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{{short description|A temperature index that accounts for the effects of humidity}}
{{humidity}}
The '''heat index''' ('''HI''') or '''humiture''' is an index that combines [[air]] [[temperature]] and [[relative humidity]], in shaded areas, to posit a  human-perceived equivalent temperature, as how hot it would feel if the [[humidity]] were some other value in the shade. The result is also known as the "felt air temperature", "[[apparent temperature]]", "real feel" or "feels like". For example, when the temperature is {{convert|32|°C}} with 70% relative humidity, the heat index is {{convert|41|°C}}.  This heat index temperature has an implied (unstated) humidity of 20%. This is the value of relative humidity for which the heat index number equals the actual air temperature.

The human body normally cools itself by [[perspiration]], or sweating. [[Heat]] is removed from the body by [[evaporation]] of that sweat. However, high relative humidity reduces the evaporation rate. This results in a lower rate of heat removal from the body, hence the sensation of being overheated. This effect is subjective, with different individuals perceiving heat differently for various reasons (such as differences in body shape, metabolic differences, differences in hydration, [[pregnancy]], [[menopause]], effects of drugs and/or [[drug withdrawal]]); its measurement has been based on subjective descriptions of how hot subjects feel for a given temperature and humidity. This results in a heat index that relates one combination of temperature and humidity to another.

Because the heat index is based on temperatures in the shade, while people often move across sunny areas, then the heat index can give a much lower temperature than actual conditions of typical outdoor activities. Also, for people exercising or active, at the time, then the heat index could give a temperature lower than the felt conditions. For example, with a temperature in the shade of {{convert|28|°C}} at 60% relative humidity, then the heat index would seem {{convert|29|°C}}, but movement across sunny areas of {{convert|39|°C}}, would give a heat index of over {{convert|58|°C}}, as more indicative of the oppressive and sweltering heat.{{Citation needed|date=August 2019}} Plus when actively working, or not wearing a hat in sunny areas, then the feels-like conditions would seem even hotter. Hence, the heat index could seem unrealistically low, unless resting inactive (idle) in heavily shaded areas.

== History ==
The heat index was developed in 1978 by [[George Winterling]] as the "humiture" and was adopted by the US's [[National Weather Service]] a year later.<ref>[http://www.news4jax.com/news/19262258/detail.html George Winterling: A Lifelong Passion For Weather] {{webarchive|url=https://web.archive.org/web/20090917055259/http://www.news4jax.com/news/19262258/detail.html |date=2009-09-17 }} [[WJXT]], April 23, 2009</ref> It is derived from work carried out by Robert G. Steadman.<ref name=SteadmanI>{{cite journal|last1=Steadman|first1=R. G.|title=The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science|journal=Journal of Applied Meteorology|date=July 1979|volume=18|issue=7|pages=861–873|doi=10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2|bibcode=1979JApMe..18..861S}}</ref><ref>{{cite journal|last1=Steadman|first1=R. G.|title=The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric Pressure on Apparent Temperature|journal=Journal of Applied Meteorology|date=July 1979|volume=18|issue=7|pages=874–885|doi=10.1175/1520-0450(1979)018<0874:TAOSPI>2.0.CO;2|bibcode=1979JApMe..18..874S}}</ref> Like the [[wind chill]] index, the heat index contains assumptions about the human body mass and height, clothing, amount of physical activity, individual heat tolerance, 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.<ref>[http://www.slate.com/id/2123486/fr/rss/ How do they figure the heat index? - By Daniel Engber - Slate Magazine<!-- Bot generated title -->]</ref>

In [[Canada]], the similar [[humidex]] (a Canadian innovation introduced in 1965)<ref>"Spring and Summer Hazards". Environment and Climate Changes. Government of Canada. Retrieved 2016-09-22.</ref> 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 {{convert|7|°C}} as a base, whereas the heat index uses a dew point base of {{convert|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 {{Who|date=October 2015}} formed by the United States and Canada to resolve differences has since been disbanded. {{citation needed|date=October 2015}}

