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{{short description|Temperature index that accounts for the effects of humidity}}
{{short description|Temperature index that accounts for the effects of humidity}}
{{humidity}}
{{humidity}}
The '''heat index''' ('''HI''') 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".{{cn|reason=At least one of these ([[Apparent temperature]]) take [[wind chill]] into account so are not equivalent.|date=October 2021}} For example, when the temperature is {{convert|32|°C}} with 70% relative humidity, the heat index is {{convert|41|°C}}. The humidity where the heat index feels like itself is typically left unstated. The heat index example in this case, 41°C, feels like 41°C only when the humidity is 21%.
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 [[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 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.
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]]".

Because the heat index is based on temperatures in the shade, while people often move across sunny areas, 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.{{citation needed|date=March 2022}}


== History ==
== 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>[http://www.slate.com/id/2123486/fr/rss/ How do they figure the heat index? - By Daniel Engber - Slate Magazine<!-- Bot generated title -->]</ref>
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}}
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==
==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/>
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/>
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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/>
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 [[parameterization|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]]".
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==
==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>
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>{{cite|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>
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 }}</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=Geophysical Fluid Dynamics Laboratory |volume= 3 |issue= 6 |pages= 563 | doi=10.1038/nclimate1827|bibcode = 2013NatCC...3..563D }}</ref>


== Table of values ==
== Table of values ==
Line 40: Line 38:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Celsius || Notes
! Temperature || Notes
|-
|-
| {{cvt|27|-|32|C|disp=br()}}
| 27–32&nbsp;°C
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in heat cramps.
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in heat cramps.
|-
|-
| {{cvt|32|-|41|C|disp=br()}}
| 32–41&nbsp;°C
| Extreme caution: heat cramps and heat exhaustion are possible. Continuing activity could result in heat stroke.
| Extreme caution: heat cramps and heat exhaustion are possible. Continuing activity could result in heat stroke.
|-
|-
| {{cvt|41|-|54|C|disp=br()}}
| 41–54&nbsp;°C
| Danger: heat cramps and heat exhaustion are likely; heat stroke is probable with continued activity.
| Danger: heat cramps and heat exhaustion are likely; heat stroke is probable with continued activity.
|-
|-
| over 54&nbsp;°C
| over {{cvt|54|C|disp=br()}}
| Extreme danger: heat stroke is imminent.
| 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>
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==
==Formula==
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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).
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>
<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
where
*HI = heat index (in degrees Fahrenheit)
* HI = heat index (in degrees Fahrenheit)
*''T'' = ambient [[dry-bulb temperature]] (in degrees Fahrenheit)
* ''T'' = ambient [[dry-bulb temperature]] (in degrees Fahrenheit)
*''R'' = relative humidity (percentage value between 0 and 100)
* ''R'' = relative humidity (percentage value between 0 and 100)

*<math display="block">\begin{align}
<blockquote><math display="inline">\begin{align}
c_1 &= -42.379, & c_2 &= 2.049\,015\,23, & c_3 &= 10.143\,331\,27,\\
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_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}.
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>
\end{align}</math></blockquote>


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

<math display="block">\begin{align}
<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_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_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}.
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>
\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:
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}
<math display="block">\begin{align}
c_1 &= 0.363\,445\,176, & c_2 &= 0.988\,622\,465, & c_3 &= 4.777\,114\,035,\\
c_1 &= 0.363\,445\,176, & c_2 &= 0.988\,622\,465, & c_3 &= 4.777\,114\,035,\\
Line 99: Line 101:
| year = 2000 | page = 60
| year = 2000 | page = 60
| isbn = 9780534372149 }}</ref>
| isbn = 9780534372149 }}</ref>

<math display="block">\begin{align}
<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 + \\
\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 + \\
Line 111: Line 114:
\end{align}</math>
\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}}.
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==
==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 [[1995 Chicago heat wave]]. Other issues with the heat index include unavailability of precise humidity data in many geographical regions, assumption that the person is healthy and has easy access to water and shade.<ref>{{cite web |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/ |website=[[Wired (magazine)|Wired]] |access-date=2022-09-21}}</ref>
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 ==
== See also ==
Line 127: Line 132:


