General

Several ECMWF thermal parameters have become operational with model cycle 49r1. They are measures of environmental heat and cold as they affect humans.  All are based on a mathematical model of human body heat balance for an adult, walking outdoors, in the shade.  Each can be considered as an adjustment to the ambient temperature based on the level of humidity, and in some cases, the also the strength of the wind.

The parameters are available for:

  • time step T+1 to T+90h at hourly intervals.
  • time step T+93h to T+144 at 3-hour intervals.
  • time steps T+150 to T+360 at 6-hour intervals.

All parameters are stored in MARS in units of Kelvin (K).

ECMWF mean radiant temperature is an ancillary variable from which the globe temperature is derived.

Apparent Temperature (AT)

Apparent Temperature is defined as the temperature (in °C) giving the same discomfort as under the current ambient temperature and humidity.  

It is derived from 2m air temperature, 2m vapour pressure, and 10m wind speed and is based on a mathematical model of human body heat balance for an adult, walking outdoors in the shade.   

Absolute humidity conforming with a dew point of 14°C is chosen as a reference.  If ambient humidity is:

  • higher than the reference humidity level, the apparent temperature will be higher than the ambient temperature.
  • lower than the reference humidity level, the apparent temperature will be lower than the ambient temperature.

Apparent Temperature is valid over a wide range of temperatures and includes the chilling effect of the wind at low temperatures.  However, assumptions within the model of the human body may cause deviation of Apparent Temperature from the true ambient Apparent Temperature. 

Example plot:

Fig8.1.18-1:

Heat Index (HI)

Heat Index is defined as the temperature (in °F) the human body perceives in shady conditions when perspiration is limited due to increased relative humidity. 

It is derived from from 2m air temperature and 2m relative humidity.  The calculation is more complex where the 2m air temperature is >80°F. 

Heat index is described in terms of danger of heat-related illnesses.




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:

Fig8.1.18-2:

Humidex

Humidex is defined as the temperature (in °C) the human body perceives in hot, humid weather.

It is derived from 2m air temperature and 2m vapour pressure.

The Humidex is described in terms of comfort.

Humidex

Effect

20 ≤ Humidex < 30Little discomfort
30 ≤ Humidex < 40Some discomfort
40 ≤ Humidex < 46Great discomfort; avoid exertion
Humidex ≥ 46Dangerous; possible heat stroke


Example plot:

Fig8.1.18-3:

Normal Effective Temperature (NET)

Normal Effective Temperature (in °C) is defined as the temperature felt by a human body and can indicate thermal exchange between the human body and the environment.

It is derived from 2m air temperature, 2m relative humidity, and wind speed at 1.2 m above the ground.

The Normal Effective Temperature is derived using the equation:

NET=37 − { (37−Ta) / (0.68 − 0.0014⋅RH + 1/(1.76+1.4⋅v(0.75)) } − 0.29⋅Ta⋅(1 − 0.01⋅RH)

Where:

  • Ta is the 2m air temperature (in °C).
  • RH is the 2m relative humidity (in %).
  • v is the wind speed at 1.2 m above the ground (in m/s).

Example plot:

Fig8.1.18-4:

Universal Thermal Climate Index (UTCI)

Universal Thermal Climate Index is defined as the air temperature of a reference outdoor environment that would produce the same physiological response as the actual environment. The complex model combines a physiological model with temperature-adaptive clothing insulation.

It is derived from 2m air temperature, 2m relative humidity, 10m wind speed, and Mean Radiant Temperature.

The Universal Thermal Climate Index is described in terms of the human internal heat or cold stress experienced while trying to maintain a thermal equilibrium with the outdoor environment.

Universal Thermal Climate Index

Heat stress

Effect

Advised treatment

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 rectal temperature (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 rectal temperature (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, rectal temperature (Tre) and skin temperature:      mean (Tskm), face (Tskfc), hand (Tskhn)                                                                      – occurrence of sweating at 30 min                                                                               – steep increase in skin wetness

Drinking >0.25Lh−1.
9 < UTCI ≤ 26No thermal stress– averaged sweat rate >100 g/h
– dynamic Thermal Sensation (DTS) at 120 min <1
– dynamic Thermal Sensation (DTS) between -0.5 and +0.5 (averaged value)
– latent heat loss >40 W, averaged over time
– plateau in rectal temperature (Tre) time gradient
0 < UTCI ≤ 9Slight cold stress– dynamic Thermal Sensation (DTS) at 120 min <-1
– local minimum of skin temperature hand (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 skin temperature face (Tskfc) <15°C (pain)
– decrease in skin temperature hand (Tskhn)
– rectal temperature (Tre) time gradient <0 K/h
– 30 min skin temperature face (Tskfc) <15°C (pain)
– skin temperature mean (Tskm) time gradient <-1 K/h (for reference)		Intensify activity. Protect face and extremities.
−27 < UTCI ≤ −13Strong cold stress– averaged face (Tskfc) <7°C (numbness)
– rectal temperature (Tre) time gradient <-0.1 K/h
– rectal temperature (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 face (Tskfc) <0°C (frostbite)
– steeper decrease in rectal temperature (Tre)
– 30 min Tskin temperature face (Tskfc) <7°C (numbness)
– occurrence of shivering
– rectal temperature (Tre) time gradient <-0.2 K/h
– averaged skin temperature face (Tskfc) <0°C (frostbite).
– 120 min skin temperature face (Tskfc) <-5°C (high risk of frostbite)		Intensify activity. Protect face and extremities (frostbite risk). Warm clothing. Reduce time outdoors.
UTCI < −40Extreme cold stress– rectal temperature (Tre) time gradient <-0.3 K/h
– 30 min skin temperature face (Tskfc) <0°C (frostbite)		Stay at home.  If necessary to go outdoors, use heavy and wind protected clothing.


