# Heat index: Wikis

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# Encyclopedia

The heat index (HI) is an index that combines air temperature and relative humidity in an attempt to determine the human-perceived equivalent temperature — how hot it feels, termed the felt air temperature. The human body normally cools itself by perspiration, or sweating, which evaporates and carries heat away from the body. However, when the relative humidity is high, the evaporation rate is reduced, so heat is removed from the body at a lower rate causing it to retain more heat than it would in dry air. Measurements have been taken based on subjective descriptions of how hot subjects feel for a given temperature and humidity, allowing an index to be made which relates one temperature and humidity combination to another at a higher temperature in drier air.

The heat index is derived from work carried out by Robert G. Steadman.[1][2] Like the wind chill index, the heat index contains assumptions about the human body mass and height, clothing, and the wind speed. Significant deviations from these will result in heat index values which do not accurately reflect the perceived temperature.[3]

In Canada, the similar humidex is used in place of the heat index. It differs from the humidex used in Canada in using relative humidity rather than dew point.

The heat index is defined so as to equal the actual air temperature when the partial pressure of water vapor is equal to a baseline value of 1.6 kPa. At standard atmospheric pressure (101.325 kPa), this baseline corresponds to a dew point of 14 °C (57 °F) and a mixing ratio of 0.01 (10 g of water vapor per kilogram of dry air).[1] This corresponds to an air temperature of 25°C and relative humidity of 50% in the sea-level psychrometric chart.

At high temperatures, the level of relative humidity needed to make the heat index higher than the actual temperature is lower than at cooler temperatures. For example, at approximately 27 °C (80 °F), the heat index will agree with the actual temperature if the relative humidity is 45%, but at about 43°C (110° F), any relative-humidity reading above 17% will make the Heat Index higher than 43°C (110 °F).

The heat index is calculated only if the actual temperature is above 27 °C (80 °F), dew point temperatures greater than 12 °C (54 °F), and relative humidities higher than 40%[4]. The heat index and humidex figures are based on temperature measurements taken in the shade and not the sun, so extra care must be taken while in the sun.

Sometimes the heat index and the wind chill are denoted collectively by the single terms "apparent temperature" or "relative outdoor temperature".

## Meteorological considerations

Outdoors in open conditions, as relative humidity increases, first haze and ultimately thicker cloud cover develops, reducing the amount of direct sunlight reaching the surface; thus there is an inverse relationship between maximum potential temperature and maximum potential relative humidity. Because of this factor, it was once believed that the highest heat index reading actually attainable anywhere on Earth is approximately 71 °C (160 °F). However, in Dhahran, Saudi Arabia on July 8, 2003, the dewpoint was 35 °C (95 °F) while the temperature was 42 °C (108 °F). The heat index at that time was 78 °C (172 °F).[5]

## Hot Tub Example

A hot tub with relative humidity of 100% and a temperature of 38 °C (100 °F) would have a heat index of 91 °C (196 °F). An increase of 5°C to 41 °C (106 °F) would yield a heat index of 112 °C (234 °F).

## Effects of the heat index (shade values)

Celsius Fahrenheit Notes
27–32 °C 80–90 °F Caution — fatigue is possible with prolonged exposure and activity. Continuing activity could result in heat cramps
32–41 °C 90–105 °F Extreme caution — heat cramps, and heat exhaustion are possible. Continuing activity could result in heat stroke
41–54 °C 105–130 °F Danger — heat cramps, and heat exhaustion are likely; heat stroke is probable with continued activity
over 54 °C over 130 °F Extreme danger — heat stroke is imminent

Note that exposure to full sunshine can increase heat index values by up to 8°C (14°F).[6]

## Formula

Here is a formula for approximating the heat index in degrees Fahrenheit, to within ±1.3 °F. It is useful only when the temperature is at least 80 °F and the relative humidity is at least 40%.

$HI = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2R + c_8 T R^2 + c_9 T^2 R^2\ \,$

where

$HI\,\!$ = Heat index (in degrees Fahrenheit)
$T\,\!$ = ambient dry-bulb temperature (in degrees Fahrenheit)
$R\,\!$ = relative humidity (in percent)
$c_1\,\!$ = -42.379
$c_2\,\!$ = 2.04901523
$c_3\,\!$ = 10.14333127
$c_4\,\!$ = -0.22475541
$c_5\,\!$ = -6.83783 × 10−3
$c_6\,\!$ = -5.481717 × 10−2
$c_7\,\!$ = 1.22874 × 10−3
$c_8\,\!$ = 8.5282 × 10−4
$c_9\,\!$ = -1.99 × 10−6.

A more accurate formula is available, involving several more terms:

$HI= \begin{bmatrix} 1& T& T^2& T^3 \end{bmatrix} \begin{bmatrix} 16.923 & 5.37941 & 7.28898\times 10^{-3}& 2.91583\times 10^{-5} \ 1.85212\times 10^{-1}& -1.00254\times 10^{-1}& -8.14971\times 10^{-4}& 1.97483\times 10^{-7} \ 9.41695\times 10^{-3}& 3.45372\times 10^{-4}& 1.02102\times 10^{-5}& 8.43296\times 10^{-10} \ -3.8646\times 10^{-5}& 1.42721\times 10^{-6}& -2.18429\times 10^{-8}& -4.81975\times 10^{-11} \end{bmatrix} \begin{bmatrix} 1\\ R\\ R^2\\ R^3 \end{bmatrix}. \,$

The referenced site displays this matrix multiplication expanded into a 16 term polynomial.

## References

1. ^ a b The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science, R. G. Steadman, Journal of Applied Meteorology, July 1979, Vol 18 No7, pp861-873 doi:10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2
2. ^ The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric Pressure on Apparent Temperature Journal of Applied Meteorology, R. G. Steadman, July 1979, Vol 18 No7, pp874-885
3. ^ How do they figure the heat index? - By Daniel Engber - Slate Magazine
4. ^ [http://www.campbellsci.com/documents/technical-papers/heatindx.pdf Heat Index Campbell Scientific Inc.
5. ^ Burt, Christopher C. (2004). Extreme Weather: A Guide & Record Book. W. W. Norton & Company. pp. 28. ISBN 0393326586.
6. ^ Closely paraphrased from the public domain article Heat Index on the website of the Pueblo, CO United States National Weather Service.