== External links ==
== External links ==
*[http://www.bom.gov.au/info/thermal_stress/ Description of wind chill & apparent temperature] Formulae in metric units
* [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
* [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]
* [https://earth.nullschool.net/#current/wind/surface/level/overlay=misery_index/winkel3 Current map of global heat index values]


{{Meteorological variables}}
{{Meteorological variables}}
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[[Category:Atmospheric thermodynamics]]
[[Category:Atmospheric thermodynamics]]
[[Category:Meteorological indices]]
[[Category:Meteorological indices]]
[[Category:Meteorological quantities]]

Latest revision as of 02:21, 13 September 2024

Humidity and hygrometry
Specific concepts
General concepts
Measures and instruments

The heat index (HI) 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. For example, when the temperature is 32 °C (90 °F) with 70% relative humidity, the heat index is 41 °C (106 °F) (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 sweat. High relative humidity reduces evaporation and cooling, increasing discomfort and potential 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 "RealFeel".

History

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The heat index was developed in 1979 by Robert G. Steadman.[1][2] 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.[3]

In Canada, the similar humidex (a Canadian innovation introduced in 1965)[4] 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 7 °C (45 °F) as a base, whereas the heat index uses a dew point base of 14 °C (57 °F).[further explanation needed] 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?] formed by the United States and Canada to resolve differences has since been disbanded.[citation needed]

Definition

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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 kPa. Quoting Steadman, "Thus, for instance, an apparent temperature of 24 °C (75 °F) refers to the same level of sultriness, and the same clothing requirements, as a dry-bulb temperature of 24 °C (75 °F) with a vapor pressure of 1.6 kPa."[1]

This vapor pressure corresponds for example to an air temperature of 29 °C (84 °F) 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 26–31 °C (79–88 °F). At standard atmospheric pressure (101.325 kPa), this baseline also 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]

A given value of relative humidity causes larger increases in the heat index at higher temperatures. For example, at approximately 27 °C (81 °F), the heat index will agree with the actual temperature if the relative humidity is 45%, but at 43 °C (109 °F), any relative-humidity reading above 18% will make the heat index higher than 43 °C.[5]

It has been suggested that the equation described is valid only if the temperature is 27 °C (81 °F) or more.[6] 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%.[5]

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 parameterized as constants in the heat index formula. Wind, for example, is assumed to be 5 knots (9.3 km/h).[5] 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 15 °F (8.3 °C) to the apparent heat compared to shade.[7] 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 "RealFeel".

Meteorological considerations

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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 71 °C (160 °F). However, in Dhahran, Saudi Arabia on July 8, 2003, the dew point was 35 °C (95 °F) while the temperature was 42 °C (108 °F), resulting in a heat index of 81 °C (178 °F).[8] On August 28, 2024, a weather station in southern Iran recorded a heat index of 82.2 °C (180.0 °F), which will be a new record if confirmed.[9]

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 35 °C (95 °F) can be fatal to healthy people; at this temperature our bodies switch from shedding heat to the environment, to gaining heat from it.[10] Thus a wet bulb temperature of 35 °C (95 °F) is the threshold beyond which the body is no longer able to adequately cool itself.[11]

Table of values

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The table below is from the U.S. National Oceanic and Atmospheric Administration. The columns begin at 80 °F (27 °C), but there is also a heat index effect at 79 °F (26 °C) and similar temperatures when there is high humidity.

