang B, Kent CW, Sun T, Theeuwes N, Järvi L, Ward H, Capel-Timms I, Chang YY, Jonsson P, Krave N, Liu D, Meyer D, Olofson F, Tan JG, Wästberg D, Xue L, Zhang Z (2018) "Urban Multi-scale Environmental Predictor (UMEP) - An integrated tool for city-based climate services." Environmental Modelling and Software 99, 70-87. doi:10.1016/j.envsoft.2017.09.020

PET Model:

• Höppe P (1999) "The physiological equivalent temperature - a universal index for the biometeorological assessment of the thermal environment." International Journal of Biometeorology 43(2), 71-75.
• Matzarakis A, Mayer H, Iziomon MG (1999) "Applications of a universal thermal index: physiological equivalent temperature." International Journal of Biometeorology 43(2), 76-84.

Human Thermal Balance:

• Fanger PO (1970) "Thermal Comfort: Analysis and Applications in Environmental Engineering." Danish Technical Press, Copenhagen.
• Gagge AP, Fobelets AP, Berglund LG (1986) "A standard predictive index of human response to the thermal environment." ASHRAE Transactions 92, 709-731.