Heat index

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 corresponds a temperature and humidity combination to a higher temperature in dry air.

The heat index is derived from work carried out by R. G. Steadman. 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.

In Canada, the similar humidex is used in place of the heat index.

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 80 °F (approximately 27 °C), the heat index will agree with the actual temperature if the relative humidity is 45%, but at 110 °F (roughly 43 °C), any relative-humidity reading above 17 % will make the Heat Index higher than 110 °F. Humidity is deemed not to raise the apparent temperature at all if the actual temperature is below approximately 68 °F (20 °C) — essentially the same temperature colder than which wind chill is thought to commence. Humidex and heat indexes 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 factor 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 160 °F (71 °C). However, in Dhahran, Saudi Arabia on July 82003, the dewpoint was 95 °F while the temperature was 108 °F. The heat index at that time was 172 °F.

A good example of the difference between heat index and true temperature would be comparing the climates of Miami and Phoenix. Miami averages around 90 °F in summer due to the easterly trade winds coming from the Atlantic Ocean, but it has a high humidity (e.g. 75%). Phoenix averages around 104 °F in summer, but typically has a low humidity (e.g. 10%). According to the heat index, the relative temperature in Miami will be 109.5 °F, but the relative temperature in Phoenix will be lowered due to the lower humidity, to around 98.6 °F. Given sunshine, Miami is likely to feel hotter than Phoenix.

Effects of the heat index (shade values)

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

Note that exposure to full sunshine can increase heat index values by up to 15 °F (8 °C).

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%.

$HI=c_{1}+c_{2}T+c_{3}R+c_{4}TR+c_{5}T^{2}+c_{6}R^{2}+c_{7}T^{2}R+c_{8}TR^{2}+c_{9}T^{2}R^{2}\ \,$

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:

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

External links

• Excellent description of wind chill & apparent temperature (heat index). Formulae in metric units
• National Science Digital Library - Heat Index
• An Introduction to Heat Index - A lesson plan that deals with heat index
• Heat Index Calculator, National Weather Service El Paso, NOAA
• Weather Images heat index chart
• Windows program for Heat Index, etc
• Hourly History from Dhahran, Saudi Arabia - Shows hourly observations from Dhahran, Saudi Arabia from July 8, 2003