The heat index is referenced to any combination of air temperature and humidity where the [[partial pressure]] of [[water vapor]] is equal to a baseline value of {{convert|1.6|kPa |abbr=~ |lk=in}}.  For example, this corresponds to an air temperature of {{convert|25|°C}} and relative humidity of 50% in the sea-level [[psychrometric chart]]. At [[standard atmospheric pressure]] (101.325 kPa), this baseline also corresponds to a [[dew point]] of {{convert|14|°C}} and a [[mixing ratio]] of 0.01 (10 g of water vapor per kilogram of dry air).<ref name=SteadmanI/>

A given value of relative humidity causes larger increases in the heat index at higher temperatures. For example, at approximately {{convert|27|°C}}, the heat index will agree with the actual temperature if the relative humidity is 45%, but at {{convert|43|°C}}, any relative-humidity reading above 18% will make the heat index higher than {{nowrap|43 °C}}.

It has been suggested that the equation described is valid only if the temperature is {{convert|27|°C}} or more, and the relative humidity is 40% or more.<ref>[http://www.campbellsci.com/documents/technical-papers/heatindx.pdf Heat Index Campbell Scientific Inc.] {{webarchive|url=https://web.archive.org/web/20100525004438/http://www.campbellsci.com/documents/technical-papers/heatindx.pdf |date=2010-05-25 }} (PDF file), CampbellSci.com.</ref>  However, a recent analysis by [http://www.iweathernet.com/educational/heat-index-calculator-and-conversion-table iWeatherNet] found the assumption to be erroneous given that the heat index/relative humidity relationship and the corresponding equilibrium temperature (the point at which the air temperature and the heat index are equal) are nonlinear.

The heat index and its counterpart the humidex both take into account only two variables, shade temperature and atmospheric moisture (humidity), thus providing only a limited estimate of [[thermal comfort]]. Wind passing over wet or sweaty skin causes evaporation and a [[wind chill]] effect that the heat index does not measure. The other major factor is sunshine; standing in direct sunlight can add up to {{convert|15|°F-change|°C-change}} to the apparent heat compared to shade.<ref>[https://www.weather.gov/safety/heat-index Heat Index] from the National Weather Service. "exposure to full sunshine can increase heat index values by up to 15°F."</ref>  There have been attempts to create a universal  [[apparent temperature]], such as the [[wet-bulb globe temperature]], "relative outdoor temperature", "feels like", or the proprietary "[[AccuWeather|RealFeel]]".

==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 was approximately {{convert|71|°C|°F}}. However, in [[Dhahran]], [[Saudi Arabia]] on July 8, 2003, the [[dew point]] was {{cvt|35|°C}} while the temperature was {{cvt|42|°C}}, resulting in a heat index of {{cvt|78|°C}}.<ref>{{Cite news|url=http://www.businessinsider.com/dhahran-saudi-arabia-most-intolerabe-heat-climate-change-2015-10|title=This Saudi city could soon face unprecedented and unlivable heat levels|work=Business Insider|access-date=2017-07-20|language=en}}</ref>

The human body requires evaporative cooling to prevent overheating.   [[Wet-bulb temperature]], and  [[Wet Bulb Globe Temperature]] are used to determine the ability of a body to eliminate excess heat.  A sustained wet-bulb temperature of about  {{convert|35|C}} can be fatal to healthy people; at this temperature our bodies switch from shedding heat to the environment, to gaining heat from it.<ref name=pnas>{{cite journal |first=S.C. |last=Sherwood |first2=M. |last2=Huber |title=An adaptability limit to climate change due to heat stress |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=107 |issue=21 |pages=9552–5 |date=25 May 2010 |pmid=20439769 |doi=10.1073/pnas.0913352107 |url=http://www.pnas.org/content/107/21/9552.full |pmc=2906879|bibcode = 2010PNAS..107.9552S }}</ref>
Thus a wet bulb temperature of  {{convert|35|C}} is the threshold beyond which the body is no longer able to adequately cool itself.<ref>{{cite journal | url=http://www.gfdl.noaa.gov/news-app/story.77 |first= John P. |last=Dunne |first2=Ronald J. |last2=Stouffer |first3=Jasmin G. |last3=John | year=2013 | title= Heat stress reduces labor capacity under climate warming | journal=Geophysical Fluid Dynamics Laboratory |volume= 3 |issue= 6 |pages= 563 | doi=10.1038/nclimate1827|bibcode = 2013NatCC...3..563D }}</ref>

