Wind Chill and Humidex
(Critique of the indices)

You can listen to a french language interview featuring this article's author at Radio-Canada's Vous êtes ici program.

Presentation

If you live in Canada, you are surely familiar with the concepts of wind chill and humidex. These indices are presented routinely during winter and summer respectively, following the temperature in the weather reports in this country.

On Environment Canada's website, we find the "Wind chill" label during winter and the "Humidex" label during summer, while the Weather Network's website uses the "Feels like" label to indicate both indices, avoiding the need for change according to season.

The section "Origins" describes how these indices were created. The section titled "Arguments against these indices" contains the principal objections concerning the wind chill. The sections "Economic Repercussions of wind chill" and "What other indices could we use instead?" were written following the reception of emails from people relating their experiences. This is followed by a mathematical discussion on the formulae used to calculate the indices.

Many pages of the Environment Canada website have been decommissioned since the release of this page in 2003. Where the information has simply moved, the hyperlinks lead to the new page; where not, they lead to the archive page on the Internet Archive WaybackMachine.

Origins

Origins of the wind chill factor

Information in this section comes mainly from the website of the creator of this index, Environment Canada. For more information, I invite you to consult this website as it is complete and explains clearly the basis of this index.

It is important to note that the wind chill factor was reconfigured in February 2001. Indeed, "although the wind chill equivalent temperature was supposed to be the temperature that would have caused the same cooling with a very light wind, such was not the case [...]"

"The original wind chill formula was derived from experiments conducted in 1939 by Antarctic explorers, Paul Siple and Charles Passel. These hardy scientists measured how long it took for water to freeze in a small plastic cylinder when it was placed outside in the wind. Over the years, the formula was modified somewhat, but remained based on the Antarctic experiments."

This formula became obsolete and in certain circumstances it created confusion. Thus in April 2000 Environment Canada held an Internet Workshop [sic] on wind chill so as to better adapt it to reality. Rather than basing it on a water cylinder, "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". Reading the assumptions taken into account for this new index is relevant. For example: "It [the wind chill] 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."

Origins of the humidex

As with the wind chill factor, the information for the humidex comes primarily from Environment Canada's website and from the Masterson and Richardson document^[1], which I obtained from Environment Canada.

"The humidex is a Canadian innovation, first used in 1965. It was devised by Canadian meteorologists to describe how hot, humid weather feels to the average person."

This index is less well documented than that of wind chill since it has not been remodeled in recent years. Although it is not on Environment Canada's website, the computation of the humidex is based on the work of J.M. Masterson and F.A. Richardson, whose study "A method of quantifying human discomfort due to excessive heat and humidity" was published in 1979 by Environment Canada. Omitting the graphs and charts indicating the various rates of humidex in Ontario, the content of this publication covers 8 pages, including a literature review.

The humidex is based on the observation that intense heat accompanied by high vapour content bring about a physical distress. In extreme cases, when the combined effects of the temperature and moisture approach the normal temperature of the body (37°C), this distress becomes dangerous for the human body.

When the humidex was created in 1979, 22 people were dying every year in Canada due to insolation or excessive heat. This represents the number of deaths caused directly by heat, but does not include heart attacks or other consequences related to hot summer days.

The humidex was thus created to quantify and encompass the degree of risk to the human body in the event of heat AND excessive moisture.

The calculation of the humidex is based on:

1. The ambient temperature;
2. Vapor pressure;
3. The dewpoint.

Although it is normal for a northern country like Canada to have an index to indicate cold and windy conditions, the need for a heat and humidity index does not seem as obvious. Humidity and heat are more severe in other countries, yet the inhabitants of those countries do not feel the need for an index. As far as I know, humidex has not been adopted in tropical countries. Since humidex became popular only once windchill caught the public eye, maybe the simple need for symmetry dictated its rise to prominence. If cold can be exaggerated, why not heat?

Arguments against these indices

1. It uses science to quantify a feeling.

I do not dispute the fact that the feeling of cold is sharper when there is wind or that we have the feeling that it is hotter during the summer when the moisture is high. My point of contention is in the invention of a quantified formula to describe this reality. Science does not have an answer for everything and creating a formula that quantifies a "feeling" illustrates the dressing-up of science for a goal to which it is unsuited and for which it will never fit. A feeling is specific to each individual. Science studies REPRODUCIBLE phenomena; this cannot, by definition, be applied to a feeling.