NOAA national weather service: heat index
Tempera­ture
Relative humidity
 80 °F (27 °C) 82 °F (28 °C) 84 °F (29 °C) 86 °F (30 °C) 88 °F (31 °C) 90 °F (32 °C) 92 °F (33 °C) 94 °F (34 °C) 96 °F (36 °C) 98 °F (37 °C) 100 °F (38 °C) 102 °F (39 °C) 104 °F (40 °C) 106 °F (41 °C) 108 °F (42 °C) 110 °F (43 °C)
40% 80 °F (27 °C) 81 °F (27 °C) 83 °F (28 °C) 85 °F (29 °C) 88 °F (31 °C) 91 °F (33 °C) 94 °F (34 °C) 97 °F (36 °C) 101 °F (38 °C) 105 °F (41 °C) 109 °F (43 °C) 114 °F (46 °C) 119 °F (48 °C) 124 °F (51 °C) 130 °F (54 °C) 136 °F (58 °C)
45% 80 °F (27 °C) 82 °F (28 °C) 84 °F (29 °C) 87 °F (31 °C) 89 °F (32 °C) 93 °F (34 °C) 96 °F (36 °C) 100 °F (38 °C) 104 °F (40 °C) 109 °F (43 °C) 114 °F (46 °C) 119 °F (48 °C) 124 °F (51 °C) 130 °F (54 °C) 137 °F (58 °C)
50% 81 °F (27 °C) 83 °F (28 °C) 85 °F (29 °C) 88 °F (31 °C) 91 °F (33 °C) 95 °F (35 °C) 99 °F (37 °C) 103 °F (39 °C) 108 °F (42 °C) 113 °F (45 °C) 118 °F (48 °C) 124 °F (51 °C) 131 °F (55 °C) 137 °F (58 °C)
55% 81 °F (27 °C) 84 °F (29 °C) 86 °F (30 °C) 89 °F (32 °C) 93 °F (34 °C) 97 °F (36 °C) 101 °F (38 °C) 106 °F (41 °C) 112 °F (44 °C) 117 °F (47 °C) 124 °F (51 °C) 130 °F (54 °C) 137 °F (58 °C)
60% 82 °F (28 °C) 84 °F (29 °C) 88 °F (31 °C) 91 °F (33 °C) 95 °F (35 °C) 100 °F (38 °C) 105 °F (41 °C) 110 °F (43 °C) 116 °F (47 °C) 123 °F (51 °C) 129 °F (54 °C) 137 °F (58 °C)
65% 82 °F (28 °C) 85 °F (29 °C) 89 °F (32 °C) 93 °F (34 °C) 98 °F (37 °C) 103 °F (39 °C) 108 °F (42 °C) 114 °F (46 °C) 121 °F (49 °C) 128 °F (53 °C) 136 °F (58 °C)
70% 83 °F (28 °C) 86 °F (30 °C) 90 °F (32 °C) 95 °F (35 °C) 100 °F (38 °C) 105 °F (41 °C) 112 °F (44 °C) 119 °F (48 °C) 126 °F (52 °C) 134 °F (57 °C)
75% 84 °F (29 °C) 88 °F (31 °C) 92 °F (33 °C) 97 °F (36 °C) 103 °F (39 °C) 109 °F (43 °C) 116 °F (47 °C) 124 °F (51 °C) 132 °F (56 °C)
80% 84 °F (29 °C) 89 °F (32 °C) 94 °F (34 °C) 100 °F (38 °C) 106 °F (41 °C) 113 °F (45 °C) 121 °F (49 °C) 129 °F (54 °C)
85% 85 °F (29 °C) 90 °F (32 °C) 96 °F (36 °C) 102 °F (39 °C) 110 °F (43 °C) 117 °F (47 °C) 126 °F (52 °C) 135 °F (57 °C)
90% 86 °F (30 °C) 91 °F (33 °C) 98 °F (37 °C) 105 °F (41 °C) 113 °F (45 °C) 122 °F (50 °C) 131 °F (55 °C)
95% 86 °F (30 °C) 93 °F (34 °C) 100 °F (38 °C) 108 °F (42 °C) 117 °F (47 °C) 127 °F (53 °C)
100% 87 °F (31 °C) 95 °F (35 °C) 103 °F (39 °C) 112 °F (44 °C) 121 °F (49 °C) 132 °F (56 °C)
Key to colors:   Caution   Extreme caution   Danger   Extreme danger


For example, if the air temperature is 96 °F (36 °C) and the relative humidity is 65%, the heat index is 121 °F (49 °C)

Effects of the heat index (shade values)

[edit]
Heat index for temperature in °C with shaded caution/danger ranges
Temperature Notes
27–32 °C
(81–90 °F) 		Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in heat cramps.
32–41 °C
(90–106 °F) 		Extreme caution: heat cramps and heat exhaustion are possible. Continuing activity could result in heat stroke.
41–54 °C
(106–129 °F) 		Danger: heat cramps and heat exhaustion are likely; heat stroke is probable with continued activity.
over 54 °C
(129 °F) 		Extreme danger: heat stroke is imminent.

