Wind Chill and Humidex
(Critique of the indices)

Miguel Tremblay
physicist
May 31, 2003

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 announced, in a quasi systematic way, following the temperature in the weather reports in this country.

For example, on December 2nd on Environment Canada's website, in the section titled "Currently", left side of the page, for Montreal, it is written "Temperature: -7°C", "Wind chill: -16". Let us note that the wind chill announced on Environment Canada's website is without unit, contrary to the one one the Weather Network's website under the heading "FEELS LIKE". The Weather Network does not have the same scientific considerations.

In summer this index would be replaced by the humidex.

The section "Origins" reports how these indices were created. The section titled "Reasons against these indices" contains the principal objections concerning the wind chill. The sections "Economic Repercussions of wind chill" and "Breaking point" were written following the reception of emails from people relating their experiences. This will be followed by a mathematical discussion on the formulae used to calculate the indices.

Origins

Origins of the wind chill

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 reinvented 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 was obsolete and in certain circumstances created confusion. Thus in april 2000 Environment Canada held an Internet Workshop [sic] on wind chill for it to be better adapted to reality. Rather than be based 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 of the assumptions taken into account for this new index is relevant. Here is an example of these assumptions: "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]. I obtained this document 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 documented than that of wind chill since it was not remodeled during 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 which published a study titled "A method of quantifying human discomfort due to excessive heat and humidity". This study was published in 1979 by Environment Canada. If one omits the graphs and the charts indicating the various rates of humidex in Ontario, the content of this publication holds on 8 pages, including a review of the literature on the humidex.

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

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

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

The calculation of the humidex is based on:

The ambient temperature;
Vapor pressure;
The dewpoint.

Reasons 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 which is unsuitable for it and which it will never belong to. A feeling is specific to each individual. Science studies REPRODUCIBLE phenomena, this can not be applied, by definition, 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 Dany Laferrière who presented the weather bulletin at TQS or Pauline Martin on the morning show of Montreal's Radio-Canada's 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 on the basis of audacity and innovation to present the forecasts. The computer graphics used to show the geographical charts, on which it is possible to see precipitation for example, is very complex and each network has its own.

As in other highly mediatized fields it is easier to attract and retain the public's attention through sensationalism as opposed to the systematic and thorough explanation of a situation or a phenomenon. This is especially true when it comes to science because, for any concept one wants to really understand, it is necessary to do an effort of research and comprehension more intense than in fields where the opinion of specialists determines the dominant train of thought (political science or economics for example).

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.

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

Rather than report two measurements (air temperature and wind speed; air temperature and moisture) to people who should assimilate their importance and their interdependence, one prefers to amalgamate them into a formula which does not correspond to anything natural. Certain organizations (The Weather Channel) and even the publication from which the humidex originated, have the audacity to convert these factors into degrees Celsius - a vulgar usurpation.

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

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 consistant?
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. The model of the human face, how, when and on who was it modeled? 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 with an average 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 the comprehension of the wind chill by Canadians. The results are eloquent and show well that this factor is misunderstood. Something that would not happen by simply reporting the speed of the wind.

From the web page Public Opinion Research on Wind Chill in Canada, "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."

We will not discuss the fact that 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. These indices, rather than inform people, they induce them in error.

Economic repercussions of wind chill

Wind chill is only used on this side of the Atlantic, i.e. North America. Europeans are 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.

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 will not assimilate the nuances, we ourselves are unable to do so. Being unable to be clear about the temperature outside, is not to our benefit.

Locally this must anger owners of companies who promote the great outdoors. For example, cross-country skiing. If it is -15°C and reported as -32 with the wind chill, would you remain in the house rather than go on a planned excursion in the forest? On the other hand, if you knew that it was -15°C and very windy, you would have the reflex to think there's no wind in the forest. Same reality. Different ways of expressing it. One way results from a mathematical blur, the other way comes 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:

H = H(T, h) = T + h, où { H is humidex index, T is temperature in °C, h = (5 / 9)(e - 10), e is the water vapor pressure in millibar (mbar) }

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:

H(T,h) and h(dew point) ⇒ H = H(T, dew point); H(T, dew point) and dew point(T, % of humidity) ⇒ H = H(T, % of humidity)

Up to now, everything is ok.

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

10 is subtracted from it. 10 is a scalar, i.e. it does not have any unit, and it is subtracted from 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:

∀ T > 7°C, (e - 10) > 0; ⇒ h > 0; ⇒ H > T

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 H must thus be higher than the temperature, which is the case with this formula. A judicious choice but, it is a choice. One could have taken 9 or 11 but they choose 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.