2. Sensationalism has no place in meteorology.

The weather is one of the rare scientific fields accessible to the entire population and one for which everyone has an opinion. The weather reporter- the difference between weather reporter and meteorologist is very important - is thus an apostle of scientific popularization, while not necessarily having a scientific background. One need only think of the novelist Dany Laferrière who presented the weather report on TQS or comedian Pauline Martin on the morning show of Montreal's Radio-Canada radio station to realize that one need not be a meteorologist to speak about weather with authority.

The weather forecast is for the general public. The channels disseminating this information, radio and especially television, compete for innovative ways to present the forecasts. The computer graphics used to show geographical maps of precipitation, for example, are very complex and each network has its own.

The wind chill factor and the humidex are creations born of the need for the media to captivate their audience. It is more impressive to state: "It is -34°C with the wind" than "It is -20°C with a wind of 40 km/h". These indices are in fact mathematical artifices used to convert factors (wind for the wind chill factor and moisture for the humidex) into easily understandable units of temperature (degrees Celsius). However, these units of temperature are not applicable to these factors. This is weather sensationalism, because the information is presented in such a way as to augment reality in order to catch the public eye.

3. An index which is a function of two measurements does not give more information than the two measurements themselves.

Rather than report two measurements (air temperature and wind speed; air temperature and moisture) and allow people to assess their relevance and interdependence, is preferable to amalgamate them into a formula which does not correspond to anything natural.

4. The wind chill makes use of debatable assumptions of which the public is unaware.

• 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. Does the speed of the wind at 1.5 meter from the ground really correspond to two thirds of the wind's velocity at 10 meters from the ground and is this consistent?

• It is based on a model of the human face, and incorporates modern heat transfer theory, specifically regarding how much heat is lost by the body to its surroundings during cold and windy days. But how, when and on whom was this model of the human face constructed? Is it possible to base a measurement on something as variable as the morphology of a human face? What happens for those who proudly wear a beard?

• 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. People would cross an intersection at an average speed of 4.8 km/h... when it's windy and cold?

The people who conceived the windchill formula did what they could to advance the cause, but the goal of quantifying a sensation is an unattainable one.

How many people know that the wind chill incorporates all these assumptions? If you have read this far, that's one more person! Environment Canada did a survey to measure Canadian's understanding of the wind chill. The results show eloquently that the factor creates confusion, which would likely not be the case through simply reporting temperature and wind speed.

The web page Public Opinion Research on Wind Chill in Canada states, "However, while there is a good understanding of wind chill on a superficial level, there are misconceptions, particularly about wind chill's effect on objects such as cars (half of respondents felt that a car could cool below the air temperature due to wind chill), or with the general notion of wind chill versus temperature, since close to 40% incorrectly said that on a windy day, even sheltered from the wind, they would feel colder than the air temperature."

Leaving aside the discussion as to whether it is possible to have a good understanding on a superficial level, it is clear that this index is not understood whereas it is clear, in my opinion, that when one is sheltered from the wind, it is not windy. Far from being informative, these indices are misleading.

Economic repercussions of wind chill

Until recently, wind chill is only used on this side of the Atlantic, i.e. North America. Europeans were unaware of the latest weather forecast fashion trend. In January 2004, a Siberian cold front struck Canada. Since we live in the information age, the famous "it was -55", which includes wind chill, was reported to Europeans. Without nuance. Without explanation. Something to inspire fear.

Update (August 2013): during the 2012-2013 winter, windchill appeared in Europe's weather bulletins following a cold wave. Humidex followed in 2013.

This propensity to use huge negative numbers is surely not advantageous for tourism. In the worst case, they will consider that Canada is a place best avoided in winter. Someone who has never known a temperature lower than -10°C or a Canadian weather forecast might be frightened. I have difficulty figuring out how to praise the beauties of winter in Canada while shouting from the rooftops that we reach temperatures of -55. At best if they discover the concept of wind chill, they will realize that temperature is a strange business in Canada. They are unlikely to catch the nuances when we ourselves are unable to do so. This inability to be clear about the temperature outside, is not to our benefit.