Exposure to full sunshine can increase heat index values by up to 8 °C (14 °F).[12]

Formula

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Comparison of NWS heat index values (circles) with the formula approximation (curves). In 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),[13] 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 ±1.3 °F (0.7 °C). It is the result of a multivariate fit (temperature equal to or greater than 80 °F (27 °C) and relative humidity equal to or greater than 40%) to a model of the human body.[1][14] This equation reproduces the above NOAA National Weather Service table (except the values at 90 °F (32 °C) & 45%/70% relative humidity vary unrounded by less than ±1, respectively).

where

  • HI = heat index (in degrees Fahrenheit)
  • T = ambient dry-bulb temperature (in degrees Fahrenheit)
  • R = relative humidity (percentage value between 0 and 100)

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)

An alternative set of constants for this equation that is within ±3 °F (1.7 °C) of the NWS master table for all humidities from 0 to 80% and all temperatures between 70 and 115 °F (21–46 °C) and all heat indices below 150 °F (66 °C) is:

A further alternate is this:[15]

where

For example, using this last formula, with temperature 90 °F (32 °C) and relative humidity (RH) of 85%, the result would be: 114.9 °F (46.1 °C).

Limitations

[edit]

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.[16]

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.[17]

See also

[edit]

References

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  1. ^ a b c d Steadman, R. G. (July 1979). "The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science". Journal of Applied Meteorology. 18 (7): 861–873. Bibcode:1979JApMe..18..861S. doi:10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2.
  2. ^ Steadman, R. G. (July 1979). "The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric Pressure on Apparent Temperature". Journal of Applied Meteorology. 18 (7): 874–885. Bibcode:1979JApMe..18..874S. doi:10.1175/1520-0450(1979)018<0874:TAOSPI>2.0.CO;2.
  3. ^ "How do they figure the heat index? - By Daniel Engber - Slate Magazine". Archived from the original on 2011-06-21. Retrieved 2008-02-01.
  4. ^ "Spring and Summer Hazards". Environment and Climate Changes. Government of Canada. Retrieved 2016-09-22.
  5. ^ a b c Heat index calculator and conversion table from iWeatherNet
  6. ^ Heat Index Campbell Scientific Inc. Archived 2010-05-25 at the Wayback Machine (PDF file), CampbellSci.com.
  7. ^ Heat Index from the National Weather Service. "exposure to full sunshine can increase heat index values by up to 15°F."
  8. ^ "This Saudi city could soon face unprecedented and unlivable heat levels". Business Insider. Retrieved 2017-07-20.
  9. ^ bne Gulf bureau (August 29, 2024), Possible record heat index of 82.2°C reported in southern Iran
  10. ^ Sherwood, S.C.; Huber, M. (25 May 2010). "An adaptability limit to climate change due to heat stress". Proc. Natl. Acad. Sci. U.S.A. 107 (21): 9552–5. Bibcode:2010PNAS..107.9552S. doi:10.1073/pnas.0913352107. PMC 2906879. PMID 20439769.
  11. ^ Dunne, John P.; Stouffer, Ronald J.; John, Jasmin G. (2013). "Heat stress reduces labor capacity under climate warming". Nature Climate Change. 3 (6): 563. Bibcode:2013NatCC...3..563D. doi:10.1038/nclimate1827.
  12. ^ "Heat Index". Pueblo, Colorado: United States National Weather Service.
  13. ^ Anderson, G. Brooke; Bell, Michelle L.; Peng, Roger D. (2013). "Methods to Calculate the Heat Index as an Exposure Metric in Environmental Health Research". Environmental Health Perspectives. 121 (10): 1111–1119. doi:10.1289/ehp.1206273. PMC 3801457. PMID 23934704.
  14. ^ 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 [1]
  15. ^ Stull, Richard (2000). Meteorology for Scientists and Engineers, Second Edition. Brooks/Cole. p. 60. ISBN 9780534372149.
  16. ^ Romps, David; Lu, Yi-Chuan (2022-08-29). "Chronically underestimated: a reassessment of US heat waves using the extended heat index". Environmental Research Letters. 17 (9). Bibcode:2022ERL....17i4017R. doi:10.1088/1748-9326/ac8945. Retrieved 2024-03-31.
  17. ^ Barber, Gregory. "The US Is Measuring Extreme Heat Wrong". Wired. Retrieved 2022-09-21.
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