Wind Chill Program

Wind Chill Science and Equations

A new wind chill formula

Wind chill is the chilling effect of the wind in combination with a low temperature.

Humans do not sense the temperature of the air directly. When we feel that it is cold, we are actually sensing the temperature of our skin. Because our skin temperature is lower when it is windy (we lose heat from our skin faster than our body can warm it), we feel that it is colder when there is wind. This sensation is what the wind chill index attempts to quantify.

It must be noted that although the wind chill index is expressed on a temperature scale (the Celsius scale in Canada), it is not a temperature: it only expresses a human sensation.

The wind chill index is determined by using a model of the skin temperature under various conditions of wind and temperature. This model, which has been validated through clinical trials (see History for more details), is iterative: it takes into account the lower skin temperature resulting from the heat loss caused by wind and cold, and of the effect of this lower skin temperature on the rate of heat loss. We can, however, approximate the model's results (to one unit) with the following equation:

where
W is the wind chill index, based on the Celsius temperature scale
T_air is the air temperature in degrees Celsius (°C), and
V_10m is the wind speed at 10 metres (standard anemometer height), in kilometres per hour (km/h).

Environment Canada's new wind chill index makes use of scientific advances to provide a more accurate and useful measure of how cold it feels when it is windy. Contrary to the old wind chill index (see Towards a new equation for wind chill, below), the new index is based on a model of how fast a human face loses heat. We chose the face because it is the part of the body most often exposed to severe winter weather, assuming the rest of the body is clothed appropriately for the weather. To validate this model, clinical trials were held in June 2001 at the Defence and Civil Institute of Environmental Medicine in Toronto, now known as DRDC-Toronto (more details on the trials can be found in the History section of this site).

In addition, the new index has been harmonized with that used in the United States (though the Farenheit scale is used there), thus giving a consistent index used throughout North America. Specifically, the new wind chill index has the following features:

• It uses wind speed calculated at the average height of the human face (about 1.5 metres) instead of the standard anemometer height of 10 metres. The correction is effected by multiplying the 10-metre value (what is indicated in weather observations) by a factor of 2/3.
   
• It is based on a model of the human face, and incorporates modern heat transfer theory, that is, the theory of how much heat is lost by the body to its surroundings during cold and windy days.
   
• It uses a calm wind threshold of 4.8 km/h; this value has been obtained by observing the speed at which people walk at intersections.
   
• It uses a consistent standard for skin tissue resistance to heat loss.

Currently, the index does not take into account any offsetting effect for wind chill due to solar radiation. Such a term may be added later (possibly in 2002).

Towards a new equation for wind chill

Prior to October 2001, Environment Canada was using the Siple-Passel wind chill equation, based on work done by Siple and Passel in Antarctica in the 1940s. Siple and Passel measured the time that water in a plastic cylinder took to freeze under different conditions of wind and temperature. From these measurements, they developed a formula to relate the cooling rate (speed at which the water froze) to the wind speed and the temperature. In metric units, the empirical relation they developed is the following:

where
C is the wind chill factor (cooling rate) in watts per square metre (W/m²);
V is the wind velocity (speed) in km/h; and
T is the temperature in °C.

The factors 18.97 and 37.62 are constants for the mathematical fit. The factor 33 is an assumed mean skin temperature in °C.

The above equation was then manipulated to determine an "equivalent temperature", which was defined as the temperature that would give the same cooling rate at a given reference wind speed, typically a person's average walking speed. The equivalent temperature equation based on the Siple-Passel equation is the following:

where
T_e is the equivalent temperature in °C;
T is the air temperature in °C;
V is the wind speed in km/h;
V_r is the reference speed, assumed to be a person's average walking speed (values from 6 to 8 km/h were in use);
and 33 is the assumed skin temperature (°C).

Again, the factors 18.97 and 37.62 are constants for the mathematical fit.

The index based on the Siple-Passel equation had some serious shortcomings:

• The reference ("walking") speed was not used consistently everywhere, thus creating variation in equivalent temperatures due not to physiology or physics, but to a different reference speed.
   
• The wind speeds that Siple and Passel used when they developed the equation was roughly the speeds at face height (less than 2 metres). However, the equation was then routinely used with the wind speed found in standard weather observations - the wind measured at 10 metres - without adjustment, even though the wind at 10 metres can be significantly higher than the wind at face height.
   
• The skin temperature was assumed to be constant at 33 degrees, even though the model was used to talk about the danger of skin freezing. This was inconsistent (skin will not freeze unless its temperature falls to about -1°C).

To facilitate the development of a new wind chill index that would address at least some of these shortcomings, Environment Canada hosted an Internet workshop on wind chill in the spring of 2000.

The Internet workshop had participants from around the world. Among the participants were Randall Osczevski of the DRDC-Toronto, which is part of the Canadian Department of National Defence, and Maurice Bluestein of Purdue University in Indiana (United States).

In the fall of 2000 the Office of the (United States) Federal Coordinator of Meteorology formed the Joint Action Group for Thermal Indices (JAG/TI), with participation from both the USA and Canada. The JAG/TI recommended that a new wind chill index be developed based on the work of Randall Osczevski and Maurice Bluestein.

The new index has been validated in clinical trials with human volunteers held in Toronto in June 2001. This index is expected to be much closer to what people actually experience when exposed to wind and low temperatures.

The History section gives more details on the clinical trials. You may also read the personal account from a volunteer in those trials.

Future developments

Scientific studies of the effects of cold on the human body continue. It is hoped that this work will lead to future improvements to Environment Canada programs.

As mentioned before, work is continuing to develop a process for including the effect of solar radiation into the wind chill index. In addition, DRDC-Toronto researchers (including Randall Osczevski) are currently working on establishing a more detailed description of the time to frostbite for different conditions. An equation to model wind chill under wet conditions is also being investigated. Such a "wet wind chill index" could be of use to mariners under freezing spray conditions, for instance.

Another outcome of the April 2000 workshop has been the establishment of Commission 6 under the International Society of Biometeorology (ISB). The ISB commission is now reviewing both cold and hot thermal indices and is expected to make a submission to the World Meteorological Organization for an international standard. In addition to improvements to the wind chill index, this work could also lead to improvements to the humidex, the index used to describe the combined effect of heat and humidity in the summer.

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