At the very least it must annoy owners of companies who promote the great outdoors. For example, if a temperature of -15°C is reported as -32 with the wind chill, might one just decide to stay home and cancel those plans for that cross-country ski excursion in the woods? On the other hand, if you knew that it was -15°C but very windy, it might occur to you, nonetheless, that maybe it won't be so bad in the forest. Same reality. Different ways of expressing it. One comes from a mathematical blur, the other from measurable quantities. Which prevails at this time?

The mathematical forge

Let us look at how these indices were forged.

Humidex

Let us begin by analyzing each term of the formula before analyzing the formula as a whole.

The formula used to calculate the humidex is:

$$\begin{array}{c}H=H\left(T,h\right)=T+h\\ where \{\begin{array}{c}H\text{ is humidex index}\hfill \\ T\text{ is temperature in °C}\hfill \\ h=\frac{5}{9}(e-10)\hfill \\ e\text{ is the water vapor pressure in millibar (mbar)}\hfill \end{array}\hfill \end{array}$$

The water vapor pressure is calculated using a modified version of the Clausius-Clapeyron formula. Without going into details, the only variable in this formula is the dewpoint. The dewpoint is itself a function of the temperature and the relative humidity. This implies that the humidex H is calculated according to two measurements:

$$\begin{array}{ccc}\hfill H\left(T,h\right)\text{and}h\left(\text{dew point}\right)& \hfill \Rightarrow & H=H\left(T,\text{dew point}\right)\hfill \\ \hfill H\left(T,\text{dew point}\right)\text{and}\text{dew point}\left(T,\text{\% of humidity}\right)& \hfill \Rightarrow & H=H\left(T,\text{\% of humidity}\right)\hfill \end{array}$$

Up to now, everything is ok.

Let us look at the work done with the water vapor pressure (e) expressed in millibars:

$$\begin{array}{c}\left(e-10\right)\end{array}$$

First of all, the number 10 is subtracted from it. But 10 is a scalar, i.e. it is unitless, and yet is subtracted from a quantity in millibars. As school children know it is incorrect to add (or subtract) values which do not have the same units. 4 apples + 5 oranges = ?

Why choose 10? Because the vapor pressure of water is always higher than 10 millibars for temperatures higher than 7°C. This implies that:

$$\begin{array}{cc}& \forall T>\mathrm{7°C},\left(e-10\right)>0\hfill \\ \hfill \Rightarrow & h>0\hfill \\ \hfill \Rightarrow & H>T\hfill \end{array}$$

In other words, from the moment the temperature is higher than 7°C, the humidex will always be higher than the ambient temperature. It is a desired result since the humidex must represent our feeling that the temperature is higher. The humidex formula allows this to be the case. A judicious choice, but, a choice nonetheless. One could have taken 9 or 11 but they chose 10.

Let us note that for temperatures lower than 7°C, the humidex formula gives a value lower than the ambient temperature. Thus the basic assumption that it feels hotter as moisture increases is not met. For this reason, use of the humidex is restricted to summer.

For temperatures below 7°C, can we conclude that high humidity levels will make it seem colder yet? Yes, because water vapor in air (humidity) increases the thermal capacity of the air. In the presence of cold air, this implies that a given volume of humid air can drain more heat than the same volume of dry air. For equal temperatures, humid air absorbs more heat than dry air and hence, increases the feeling of cold. Why then is moisture not taken into account in the computation of winter temperatures?

Probably because there is already an index for the temperature in winter (wind chill) which takes into account the speed of the wind. Given the formula for wind chill (see below), it is almost unthinkable, even impossible, to introduce another variable to it. Let's ignore humidity when it's cold; it's simpler for the average citizen.

Let us continue our mathematical discussion. Recalling the formula of the humidex:

$$\begin{array}{c}H=T+\frac{5}{9}\left(e-10\right)\end{array}$$

But where does the 5/9 factor comes from? The original calculation comes from Americans, who may have used Fahrenheit degrees. The 5/9 factor thus probably comes from the Fahrenheit to Celsius conversion formula.

