The following 9 new parameters become operational with model cycle 49r1:

They are available from time step T+1 to T+90h at hourly intervals, from time step T+93h to T+144 at 3-hour intervals, and from T+150 to T+360 at 6-hour intervals.

The first seven parameters are measures of environmental heat and cold as it affects humans. The mean radiant temperature is an ancillary variable from which the globe temperature is derived.

All parameters are stored in MARS in units of Kelvin (K) and calculated via the thermofeel Python library (available on github).


Apparent Temperature (AT)

Parameter ID: 260255

Definition: The AT is defined as the temperature producing the same amount of discomfort as that experienced under the current ambient temperature and humidity. The AT is based on a mathematical model of human body heat balance for an adult, walking outdoors, in the shade and can be considered as an adjustment to the ambient temperature based on the level of humidity. Absolute humidity that conforms with a dew point of 14°C is chosen as a reference. If humidity is higher than the reference humidity level, then the AT will be higher than the ambient temperature; if humidity is lower than the reference, then AT will be lower than the ambient temperature. AT is valid over a wide range of temperatures and includes the chilling effect of the wind at low temperatures (Steadman 1984). The amount of deviation between AT and the actual ambient temperature is controlled by the assumptions of the human body heat balance model.

Calculation: The AT (in °C) is derived from 2m air temperature

T_a\!

(in °C), vapour pressure

vp\!

 (in hPa, via relative humidity

RH\!

and

T_a\!

) and 10m wind speed

va\!

(in m/s):

AT = T_a + 0.33 \cdot vp - 0.7 \cdot va - 4.0

Scale: There is no universal scale for the AT.

Example plot:

References:


Heat Index (HI)

Parameter ID: 260004

Definition: The HI is defined as the temperature the human body perceives when its evaporative cooling mechanism (perspiration) is limited due to increased relative humidity.

Calculation: The starting point for calculating HI (in °F) is given by the two equations below.

If 2m air temperature

T_a\!

is below 80°F (26.7°C):

HI = 0.5 \cdot \left\{T_a + 61.0 + [(T_a-68.0)\cdot1.2] + (RH\cdot0.094)\right\}

If 2m air temperature

T_a\!

 is equal to or above 80°F (26.7°C):

\begin{gathered} HI = -42.379 + 2.04901523 \cdot T_a + 10.14333127 \cdot RH - 0.22475541 \cdot T_a \cdot RH +\\
- 0.00683783 \cdot {T_a\!^2} - 0.05481717 \cdot R{H^2} + 0.00122874 \cdot {T_a\!^2} \cdot RH + \\
+ 0.00085282 \cdot T_a \cdot R{H^2} - 0.00000199 \cdot {T_a\!^2} \cdot R{H^2} \\ \end{gathered}

where 

RH

(in %) is 2m relative humidity. 

Further adjustments to the above equations are then applied in circumstances where values of 2m air temperature and relative humidity fall into particular ranges (see the Rothfusz reference for details).

Scale: The HI refers to shady conditions and is described in terms of danger to heat-related illnesses.

HI range [°C]ClassificationEffect on the body
26.7 ≤ HI < 32.2CautionFatigue possible with prolonged exposure and/or physical activity
32.2 ≤ HI < 39.4Extreme cautionHeat stroke, heat cramps, or heat exhaustion possible with prolonged exposure and/or physical activity
39.4 ≤ HI < 51.1DangerHeat cramps or heat exhaustion likely, and heat stroke possible with prolonged exposure and/or physical activity
HI ≥ 51.1Extreme dangerHeat stroke highly likely

Example plot:

References:


Humidex

Parameter ID: 261016

Definition: The Humidex (short for “humidity index”) is defined as the temperature the human body perceives in hot, humid weather.

Calculation: The Humidex (in °C) is derived from 2m air temperature

T_a\!

(in °C) and vapor pressure

vp

(in hPa):

Humidex = T_a + 0.5555 \cdot \left( {vp - 10} \right)

Scale: The Humidex is described in terms of comfort.

