Wind chill

A surface loses heat through conduction, evaporation, convection, and radiation.{{cite book|author1=Vincent J. Schaefer|author2=John A. Day|author3=Jay Pasachoff|title=A Field Guide to the Atmosphere|url=https://books.google.com/books?id=q0QI19T_POkC|year=1998|publisher=Houghton Mifflin Harcourt|isbn=0-395-97631-6}} The rate of convection depends on both the difference in temperature between the surface and the fluid surrounding it and the velocity of that fluid with respect to the surface. As convection{{clarify|Is the heat transfer in this layer not primarily conduction?|date=April 2024}} from a warm surface heats the air around it, an insulating boundary layer of warm air forms against the surface. Moving air disrupts this boundary layer, or epiclimate, carrying the warm air away, thereby allowing cooler air to replace the warm air against the surface and increasing the temperature difference in the boundary layer. The faster the wind speed, the more readily the surface cools.{{citation needed|date=April 2024}} Contrary to popular belief, wind chill does not refer to how cold things get, and they will only get as cold as the air temperature. This means radiators and pipes cannot freeze when wind chill is below freezing and the air temperature is above freezing.{{Cite web |title=Windchill Terms and Definitions |url=http://www.weather.gov/os/windchill/windchillglossary.shtml |url-status=dead |archive-url=https://web.archive.org/web/20080917044758/http://www.weather.gov/os/windchill/windchillglossary.shtml |archive-date=September 17, 2008 |access-date=July 3, 2024 |website=National Oceanic and Atmospheric Administration}}

Many formulas exist for wind chill because, unlike temperature, wind chill has no universally agreed-upon standard definition or measurement. All the formulas attempt to qualitatively predict the effect of wind on the temperature humans perceive. Weather services in different countries use standards unique to their country or region; for example, the U.S. and Canadian weather services use a model accepted by the National Weather Service. That model has evolved over time.

The first wind chill formulas and tables were developed by Paul Allman Siple and Charles F. Passel working in the Antarctic before the Second World War,{{cite web| url = https://sciencing.com/calculate-wind-chill-factor-5981683.html| title = How to Calculate a Wind Chill Factor| last = Kozlowski| first = Rosann| date = 30 March 2020| website = sciencing.com| access-date = 5 October 2021}} and were made available by the National Weather Service by the 1970s. They were based on the cooling rate of a small plastic bottle as its contents turned to ice while suspended in the wind on the expedition hut roof, at the same level as the anemometer. The so-called Windchill Index provided a pretty good indication of the severity of the weather.

In the 1960s, wind chill began to be reported as a wind chill equivalent temperature (WCET), which is theoretically less useful. The author of this change is unknown, but it was not Siple or Passel as is generally believed.{{Citation needed|date=December 2009}} At first, it was defined as the temperature at which the windchill index would be the same in the complete absence of wind. This led to equivalent temperatures that exaggerated the severity of the weather. Charles EaganEagan, C. (1964). Review of research on military problems in cold regions. C. Kolb and F. Holstrom eds. TDR-64-28. Arctic Aeromed. Lab. p 147–156. realized that people are rarely still and that even when it is calm, there is some air movement. He redefined the absence of wind to be an air speed of {{convert|1.8|m/s|km/h mph}}, which was about as low a wind speed as a cup anemometer could measure. This led to more realistic (warmer-sounding) values of equivalent temperature.

Equivalent temperature was not universally used in North America until the 21st century. Until the 1970s, the coldest parts of Canada reported the original Wind Chill Index, a three- or four-digit number with units of kilocalories/hour per square metre. Each individual calibrated the scale of numbers personally, through experience. The chart also provided general guidance to comfort and hazard through threshold values of the index, such as 1400, which was the threshold for frostbite.

The original formula for the index was:*Woodson, Wesley E. (1981). Human Factors Design Handbook, page 815. McGraw-Hill. {{ISBN|0-07-071765-6}}[https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690003109_1969003109.pdf Aquation 55, page 6-113]

$$WCI=\backslash left(10\backslash sqrt\{v\}-v+10.5\backslash right)\; \backslash cdot\; \backslash left(33-T\_\backslash mathrm\{a\}\backslash right),$$

where:

• WCI = wind chill index, kg⋅cal/m²/h
• v = wind velocity, m/s
• T_a = air temperature, °C

In November 2001, Canada, the United States, and the United Kingdom implemented a new wind chill index developed by scientists and medical experts on the Joint Action Group for Temperature Indices (JAG/TI).{{cite web|url=http://www.ec.gc.ca/meteo-weather/default.asp?lang=n&n=5FBF816A-1#wc6 |title=Environment Canada – Weather and Meteorology – Canada's Wind Chill Index |publisher=Ec.gc.ca |access-date=2013-08-09}}{{cite web|title=Meteorological Tables, Wind Chill. August, 2001 Press Release|url=http://www.erh.noaa.gov/er/iln/tables.htm|publisher=National Weather Service|access-date=14 January 2013}}{{cite web|title=Wind Chill|url=http://www.bbc.co.uk/weather/features/understanding/wind_chill.shtml|archive-url=https://web.archive.org/web/20101011123948/http://www.bbc.co.uk/weather/features/understanding/wind_chill.shtml|archive-date=11 October 2010|work=BBC Weather, Understanding weather|publisher=BBC}} It is determined by iterating a model of skin temperature under various wind speeds and temperatures using standard engineering correlations of wind speed and heat transfer rate. Heat transfer was calculated for a bare face in wind, facing the wind, while walking into it at {{convert|1.4|m/s|km/h+mph|abbr=on}}. The model corrects the officially measured wind speed to the wind speed at face height, assuming the person is in an open field.{{cite journal|last1=Osczevski|first1=Randall|last2=Bluestein|first2=Maurice|title=The new wind chill equivalent temperature chart|journal=Bulletin of the American Meteorological Society|date=2005|volume=86|issue=10|pages=1453–1458|doi=10.1175/BAMS-86-10-1453|doi-broken-date=2 December 2024 |bibcode=2005BAMS...86.1453O|doi-access=free}} The results of this model may be approximated, to within one degree, from the following formulas.