From millibars, we subtract a scalar (10), then we multiply by a fraction (5/9). What do we do with the result? We add to it the ambient temperature in... degrees Celsius.

The humidex is a formula which tries to equate a feeling to a measure by the use of "illegal" mathematical tactics like adding millibars and degrees Celsius.

Wind chill

Let us examine the wind chill formula:

$$\begin{array}{cc}\multicolumn{2}{c}{R=\mathrm{13,12}+\mathrm{0,6215}\times T-\mathrm{11,37}\times V^{\mathrm{0,16}}+\mathrm{0,3965}\times T\times V^{\mathrm{0,16}}}\\ \text{where }\{\begin{array}{l}R\text{ is the wind chill index}\\ T\text{ is the air temperature in degrees Celsius (°C)}\\ V\text{ is the wind speed at 10 metres (standard anemometer height), in kilometres per hour (km/h).}\end{array}\end{array}$$

The first striking feature is that the wind speed is given to the power of 0.16. I ignore the meaning of wind speed in km/h to the power of 0.16.

Second striking feature is the addition of a scalar (13.12) to degrees Celsius (0.6215*T), then with km/h to the power of 0.16 (!), and finally with °C multiplied by km/h always to the power of 0.16.

The new and improved wind chill is less open to analysis than is the humidex. The humidex is based on the thermodynamic equations of the vapor pressure and the ambient water content, while wind chill is a construction of another kind.

The wind chill formula incorporates the assumptions explained above as well as constants which have been deduced. However the deduction of these constants is not documented on Environment Canada's website, although there is a page titled "Wind Chill Science and Equations".

We have doubt regarding the ways in which the assumptions were incorporated in the wind chill formula. It is most probably an adjustment made in order for the feelings of the 12 subjects (6 men and 6 women aged 22 to 45 years old) representing mankind be in line with the data (temperature and wind speed) of the tests.

Let us stress that the only person identified in these tests (read the testimonial) is a meteorologist. One can question the representativeness of a meteorologist when it is a question of temperature. He will certainly not have the same opinion as the average man in the street citizen, whereas he is supposed to account for 1/12 of humanity. The profession of the 11 other participants is not given, but it is likely, extrapolating from the first case, that they are colleagues of those performing the experiment. If this is the case, not only is the sample extremely small (12 people), but the methodology used to deduce what is felt by the average person would be more than doubtful.

What other indices could we use instead?

Although humidex and windchill became popular because they twist reality toward spectacular values, they convey useful information. There are cases where wind associated with cold, or humidity associated with heat, become a health hazard. When such is not the case and humans are not at risk, it could be argued that these indices should not be used, or at least it should be stated in a clear and simple manner that there is no danger.

So, instead of leaving these indices behind, would it be possible to reframe or replace them so as to return them to their original purpose: make the public aware of the risks associated with specific weather conditions? Here are my propositions.

Replace wind chill by the number of minutes for frostbite to occur

A more useful parameter to convey information taking into account both cold and wind would be the number of minutes needed for frostbite to occur on exposed skin. This proposition is taken from the table for windchill interpretation on the Environment Canada website.

These values are approximations based on Environment Canada data for the number of minutes needed for frostbite to occur on exposed skin with respect to temperature and wind speed. Some values were interpolated.

	-12°C	-14°C	-16°C	-18°C	-20°C	-22°C	-24°C	-26°C	-28°C	-30°C	-32°C	-34°C	-36°C	-38°C	-40°C
10 km/h	> 30	> 30	> 30	> 30	> 30	26	23	19	14	10	9	7	6	5	4
15 km/h	> 30	> 30	> 30	> 30	28	23	19	15	10	9	7	6	5	4	2
20 km/h	> 30	> 30	> 30	30	26	21	15	12	9	8	6	5	4	3	< 2
25 km/h	> 30	> 30	> 30	28	23	19	14	10	9	7	5	4	3	2	< 2
30 km/h	> 30	> 30	> 30	26	21	17	12	10	8	6	5	4	3	< 2	< 2
35 km/h	> 30	> 30	30	24	21	15	10	9	7	5	5	3	2	< 2	< 2
40 km/h	> 30	> 30	28	24	19	14	10	9	7	5	4	3	< 2	< 2	< 2
45 km/h	> 30	> 30	28	23	17	14	10	8	6	5	4	2	< 2	< 2	< 2
50 km/h	> 30	> 30	26	21	17	12	9	7	6	5	3	2	< 2	< 2	< 2
55 km/h	> 30	30	26	21	15	10	9	7	5	4	3	2	< 2	< 2	< 2
60 km/h	> 30	30	24	19	15	10	9	7	5	4	3	< 2	< 2	< 2	< 2
65 km/h	> 30	28	24	19	14	10	8	7	5	4	2	< 2	< 2	< 2	< 2
70 km/h	> 30	28	23	17	14	10	8	6	5	4	2	< 2	< 2	< 2	< 2

Inherent in this argument is that the windchill would not appear in the forecasts most of the time. This would prevent the spread of misinformation when the actual temperature is warmer than -20°C, which is to say the most prevalent situation in the most densely populated latitudes of Canada and Europe. In this way, we would eliminate the superfluous usage of this index, which only serves to drown facts in sensationalism in any case. But for situations when frostbite can occur, people in the affected zones must be made aware of the danger. By only giving the number of minutes for frostbite to occur, the public can easily assess the situation because it seldom hears that information and can quickly grasp the meaning of the value. There would be no more confusion about cars not starting below -25°C, because the extra information is about human security, all about time for frostbite to occur.

By using the number of minutes for frostbite to occur, that would reframe the windchill to its original purpose: to alert the public of health hazards and offer relevant information for further action.

Replace humidex with the dew point

Humidex is harder to replace than windchill. Danger coming from heat depends on lots of parameters: age, region (urban or not), type of activity (light work, leisure, etc.), ventilation, sun exposure, etc. One only needs to read about guidelines for work under heat conditions to grasp this complexity.

So, instead of finding a new index, why not use a measurement that is taken at all weather stations and that is included in all weather forecast bulletins? An important thermodynamical measurement that gives the quantity of water in air is the dew point.

The combination of dew point and air temperature gives an idea of the evaporation rate and of the needed energy for temperature rising.

In summer, the rate of evaporation is the most important factor, as a large difference between the dew point and temperatures suggests a faster evaporation rate, and a small difference a slower rate. A large difference thus makes sweat evaporate faster, allowing the body to regulate its temperature more easily, and inversely for small differences.

In winter, a dew point close to the actual temperature will provoke faster condensation on the interior layer of clothing, accelerating heat transfer to the outside (liquid water has much higher thermal absorption and conductivity than air, for both dry and humid air). This explains why the feeling of cold is more intense when humidity is high. A trip to London during winter suffices to convince that a -2°C temperature with a dew point at -4°C feels much colder than the same temperature with a dew point around -10°C, which is more likely in Quebec. The reason for this is that the body must radiate more energy to keep the air warm inside the clothing in the London case than in the Quebec one, condensed water in clothing making the heat escape to the outside.

The dew point value gives useful information for humans, for both winter and summer. It is a central variable in weather phenomenon studies, and we would all benefit from knowing more about it, for our own security as well as to assess general weather conditions around us.

Conclusion

It is astonishing that the continued use of these smoke screen indices such as wind chill and humidex are not denounced more widely. The creation of this web page is an attempt to correct this situation. Being Canadian creations, it is appropriate that shedding light on the situation comes from the same place. My wish is that people understand what these indices really are and that weather announcers do the work of informing instead of "feeling".

You are welcomed to reach me by e-mail for all comments.

Links

• Testimony of one of the participants of the windchill factor tests
• Description of the new windchill factor formula

• Environment Canada
• The Weather Network
• The dewpoint.
• Vapor pressure definition

Reference

[1] MASTERSON, J. and RICHARDSON, F. A., 1979 : Humidex, A Method of Quantifying Human Discomfort Due to Excessive Heat and Humidity. Downsview, Ontario: Environment Canada. 45p.