Humidex range [°C]Degree of comfort
20 ≤ Humidex < 30Little discomfort
30 ≤ Humidex < 40Some discomfort
40 ≤ Humidex < 46Great discomfort; avoid exertion
Humidex ≥ 46Dangerous; possible heat stroke

Example plot:

References:


Normal Effective Temperature (NET)

Parameter ID: 261018

Definition: The NET is defined as the temperature felt by a human body for certain combinations of the following meteorological parameters: air temperature, relative humidity of air, and wind speed, which together can determine the thermal exchange between the human body and the environment. The NET is based on a model that considers normal atmospheric pressure and a normal human body temperature (37°C).

Calculation: The NET (in °C) is derived from 2m air temperature

T_a\!

(in °C), 2m relative humidity

RH

(in %), and wind speed at 1.2 m above the ground

v

(in m/s):

NET = 37 - \frac{{37 - T_a}}{{0.68 - 0.0014 \cdot RH + \frac{1}{{1.76 + 1.4 \cdot {{v}^{{0.75}}}}}}} - 0.29 \cdot T_a \cdot \left( {1 - 0.01 \cdot RH} \right)

Scale: There is no universal scale for the NET.

Example plot:

References:


Universal Thermal Climate Index (UTCI)

Parameter ID: 261001

Definition: The UTCI is defined as the air temperature of a reference outdoor environment that would elicit in the human body the same physiological response (sweat production, shivering, skin wettedness, skin blood flow and rectal, mean skin and face temperatures) as the actual environment. The reference environment is defined as a condition of relatively calm air, i.e. wind speed 0.5 m/s at 10 m above the ground, no additional thermal irradiation (i.e. radiant temperature equal to air temperature), 50% relative humidity (except for air temperatures > 29°C when a cap is used instead, to make the reference relative humidity value always correspond to a vapour pressure of 20hPa) where an average person walks at 4 km/h, generating a metabolic rate equal to 135 W/m2 ≃ 2.3 MET. The model represents the human body's response by combining an advanced dynamic multi-node physiological model with a state-of-the-art temperature-adaptive clothing insulation model for outdoor climates.

Calculation: The UTCI (in °C) is derived from 2m air temperature

T_a\!

(in °C), relative humidity

RH

(in %), 10m wind speed

va

(in m/s) and mean radiant temperature

MRT

(in °C) via a sixth degree polynomial equation:

UTCI = T_a + f\left(T_a, RH, va, MRT \right)

The equation is valid for input parameter values within specific ranges, namely 

-50°C ≤ T_a ≤ +50°C

, 

-30°C ≤ MRT - T ≤ +70°C

, and

RH ≤ 100\%

. Furthermore, va is capped at 17 m/s as higher speeds have been observed to generate extremely low UTCI values.

Scale: The UTCI is described in terms of the internal heat stress or cold stress the human body experiences in its attempt to maintain a thermal equilibrium with the surrounding outdoor environment. Each category, defined by a specific range of UTCI values, corresponds to a well-defined set of human physiological responses.