The standard wind chill formula for Environment Canada is:

$$T\_\backslash mathrm\{wc\}=13.12\; +\; 0.6215\; T\_\backslash mathrm\{a\}-11.37\; v^\{+0.16\}\; +\; 0.3965\; T\_\backslash mathrm\{a\}\; v^\{+0.16\},$$

where T_wc is the wind chill index, based on the Celsius temperature scale; T_a is the air temperature in degrees Celsius; and v is the wind speed at {{cvt|10|m|ft}} standard anemometer height, in kilometres per hour.{{cite web |url=http://climate.weatheroffice.gc.ca/prods_servs/normals_documentation_e.html |title=Calculation of the 1971 to 2000 Climate Normals for Canada |publisher=Climate.weatheroffice.gc.ca |date=2013-07-10 |access-date=2013-08-09 |url-status=dead |archive-url=https://web.archive.org/web/20130627223738/http://climate.weatheroffice.gc.ca/prods_servs/normals_documentation_e.html |archive-date=2013-06-27 }}

When the temperature is {{convert|-20|°C|°F}} and the wind speed is {{convert|5|km/h|mph|0|abbr=on}}, the wind chill index is −24. If the temperature remains at −20 °C and the wind speed increases to {{convert|30|km/h|mph|abbr=on}}, the wind chill index falls to −33.

The equivalent formula in US customary units is:

$$T\_\backslash mathrm\{wc\}=35.74+0.6215\; T\_\backslash mathrm\{a\}-35.75\; v^\{+0.16\}+0.4275\; T\_\backslash mathrm\{a\}\; v^\{+0.16\},$$

where T_wc is the wind chill index, based on the Fahrenheit scale; T_a is the air temperature in degrees Fahrenheit; and v is the wind speed in miles per hour.{{cite web|url=http://www.nws.noaa.gov/om/cold/wind_chill.shtml |title=A chart of windchills based on this formula |publisher=Weather.gov |date=2009-12-17 |access-date=2017-04-13}}

Windchill temperature is defined only for temperatures at or below {{convert|10|°C|°F}} and wind speeds above {{convert|4.8|km/h|mph|abbr=on}}.{{cite web |url=http://www.weather.gov/os/windchill/index.shtml |title=NWS Wind Chill Index |publisher=Weather.gov |date=2009-12-17 |access-date=2013-08-09 |url-status=dead |archive-url=https://web.archive.org/web/20110918010232/http://www.weather.gov/os/windchill/index.shtml |archive-date=2011-09-18 }}

As the air temperature falls, the chilling effect of any wind that is present increases. For example, a {{convert|16|km/h|mph|0|abbr=on}} wind will lower the apparent temperature by a wider margin at an air temperature of {{convert|-20|°C|°F}} than a wind of the same speed would if the air temperature were {{convert|-10|°C|°F}}.

File:Windchill effect en.svg|alt=Graph of degrees of wind chill for wind speed and air temperature|Celsius wind chill index

File:WindChill Comparison.GIF|Comparison of old and new wind chill values at {{convert|-15|°C|°F}}|alt=Graph comparing "old" and "new" wind chill values by wind speed at 15 °C air temperature

File:Windchill calculator.jpg|alt=Picture of a manual wind chill calculator|Wind chill calculator

The 2001 WCET is a steady-state calculation (except for the time-to-frostbite estimates).{{cite journal|last1=Tikuisis|first1=Peter|last2=Osczevski|first2=Randall J.|title=Facial Cooling During Cold Air Exposure|journal=Bulletin of the American Meteorological Society|date=2003|volume=84|issue=7|pages=927–933|doi=10.1175/BAMS-84-7-927|doi-broken-date=1 November 2024 |bibcode=2003BAMS...84..927T}} There are significant time-dependent aspects to wind chill because cooling is most rapid at the start of any exposure, when the skin is still warm.

{{excerpt|Apparent temperature#Australian apparent temperature}}

{{reflist}}

{{commons category}}

{{wiktionary}}

• [http://www.eol.ucar.edu/homes/rilling/wc_table.html National Center for Atmospheric Research] Table of wind chill temperatures in Celsius and Fahrenheit
• [https://earth.nullschool.net/#current/wind/surface/level/overlay=misery_index/winkel3 Current map of global wind chill values]
• [https://www.weather.gov/epz/wxcalc_windchill Wind chill calculator] at the US National Weather Service

{{Meteorological variables}}

{{DEFAULTSORT:Wind Chill}}

Category:Atmospheric thermodynamics

Category:Meteorological indices

Category:Meteorological quantities

Category:Units of meteorology measurement