Heat index

 

The heat index (HI) or humiture is an index that combines air temperature and relative humidity in an attempt to determine the human-perceived equivalent temperature — how hot it feels. The result is also known as the "felt air temperature" or "apparent temperature". For example, when the temperature is 90 °F (32 °C) with very high humidity, the heat index can be about 105 °F (41 °C).

The human body normally cools itself by perspiration, or sweating. The evaporation of water needs heat that is absorbed from the body to yield water vapor. However, a higher relative humidity reduces the evaporation rate because of the higher vapor content. This results in a slower heat removal from the body, hence the overheat sensation. this effect being subjective, its measurement has been based on subjective descriptions of how hot subjects feel for a given temperature and humidity. This results in the heat index that relates one combination of temperature and humidity to another one at higher temperature and lower humidity.

History

The heat index was developed in 1978 by George Winterling as the "humiture" and was adopted by the USA's National Weather Service a year later. It is derived from work carried out by Robert G. Steadman. Like the wind chill index, the heat index contains assumptions about the human body mass and height, clothing, amount of physical activity, thickness of blood, sunlight and ultraviolet radiation exposure, 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. While both the humidex and the heat index are calculated using dew point, the humidex uses a dew point of 45 °F (7 °C) as a base, whereas the heat index uses a dew point base of 57 °F (14 °C). Further, the heat index uses heat balance equations which account for many variables other than vapor pressure, which is used exclusively in the humidex calculation. A joint committee formed by the United States and Canada to resolve differences has since been disbanded.

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). This corresponds to an air temperature of 25 °C (77 °F) 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.

The formula described is considered valid 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%. 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. The heat index also does not factor in the effects of wind, which lowers the apparent temperature.

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

Meteorological considerations

Outdoors in open conditions, as the relative humidity increases, first haze and ultimately a 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), resulting in a heat index of 78 °C (172 °F). This is comparable to the temperatures that are recommended to kill bacteria in many meat products, and it is common in a sauna. High heat-index values also indicate that intense thunderstorms are approaching, depending on the intensity of the cold front, causing more violent storms.

Table of Fahrenheit heat index values

This table is from the U.S. National Oceanic and Atmospheric Administration.

NOAA national weather service: heat index

		temperature (°F)
		80	82	84	86	88	90	92	94	96	98	100	102	104	106	108	110
Relative Humidity (%)
	40	80	81	83	85	88	91	94	97	101	105	109	114	119	124	130	136
	45	80	82	84	87	89	93	96	100	104	109	114	119	124	130	137
	50	81	83	85	88	91	95	99	103	108	113	118	124	131	137
	55	81	84	86	89	93	97	101	106	112	117	124	130	137
	60	82	84	88	91	95	100	105	110	116	123	129	137
	65	82	85	89	93	98	103	108	114	121	128	136
	70	83	86	90	95	100	105	112	119	126	134
	75	84	88	92	97	103	109	116	124	132
	80	84	89	94	100	106	113	121	129
	85	85	90	96	102	110	117	126	135
	90	86	91	98	105	113	122	131
	95	86	93	100	108	117	127
	100	87	95	103	112	121	132

  Caution

  Extreme Caution

  Danger

  Extreme Danger

The Heat Index is a measure of how hot it really feels when relative humidity is factored with the actual air temperature.

To find the Heat Index temperature, look at the Heat Index chart above. For example, if the air temperature is 96°F and the relative humidity is 65%, the heat index—how hot it feels—is 121°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

Exposure to full sunshine can increase heat index values by up to 8 °C (14 °F).

Formula

The formula below approximates the heat index in degrees Fahrenheit, to within ±1.3 °F. It is the result of a multivariate fit (temperature equal to or greater than 80°F and relative humidity equal to or greater than 40%) to a model of the human body. This equation reproduces the above NOAA National Weather Service table (except the values at 90°F & 45%/70% relative humidity vary unrounded by less than -1/+1, respectively).

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

where

$\mathrm{HI}\,\!$ = heat index (in degrees Fahrenheit)

$T\,\!$ = ambient dry-bulb temperature (in degrees Fahrenheit)

$R\,\!$ = relative humidity (in percent)

$c_1 = -42.379, \,\!$ $c_2 = 2.04901523, \,\!$ $c_3 = 10.14333127,\,\!$ $c_4 = -0.22475541, \,\!$ $c_5 = -6.83783 \times 10^{-3},\,\!$ $c_6 = -5.481717 \times 10^{-2},\,\!$ $c_7 = 1.22874 \times 10^{-3}, \,\!$ $c_8 = 8.5282 \times 10^{-4}, \,\!$ $c_9 = -1.99 \times 10^{-6}.\,\!$

An alternative set of constants for this equation that is within 3 degrees of the NWS master table for all humidities from 0 to 80% and all temperatures between 70 and 115 °F and all heat indexes < 150 °F is

$c_1 = 0.363445176, \,\!$ $c_2 = 0.988622465, \,\!$ $c_3 = 4.777114035, \,\!$ $c_4 = -0.114037667, \,\!$ $c_5 = -0.000850208, \,\!$ $c_6 = -0.020716198, \,\!$ $c_7 = 0.000687678, \,\!$ $c_8 = 0.000274954, \,\!$ $c_9 = 0 \,\!$ $(c_9 \,\!$ $unused).$

A further alternate is this:

$\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2 + c_{10} T^3 + c_{11} R^3 + c_{12} T^3 R + c_{13} T R^3 + c_{14} T^3 R^2 + c_{15} T^2 R^3 + c_{16} T^3 R^3\ \,$

where

$c_1 = 16.923, \,\!$ $c_2 = 0.185212, \,\!$ $c_3 = 5.37941,\,\!$ $c_4 = -0.100254, \,\!$ $c_5 = 9.41695 \times 10^{-3},\,\!$ $c_6 = 7.28898 \times 10^{-3},\,\!$ $c_7 = 3.45372\times 10^{-4}, \,\!$ $c_8 = -8.14971 \times 10^{-4}, \,\!$ $c_9 = 1.02102 \times 10^{-5},\,\!$ $c_{10} = -3.8646 \times 10^{-5},\,\!$ $c_{11} = 2.91583 \times 10^{-5},\,\!$ $c_{12} = 1.42721 \times 10^{-6},\,\!$ $c_{13} = 1.97483 \times 10^{-7},\,\!$ $c_{14} = -2.18429 \times 10^{-8},\,\!$ $c_{15} = 8.43296 \times 10^{-10},\,\!$ $c_{16} = -4.81975 \times 10^{-11}.\,\!$

For example, using this last formula, with temperature 90 °F (32 °C) and relative humidity (RH) of 85%, the result would be: Heat index for 90 °F, RH 85% =114.9.

See also

• Humidex
• Wind chill

External links

• Description of wind chill & apparent temperature Formulae in metric units
• Heat Index Calculator Calculates both °F and °C