UTCI range [°C]Stress categoryPhysiological responsesMeasures
UTCI > 46Extreme heat stress– increase in rectal temperature (Tre) time gradient
– steep decrease in total net heat loss
– averaged sweat rate >650 g/h, steep increase		Temporary body cooling. No physical activity. Drinking >0.5Lh−1 water necessary.
38 < UTCI ≤ 46Very strong heat stress– core to skin temperature gradient < 1K (at 30 min)
– increase in Tre at 30 min		Temporary use of air conditioning. Shaded places necessary. Reduce physical activity. Drinking >0.5Lh−1 water.
32 < UTCI ≤ 38Strong heat stress– dynamic Thermal Sensation (DTS) at 120 min >+2
– averaged sweat rate > 200 g/h
– increase in Tre at 120 min
– latent heat loss >40 W at 30 min
– instantaneous change in skin temperature > 0 K/min		Shaded places. Drinking >0.25Lh−1 water. Temporarily reduce physical activity.
26 < UTCI ≤ 32Moderate heat stress– change of slopes in sweat rate, Tre and skin temperature: mean (Tskm), face (Tskfc), hand (Tskhn)
– occurrence of sweating at 30 min
– steep increase in skin wettedness		Drinking >0.25Lh−1.
9 < UTCI ≤ 26No thermal stress– averaged sweat rate > 100 g/h
– DTS at 120 min < 1
– DTS between -0.5 and +0.5 (averaged value)
– latent heat loss >40 W, averaged over time
– plateau in Tre time gradient
0 < UTCI ≤ 9Slight cold stress– DTS at 120 min < -1
– local minimum of Tskhn (use gloves)		Some warm clothing, e.g. gloves and hat.
-13 < UTCI ≤ 0Moderate cold stress– skin blood flow at 120 min lower than at 30 min (vasoconstriction)
– averaged Tskfc < 15°C (pain)
– decrease in Tskhn
– Tre time gradient < 0 K/h
– 30 min face skin temperature < 15°C (pain)
– Tmsk time gradient < -1 K/h (for reference)		Intensify activity. Protect face and extremities.
−27 < UTCI ≤ −13Strong cold stress– averaged Tskfc < 7°C (numbness)
– Tre time gradient < -0.1 K/h
– Tre decreases from 30 to 120 min
– increase in core to skin temperature gradient		Intensify activity. Protect face and extremities. Warm clothing.
−40 < UTCI ≤ −27Very strong cold stress– 120 min Tskfc < 0°C (frostbite)
– steeper decrease in Tre
– 30 min Tskfc < 7°C (numbness)
– occurrence of shivering
– Tre time gradient < -0.2 K/h
– averaged Tskfc < 0°C (frostbite).
– 120 min Tskfc < -5°C (high risk of frostbite)		Intensify activity. Protect face and extremities (frostbite risk). Warm clothing. Reduce time outdoors.
UTCI < −40Extreme cold stress– Tre time gradient < -0.3 K/h
– 30 min Tskfc < 0°C (frostbite)		Stay at home. If necessary to go outdoors, use heavy and wind protected clothing.

Example plot:

References:


Wet Bulb Globe Temperature (WBGT)

Parameter ID: 261014

Definition: The WBGT represents the thermal environment to which an individual is exposed and its value gives a first approximation of the heat stress on a person. The WBGT is an ISO (International Organization for Standardization) screening method to establish the presence or absence of heat stress.

Calculation: The WBGT (in °C) is derived from 2m air temperature

T_a\!

(in °C) and 2m dew point temperature (in °C), 10m wind speed (in m/s) and mean radiant temperature (in °C) via the natural wet bulb temperature

T_{NW}

 and the globe temperature

T_g

(both in °C):

WBGT = 0.7 \cdot T_{NW} + 0.2 \cdot T_{g} + 0.1 \cdot T_a

Scale: The WBGT is described in terms of the heat-related risk to human health. WBGT scales are generally tailored to the geographical area of interest. One scale that has been adopted at the global scale is that by Lucas et al. (2014).

WCF range [°C]Exposure risk
20 ≤ WBGT < 25Low Risk
25 ≤ WBGT < 31Moderate risk
WBGT ≥ 31High risk

Example plot:

References:


Wind Chill Factor (WCF)

Parameter ID: 260005

Definition: The WCF is defined as the air temperature of an equivalent environment that, under calm wind conditions, would entail the same skin surface heat loss to the environment as in the actual, windy, environment. The WCF takes into account the assumptions of convective and radiative heat loss described in modern heat transfer theory, and assumes no impact from the sun. The equivalent environment considers a still airspeed of 1.34 m s−1 (average walking speed) and a wind speed at face level (i.e., it assumes that the adult is walking into the wind).

Calculation: The WCF (in °C) is derived from 2m air temperature

T_a\!

(in °C) and 10m wind speed

va

(in m/s):

WCF = 13.12 + 0.6215 \cdot T_a - 11.37 \cdot {va}^{{0.16}} + 0.3965 \cdot T_a \cdot {va}^{{0.16}}

Scale: The WCF is described in terms of the risk incurred by human skin, based on the rate of heat loss caused by exposure to wind and low temperatures.

WCF range [°C]Exposure riskHealth concerns
0 ≤ WCF < -10Low Risk

– Slight increase in discomfort

-10 ≤ WCF < -28Moderate risk

– Uncomfortable
– Risk of hypothermia and frostbite if outside for long periods without adequate protection.