Example plot:

Fig8.1.18-5:

Wet Bulb Globe Temperature (WBGT)

The Wet Bulb Globe Temperature 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 Wet Bulb Globe Temperature is an International Organization for Standardization (ISO) screening method to establish the presence or absence of heat stress.

Wet Bulb Globe Temperature (WBGT) is derived using the equation:

WBGT = 0.7⋅TNW + 0.2⋅Tg + 0.1⋅Ta

Where:

  • Ta is the 2m air temperature (in °C)
  • Td is the 2m dew point temperature (in °C)
  • TNW is the the natural wet bulb temperature (in °C)
  • Tg is the globe temperature (in °C)


The Wet Bulb Globe Temperature is described in terms of the heat-related risk to human health. Scales are generally tailored to the geographical area of interest.  One scale that has been adopted at the global scale is:

Wet Bulb Globe Temperature

Risk

20 ≤ WBGT < 25Low Risk
25 ≤ WBGT < 31Moderate risk
WBGT ≥ 31High risk


Example plot:

Fig8.1.18-6:

Wind Chill Factor (WCF)

The Wind Chill Factor 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.  It 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 ms−1 (average walking speed) and a wind speed at face level (i.e., it assumes that the adult is walking into the wind).


Wind Chill Factor (in °C) is derived via the equation:

WCF = 13.12 + 0.6215⋅Ta − 11.37⋅va⋅0.16 + 0.3965⋅Ta⋅0.16⋅va

Where:

  • Ta is the 2m air temperature Ta (in °C). and 10m wind speed va (in m/s):
  • va is the 10m wind speed va (in m/s).


The Wind Chill Factor 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.

Wind Chill Factor

Risk

Effect

0 ≥ WCF > -10Low Risk

– Slight increase in discomfort

-10 ≥ WCF > -28

Moderate 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:

Fig8.1.18-7:

Fig8.1.18-8: Forecast wind chill factor during a strong surge of very cold air southwards across the United States.  Low wind-chill extended to the southern gulf states (as did snow).  Extended areas with high to severe risk of frostbite and hypothermia across the region. A small area of extreme risk (outdoor conditions are hazardous) over Montana/Alberta area.

Mean Radiant Temperature (MRT)

Mean Radiant Temperature 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).  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 Mean Radiant Temperature is an international standard for thermal environment ergonomics according to the International Organization for Standardization (ISO).  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

Fig8.1.18-9: Graphical explanation of the mean radiant temperature (MRT). Adapted from Kántor and Unger (2011).


Mean Radiant Temperature (in °C) is derived via the equation:

MRT={1σ[fa⋅Ldnsurf + fa⋅Lupsurf + air⋅εp⋅(fa⋅Sdn,diffusesurf + fa⋅Supsurf + fp⋅I∗)]} 0.25

where:

  • Sdn, diffusesurf is the isotropic diffuse solar radiation (Jm-2).
  • SUPsurf is the solar radiation reflected from the surface (Jm-2).
  • Ldnsurf is the surface thermal radiation downwards (Jm-2).
  • Lupsurf is the surface thermal radiation upwards (Jm-2).
  • I∗ is the radiation intensity of the sun on a surface perpendicular to the incident radiation direction (Jm-2).
  • fa is the angle factors set to 0.5
  • fp is the surface projection factor determined from the solar elevation angle;
  • σ is the Stefan–Boltzmann constant (5.67 × 10−8 W/m2K4),
  • εp is the emissivity of the clothed human body (standard value 0.97)
  • air is the absorption coefficient of the body surface area irradiated by solar radiation (standard value 0.7).

Example plot:

Fig8.1.18-10:

Globe temperature

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

The globe temperature Tg (in °C) is derived solving the equation below for Tg: 

MRT=[(Tg + 273.15)⋅4 + 1.1⋅108v⋅0.6⋅ε⋅D⋅0.4 × (Tg−Ta)]⋅1/4−273.15

where:

  • MRT is the Mean Radiant Temperature (in °C)
  • Ta is the 2m air temperature Ta (in °C)
  • v is the wind speed at 1.1m (in m/s)
  • ε is the emissivity set to 0.95
  • D is the diameter of sphere  set to 0.15 m.

Example plot:

Fig8.1.18-11:

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