== Table of values ==
The table below is from the U.S. [[National Oceanic and Atmospheric Administration]]. The columns begin at {{cvt|80|F}}, but there is also a heat index effect at {{cvt|79|F}} and similar temperatures when there is high humidity.
{{HeatTable}}

For example, if the air temperature is {{convert|96|F|C}} and the relative humidity is 65%, the heat index is 121&nbsp;°F / 49&nbsp;°C.

==Effects of the heat index (shade values)==
{| class="wikitable"
|-
! Celsius || Fahrenheit || Notes
|-
| 26–32&nbsp;°C || 80–90&nbsp;°F
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in [[heat cramp]]s.
|-
| 32–41&nbsp;°C || 90–105&nbsp;°F
| Extreme caution: [[heat cramp]]s and [[heat exhaustion]] are possible. Continuing activity could result in [[heat stroke]].
|-
| 41–54&nbsp;°C || 105–130&nbsp;°F
| Danger: [[heat cramp]]s and [[heat exhaustion]] are likely; [[heat stroke]] is probable with continued activity.
|-
| over 54&nbsp;°C || over 130&nbsp;°F
| Extreme danger: [[heat stroke]] is imminent.
|-
|}

Exposure to full sunshine can increase heat index values by up to 8&nbsp;°C (14&nbsp;°F).<ref name=Pueblo>[https://web.archive.org/web/20110629041320/http://www.crh.noaa.gov/pub/heat.php Heat Index] on the website of the Pueblo, CO United States National Weather Service.</ref>

==Formula==
There are many formulae devised to approximate the original tables by Steadman. Anderson et al. (2013),<ref>{{Cite journal | doi=10.1289/ehp.1206273| pmid=23934704| pmc=3801457|title = Methods to Calculate the Heat Index as an Exposure Metric in Environmental Health Research| journal=Environmental Health Perspectives| volume=121| issue=10| pages=1111–1119|year = 2013|last1 = Anderson|first1 = G. Brooke| last2=Bell| first2=Michelle L.| last3=Peng| first3=Roger D.}}</ref> NWS (2011), Jonson and Long (2004), and Schoen (2005) have lesser residuals in this order. The former two are a set of polynomials, but the third one is by a single formula with exponential functions.

The formula below approximates the heat index in degrees Fahrenheit, to within ±{{cvt|1.3|F-change|1}}. It is the result of a multivariate fit (temperature equal to or greater than {{cvt|80|F}} and relative humidity equal to or greater than 40%) to a model of the human body.<ref name="SteadmanI" /><ref>Lans P. Rothfusz. "The Heat Index 'Equation' (or, More Than You Ever Wanted to Know About Heat Index)", Scientific Services Division (NWS Southern Region Headquarters), 1 July 1990 [https://www.weather.gov/media/ffc/ta_htindx.PDF]</ref> This equation reproduces the above NOAA National Weather Service table (except the values at {{cvt|90|F}} & 45%/70% relative humidity vary unrounded by less than ±1, respectively).
:<math>\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 </math>

where
:HI = heat index (in degrees Fahrenheit)
:''T'' = ambient [[dry-bulb temperature]] (in degrees Fahrenheit)
:''R'' = relative humidity (percentage value between 0 and 100)
:<math>\begin{align}
c_1 &= -42.379, & c_2 &= 2.049\,015\,23, & c_3 &= 10.143\,331\,27,\\
c_4 &= -0.224\,755\,41, & c_5 &= -6.837\,83 \times 10^{-3}, & c_6 &= -5.481\,717 \times 10^{-2},\\
c_7 &= 1.228\,74 \times 10^{-3}, & c_8 &= 8.5282 \times 10^{-4}, & c_9 &= -1.99 \times 10^{-6}.
\end{align}</math>

The following coefficients can be used to determine the heat index when the temperature is given in degrees Celsius, where
:HI = heat index (in degrees Celsius)
:''T'' = ambient [[dry-bulb temperature]] (in degrees Celsius)
:''R'' = relative humidity (percentage value between 0 and 100)

* c<sub>1</sub> = -8.78469475556
* c<sub>2</sub> = 1.61139411
* c<sub>3</sub> = 2.33854883889
* c<sub>4</sub> = -0.14611605
* c<sub>5</sub> = -0.012308094
* c<sub>6</sub> = -0.0164248277778
* c<sub>7</sub> = 0.002211732
* c<sub>8</sub> = 0.00072546
* c<sub>9</sub> = -0.000003582

An alternative set of constants for this equation that is within ±{{cvt|3|F-change}} of the NWS master table for all humidities from 0 to 80% and all temperatures between {{cvt|70|and(-)|115|F}} and all heat indices below {{cvt|150|F}} is:
:<math>\begin{align}
c_1 &= 0.363\,445\,176, & c_2 &= 0.988\,622\,465, & c_3 &= 4.777\,114\,035,\\
c_4 &= -0.114\,037\,667, & c_5 &= -8.502\,08 \times 10^{-4}, & c_6 &= -2.071\,6198 \times 10^{-2},\\
c_7 &= 6.876\,78 \times 10^{-4}, & c_8 &= 2.749\,54 \times 10^{-4}, & c_9 &= 0.
\end{align}</math>

A further alternate is this:<ref>
{{cite book
 | last = Stull | first = Richard
 | authorlink =
 | title = Meteorology for Scientists and Engineers, Second Edition
 | url = https://books.google.com/?id=QrYRAQAAIAAJ&dq=Meteorology+for+Scientists+and+Engineers&q=5.37941#search_anchor
 | publisher = Brooks/Cole
 | year = 2000 | page = 60
 | doi =
 | isbn = 9780534372149 }}</ref>
:<math>\begin{align}
\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 + \\
&\quad {} + 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
\end{align}</math>

where
:<math>\begin{align}
c_1 &= 16.923, & c_2 &= 0.185\,212, & c_3 &= 5.379\,41, & c_4 &= -0.100\,254,\\
c_5 &= 9.416\,95 \times 10^{-3}, & c_6 &= 7.288\,98 \times 10^{-3}, & c_7 &= 3.453\,72\times 10^{-4}, & c_8 &= -8.149\,71 \times 10^{-4},\\
c_9 &= 1.021\,02 \times 10^{-5}, & c_{10} &= -3.8646 \times 10^{-5}, & c_{11} &= 2.915\,83 \times 10^{-5}, & c_{12} &= 1.427\,21 \times 10^{-6},\\
c_{13} &= 1.974\,83 \times 10^{-7}, & c_{14} &= -2.184\,29 \times 10^{-8}, & c_{15} &= 8.432\,96 \times 10^{-10}, & c_{16} &= -4.819\,75 \times 10^{-11}.
\end{align}</math>

For example, using this last formula, with temperature {{convert|90|F|C}} and relative humidity (RH) of 85%, the result would be: {{heat index|90|85}}.

== See also ==
* [[Apparent temperature]]
* {{section link|Thermal comfort|Interplay of temperature and humidity}}
* [[Humidex]]
* [[Wet-bulb temperature]]
* [[Wind chill]]

==References==
{{Reflist}}

== External links ==
*[http://www.bom.gov.au/info/thermal_stress/ Description of wind chill & apparent temperature] Formulae in metric units
*[http://www.wpc.ncep.noaa.gov/html/heatindex.shtml Heat Index Calculator] Calculates both °F and °C
*[https://earth.nullschool.net/#current/wind/surface/level/overlay=misery_index/winkel3 Current map of global heat index values]

{{Meteorological variables}}

{{DEFAULTSORT:Heat Index}}
[[Category:Atmospheric thermodynamics]]
[[Category:Meteorological indices]]