-28 ≤ WCF < -40High risk

– High risk of frostnip or frostbite: Check face and extremities for numbness or whiteness.
– High risk of hypothermia if outside for long periods without adequate clothing or shelter from wind and cold.

-40 ≤ WCF < -48Very high risk

– Very high risk of frostbite: Check face and extremities for numbness or whiteness.
– Very high risk of hypothermia if outside for long periods without adequate clothing or shelter from wind and cold.

-48 ≤ WCF < -55Severe risk

– Severe risk of frostbite: Check face and extremities frequently for numbness or whiteness.
– Severe risk of hypothermia if outside for long periods without adequate clothing or shelter from wind and cold.

WCF ≥ -55Extreme risk

– Outdoor conditions are hazardous.

Example plot:

References:


Mean Radiant Temperature (MRT)

Parameter ID: 261002

Definition: The MRT is defined as the uniform temperature of a fictive black-body radiation enclosure which would result in the same net radiation energy exchange with a human subject as the actual, more complex radiation environment (Figure 1). In other words, it is the numerical representation of how human beings experience radiation. It applies to a human subject placed in an outdoor environment and irradiated by solar and thermal radiation both directly and diffusely. The MRT is an international standard for thermal environment ergonomics according to the International Organization for Standardization. It is also a standard for thermal environmental conditions for human occupancy according to the American Society of Heating, Refrigerating and Air-Conditioning Engineers.


image-2024-7-22_16-22-25.png

Figure 1: Graphical explanation of the mean radiant temperature (MRT). Adapted from Kántor and Unger (2011).


Calculation: The MRT (in °C)  is derived from the isotropic diffuse solar radiation

{S}_{\mathrm{surf}}^{\mathrm{dn},\mathrm{diffuse}}

, the surface-reflected solar radiation

{S}_{\mathrm{surf}}^{\mathrm{UP}}

, the surface thermal radiation downwards

{L}_{\mathrm{surf}}^{\mathrm{dn}}

, the surface thermal radiation upwards

{L}_{\mathrm{surf}}^{\mathrm{up}}

and the radiation intensity of the Sun on a surface perpendicular to the incident radiation direction

I^*

(all in J m-2) via the Stefan–Boltzmann equation:

{\mathrm{MRT}}={\left\{\frac{1}{\sigma}\left[{f}_a\ {L}_{\mathrm{surf}}^{\mathrm{dn}}+{f}_a\ {L}_{\mathrm{surf}}^{\mathrm{up}}+\frac{a_{ir}}{\varepsilon_p}\left({f}_a\ {S}_{\mathrm{surf}}^{\mathrm{dn},\mathrm{diffuse}}+{f}_a\ {S}_{\mathrm{surf}}^{\mathrm{up}}+{f}_p\ {I}^{\ast}\right)\right]\right\}}^{0.25}

with the angle factors 

f_a

 set to 0.5 and the surface projection factor 

f_p

determined from the solar elevation angle; 

\sigma

is the Stefan–Boltzmann constant (5.67 × 10−8 W/m2K4),

\varepsilon_p

is the emissivity of the clothed human body (standard value 0.97) and

a_{ir}

is the absorption coefficient of the body surface area irradiated by solar radiation (standard value 0.7).

Example plot:

References:


Globe temperature

Parameter ID: 261015

Definition: The (black) globe temperature is an indirect measurement of the radiant heat load of the environment. Its name comes from the way the parameter is measured, i.e. via a thermometer installed inside a hollow copper sphere painted matte black.

Calculation: The globe temperature 

T_g\;

(in °C) is derived from 2m air temperature

T_a

(in °C), the mean radiant temperature

MRT

(in °C), and wind speed at 1.1m

v\!

 (in m/s) by solving the equation below for 

T_g
MRT = \left[ \left(T_g + 273.15\right)^4  + \frac{1.1 \cdot 10^8 {v}^{0.6}}{\varepsilon D^{0.4}}\times \left( T_g - T_a \; \right) \right]^{1/4} - 273.15

with the emissivity 

\varepsilon = 0.95

 and the diameter of sphere 

D = 0.15

m.

Example plot:

References: