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{{short description|Temperature index that accounts for the effects of humidity}}
{{humidity}}
The '''heat index''' ('''HI''') is an index that combines [[air]] [[temperature]] and [[relative humidity]], in [[shade (shadow)|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 (shadow)|shade]]. For example, when the temperature is {{convert|32|°C}} with 70% relative humidity, the heat index is {{convert|41|°C}} (see table below). The heat index is meant to describe experienced temperatures in the shade, but it does not take into account heating from direct sunlight, physical activity or cooling from wind. 

The human body normally cools itself by [[evaporation]] of [[perspiration|sweat]]. High relative humidity reduces evaporation and cooling, increasing discomfort and potential [[Hyperthermia|heat stress]]. Different individuals perceive heat differently due to body shape, metabolism, level of hydration, [[pregnancy]], or other physical conditions. Measurement of perceived temperature has been based on reports of how hot subjects feel under controlled conditions of temperature and humidity. Besides the heat index, other measures of [[apparent temperature]] include the Canadian [[humidex]], the [[wet-bulb globe temperature]], "relative outdoor temperature", and the proprietary "[[AccuWeather#RealFeel temperature|RealFeel]]".

== History ==
The heat index was developed in 1979 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|doi-access=free}}</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|doi-access=free}}</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>{{Cite web |url=http://www.slate.com/id/2123486/fr/rss/ |title=How do they figure the heat index? - By Daniel Engber - Slate Magazine<!-- Bot generated title --> |access-date=2008-02-01 |archive-date=2011-06-21 |archive-url=https://web.archive.org/web/20110621004825/http://www.slate.com/id/2123486/fr/rss |url-status=dead }}</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}}.{{explain|reason= doesn't the heat index simply use relative humidity?|date=November 2022}} 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}}

==Definition==
[[File:Heat index perspective plot.png|thumb|A generalized view of the heat index showing how the perception of heat by the human body increases with temperature but more rapidly at higher humidity levels.]]

The heat index of a given combination of ([[dry-bulb]]) temperature and humidity is defined as the dry-bulb temperature which would feel the same if the water vapor pressure were 1.6&nbsp;[[kilopascal|kPa]]. Quoting Steadman, "Thus, for instance, an apparent temperature of {{cvt|24|C}} refers to the same level of sultriness, and the same clothing requirements, as a dry-bulb temperature of {{cvt|24|C}} with a vapor pressure of 1.6 kPa."<ref name=SteadmanI/>

This vapor pressure corresponds for example to an air temperature of {{cvt|29|°C}} and relative humidity of 40% in the sea-level [[psychrometric chart]], and in Steadman's table at 40% RH the apparent temperature is equal to the true temperature between {{cvt|26|-|31|°C}}. At [[standard atmospheric pressure]] (101.325 kPa), this baseline also corresponds to a [[dew point]] of {{cvt|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 {{cvt|27|°C}}, the heat index will agree with the actual temperature if the relative humidity is 45%, but at {{cvt|43|°C}}, any relative-humidity reading above 18% will make the heat index higher than {{nowrap|43 °C}}.<ref name=iweathernet>[http://www.iweathernet.com/educational/heat-index-calculator-and-conversion-table Heat index calculator and conversion table] from iWeatherNet</ref>

It has been suggested that the equation described is valid only if the temperature is {{cvt|27|°C}} 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> The relative humidity threshold, below which a heat index calculation will return a number equal to or lower than the air temperature (a lower heat index is generally considered invalid), varies with temperature and is not linear. The threshold is commonly set at an arbitrary 40%.<ref name=iweathernet/>

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]]. Additional factors such as wind, sunshine and individual clothing choices also affect perceived temperature; these factors are [[Parametrization (atmospheric modeling)|parameterized as constants]] in the heat index formula. Wind, for example, is assumed to be {{convert|5|knots|km/h}}.<ref name=iweathernet/> 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 {{cvt|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|81|°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>  On August 28, 2024, a weather station in southern Iran recorded a heat index of {{cvt|82.2|°C}}, which will be a new record if confirmed.<ref>{{citation|url=https://www.intellinews.com/possible-record-heat-index-of-82-2-c-reported-in-southern-iran-340967/|title=Possible record heat index of 82.2°C reported in southern Iran|author=bne Gulf bureau|date=August 29, 2024}}</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 {{cvt|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 |first1=S.C. |last1=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 |pmc=2906879|bibcode = 2010PNAS..107.9552S |doi-access=free }}</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 |first1= John P. |last1=Dunne |first2=Ronald J. |last2=Stouffer |first3=Jasmin G. |last3=John | year=2013 | title= Heat stress reduces labor capacity under climate warming | journal= Nature Climate Change|volume= 3 |issue= 6 |pages= 563 | doi=10.1038/nclimate1827|bibcode = 2013NatCC...3..563D |url-access=subscription }}</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 {{convert|121|F|C}}

==Effects of the heat index (shade values)==
[[File:Heat index plot.svg|thumb|upright=1.4|Heat index for temperature in °C with shaded caution/danger ranges]]
{| class="wikitable"
|-
! Heat&nbsp;index ||  Notes
|-
| {{cvt|27|-|32|C|disp=br()}}
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in heat cramps.
|-
| {{cvt|32|-|41|C|disp=br()}}
| Extreme caution: heat cramps and heat exhaustion are possible. Continuing activity could result in heat stroke.
|-
| {{cvt|41|-|54|C|disp=br()}}
| Danger: heat cramps and heat exhaustion are likely; heat stroke is probable with continued activity.
|-
| over {{cvt|54|C|disp=br()}}
| 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"]. Pueblo, Colorado: United States National Weather Service.</ref>

==Formula==
[[File:heat_index_graph.svg|thumb|link={{filepath:heat_index_graph.svg}}|Comparison of NWS heat index values (circles) with the formula approximation (curves). In [{{filepath:heat_index_graph.svg}} the SVG file,] hover over a graph to highlight it.]]
There are many formulas 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 display="block">\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)

<blockquote><math display="inline">\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></blockquote>

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)

<blockquote><math display="inline">\begin{align}
c_1 &= -8.784\,694\,755\,56, & c_2 &= 1.611\,394\,11, & c_3 &= 2.338\,548\,838\,89,\\
c_4 &= -0.146\,116\,05, & c_5 &= -0.012\,308\,094, & c_6 &= -0.016\,424\,827\,7778,\\
c_7 &= 2.211\,732 \times 10^{-3}, & c_8 &= 7.2546 \times 10^{-4}, & c_9 &= -3.582 \times 10^{-6}.
\end{align}</math></blockquote>

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 display="block">\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
 | title = Meteorology for Scientists and Engineers, Second Edition
 | url = https://books.google.com/books?id=QrYRAQAAIAAJ&q=5.37941
 | publisher = Brooks/Cole
 | year = 2000 | page = 60
 | isbn = 9780534372149 }}</ref>

<math display="block">\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 display="block">\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: {{convert|{{heat index|90|85|disp=out}}|F|C}}.

==Limitations==
The heat index does not work well with extreme conditions, like [[supersaturation]] of air, when the air is more than 100% saturated with water. David Romps, a physicist and climate scientist at the [[University of California, Berkeley]] and his graduate student Yi-Chuan Lu, found that the heat index was underestimating the severity of intense heat waves, such as the [[1995 Chicago heat wave]].<ref>{{cite journal |last1=Romps |first1=David |last2=Lu |first2=Yi-Chuan |date=2022-08-29 |title=Chronically underestimated: a reassessment of US heat waves using the extended heat index |url=https://iopscience.iop.org/article/10.1088/1748-9326/ac8945/meta |journal= Environmental Research Letters |volume=17 |issue=9 |doi=10.1088/1748-9326/ac8945 |bibcode=2022ERL....17i4017R |access-date=2024-03-31}}</ref> 

Other issues with the heat index include the unavailability of precise humidity data in many geographical regions, the assumption that the person is healthy, and the assumption that the person has easy access to water and [[Shade (shadow)|shade]].<ref>{{cite magazine |last1=Barber |first1=Gregory |title=The US Is Measuring Extreme Heat Wrong |url=https://www.wired.com/story/the-us-is-measuring-extreme-heat-wrong/ |magazine=[[Wired (magazine)|Wired]] |access-date=2022-09-21}}</ref>

== 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]]
[[Category:Meteorological quantities]]