Can we conclude that high level of moisture, when temperatures are lower than 7°C, gives the impression it is colder? In my humble opinion, as with that of all the people to whom I asked, the answer is yes. Then, why is moisture not taken into account in the computation of winter temperatures? Two reasons explain this.

Studies performed on American soldiers have shown that level of moisture do not have any influence on our perception of the temperature in winter. (note: unfortunately I was not able to re-locate the web page where I read this. If you have information on this subject, please contact me).
There is already an index for the temperature in winter (wind chill) which takes into account the speed of wind. Given the formula for wind chill (see below), it is almost unthinkable, even impossible, to introduce another variable to it.

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

Where does the 5/9 factor come from? Not having found any explanation in the literature, I will make the following theory: this factor make it possible to obtain a value from (e-10) which can reasonnably be added to the temperature in degrees Celsius. One need only think of a humidex with values hovering around 1000, if one had chosen 5000/9 instead of 5/9 for example. It is easier to see that the psychological impact is weaker than the one caused by a number which makes it possible for the humidex to resemble the temperature. If I told you "It was 3500 with the humidex", the impact is less than if I say "It was 45 with the humidex". It is a mathematical 'coup de théâtre'. The numbers were selected to resemble those we are used to.

Let us recap. 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. Nothing less.

Take H:

and say that it is in degrees Celsius. And here, you have just created the humidex.

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:

$R = 13,12 + 0,6215T - 11,37(V^0,16) + 0,3965T(V^0,16) where { R is the wind chill index; T is the air temperature in degrees Celsius (°C); V is the wind speed at 10 metres (standard anemometer height), in kilometres per hour (km/h) }$

First striking feature, the wind speed is to the power of 0.16. Astonishing. If you know or if you have any idea why this is contact me. Please.

Second striking feature, the addition of a scalar (13.12) to degrees Celsius (0.6215*T), then with km/h at the power of 0.16 (!), and finally with °C multiplied by km/h always at the power of 0.16. This is why I am surprised and astonished that the Weather Channel's website presents the wind in degree Celsius.

The new and improved wind chill is less subject to analysis as that performed on 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 deducted. 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". The web page on the program of Environment Canada on wind chill refers even to this hyperlink as follows: "Here you'll find the actual equation for calculating wind chill and how it was developed". False. They give the formula and what it is based on, but not how it was developed.

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

Let us stress that the only person identified for these tests (read the testimony) is a meteorologist. We can question ourselves about the representativeness of a meteorologist when it is a question of temperature. He does not certainly have the opinion of the average citizen, whereas he is supposed to account for 1/12 of humanity. This story does not tell the profession of the 11 other participants but it is thinkable, having only one case to extrapolate, that they are colleagues of the people having performed the experiment. If it were the case, not only is the sample extremely reduced (12 people), but the methodology used to deduce what is felt by ordinary people would be more than doubtful.

Breaking point

Usage of the wind chill and of the humidex in Canada dates backs to the beginning of the Nineties. It is for this reason that a revision of the wind chill was necessary. This index existed since 1940 and nobody complained about it. While using it more and more in the media, people realized some aberrations. These aberrations are corrected by the new wind chill; they "rectified" the curve representing the temperature felt.

In the winter of 2004, when the temperatures of the 10 Canadian provinces were announced at the radio of Radio-Canada (CBC), they also indicated the wind chill. This bulletin consisted of a series of 10 city names and 20 temperatures! It is long to listen to. Only a year before this method of doing things did not exist.

The question raised by this dynamic is, how far will the use of the wind chill spread. The media have already adopted it. Do the weather stations of the airports use it? Ski resorts? The army?

The media is not known for its restraint when it comes to hype. With the increasing use of these indices, it is natural to wonder when the breaking point will be reached. What will it take for the truth about these creatures to be revealed?

The publication of this web page is certainly a beginning. I attentively scan the media to see from where the first major crisis caused by the usage of these factors (humidex and wind chill) will come. Perhaps our awakening will come from the perception (incomprehension?) that foreigners have of these indices. We are forced to question their significance to be able to explain them. This inevitably leads to the conclusion that their existence, without speaking about their use, is an error.

When will this instant come?

Conclusion

It is astonishing that the smoke screens that are these indices - the wind chill and the humidex - are not exposed. The reason for the creation of this web page is to correct this situation. These indices being a Canadian creation, it is normal that the light on their reality come from the same place. My wish is that people understand what these indices really are, that the weather annoncers do their job of informing instead of "feeling".

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

References

[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.

Wind Chill and Humidex (Critique of the indices)

Creation : May 31st, 2003

Villeray

N 45° 33′ W 73° 36′