The Problem With Wind Chill

In December 2013, Environment Canada announced that there will changes to how the organization’s meteorological service will issue warnings when it comes to extreme cold. Currently, the only warning that can be issued for extreme cold is a wind chill warning which has three parameters:

  1. The wind chill exceeds some arbitrary threshold based on geography.
  2. The wind is greater than or equal to 15km/h
  3. The conditions will last for 3 hours or longer.

Environment Canada plans to move to an Extreme Cold warning which will account not just for wind chill, but for temperature as well. They’ve been working together with Health Canada to develop a new criteria (hopefully) based on when the cold is a significant impact or health risk to individuals. Without question, the best part of this new plan is the inclusion of temperature as something that can be warned for instead of relying primarily on wind chill.

What’s Wrong With Wind Chill Warnings?

Wind chill warnings are one of the most problematic warnings that Environment Canada has. I’m going to take a moment to step through the current criteria (keeping in mind my main “data bank” is for sites located in the Prairies) and point out the problematic aspects of each criteria. I’m then going to take a quick look at how the wind chill number is calculated and explain to you why it’s nearly useless in real-world settings.

The wind chill exceeds some arbitrary threshold based on geography. As it stands, there are multiple thresholds on the Prairies for wind chill warnings. Over much of the populated regions (south of the tree line), the required wind chill value is ≤ -40. For a few regions in the northern Prairies it’s ≤ -45, and for Churchill it’s -50.

Why the discrepancy?

It seems to simply be that some places see colder wind chills more frequently. Winnipeg rarely, and I mean rarely sees a wind chill of -50. It happens in Churchill a couple times a winter. To avoid having warnings out all the time, the criteria is simply lower. In British Columbia, where they have “arctic outflow” warnings instead of wind chill warnings, their criteria is -25. Winnipeg spends a good chunk of winter with actual temperatures below BC’s warning criteria for wind chill. Certainly the cold doesn’t affect people’s body differently based on geography, so there’s a less-than-scientific methodology being used to set the criteria.

The wind is greater than or equal to 15km/h. This can be particularly problematic on the Prairies. Contrary to the title, a vast majority of the wind chill warnings issued on the Prairies occur for events with very cold temperatures and fairly light winds. Rare are the cases such as Regina just before Christmas where bitterly cold temperatures combine with significant winds. Many wind chill warnings occur with winds ≤ 20km/h as a strong ridge of high pressure settles over the area. In these cases, winds will often fluctuate between 10-20km/h through the night[1]. In addition, most anemometers have an error threshold of 3-4km/h (this is partly why winds of 5km/h or less are called “Calm”), so even if you’re at 10km/h or 20km/h, statistically you could easily be right around 15km/h.

The reason that this is such a problem is that most wind chill warnings on the Prairies occur in situations where you have very little synoptic (large-scale) forcing of the wind field. Winds are often driven by the drainage of cold air and can be highly variable over short distances. 15km/h is so low that you don’t know if you’re outside your margin of error on the wind speed, and you can’t really forecast what the winds will do since it’s all driven by local effects.

The conditions will last for 3 hours or longer. This one is one that has never made sense to me; they tell us that “exposed skin can freeze in 5 minutes or less” but require that condition to last for 3 hours to issue a warning for it. Is it dangerous? If it can cause you to lose the end of your nose in 10-15 minutes, why wait for such a long duration to warn people? The requirement for the duration is extremely out of sync with the duration the threat needs to have significant impact.

So we’ve covered how the criteria is somewhat arbitrary, based more in climatology than physical impacts, the wind speed criteria is set at a level that makes it nearly impossible to be certain whether or not you’re actually hitting the speeds needed or to even forecast wind speeds to the precision required in a variable wind-speed environment and how warnings require a duration of the condition that is far, far longer than the time the threat needs to make significant impact on an individual.

All that being said, wind chill itself is the biggest problem with wind chill warnings.

The way that wind chill has been reported over the years has changed; prior to 2001, wind chill was reported using units of W/m2 and had numbers generally between 1000-3000. This was a measure of the amount of energy leaving your skin thanks to the wind and was fairly straight forward. In 2001, however, we moved to what is called the wind chill equivalent temperature which was built on work by the Joint Action Group for Temperature Indicies (JAG/IT). The new index was based off of standard engineering models for wind speeds and heat transfer rate.

The model developed by the JAG/IT was a complex interdependent series of equations which relied on around 10 variables to produce an outcome. Environment Canada did further research with 12 volunteers (6 men, 6 women), covering them with temperature probes and throwing them in a refrigerated wind tunnel (those poor souls) to try and find a “standard” set of variables to use. They then solved the system of equations with a linear regression to the following formula:

[T_{WC} = 13.12 + 0.6215T_{a} – 11.37V^{+0.16} + 0.3965T_{a}V^{+0.16}]

In this case, (T_{WC}) is the wind chill index, (T_{a}) is the air temperature in degrees celsius (°C), and V is the wind speed at 10 meters (standard anemometer height) in km/h. This equation produces the number that we see in the current observations and forecasts:

Clear. Becoming partly cloudy overnight. Wind becoming north 20 km/h overnight. Low minus 34. Extreme wind chill minus 44.

The devil is in the details, however. The number that equation produces is not a temperature; in fact, the number it spits out has no units whatsoever. It’s a “feels like” in the truest sense of the term; the equation is calibrated to °C but a temperature it does not produce.

Wind chill values at various wind speeds and air temperatures.
Wind chill values at various wind speeds and air temperatures.

The other thing worth noting is all those weird numbers. Where did 13.12 come from? What’s with 0.6215 and 11.37? I’ve heard of squaring things, but what’s with an exponent of 0.16?

Those are all coefficients that were determined in the linear regression of the series of equations to produce a single equation that requires only wind speed and temperature. To put it in simpler terms, those numbers are assumptions.

A Boatload of Assumptions

In fact, there are a whole host of assumptions that go into simplifying this complex system into a single equation. In total there are 7 key components of calculating wind chill that need to be accounted for which can be broken into two groups: body parameters and environmental parameters. First, the body parameters:

  1. Height of Face
  2. Width of Face
  3. Walking Speed
  4. Body Thermal Conductance

These are all choices that are made to account for the person the wind is blowing against. Numbers 1 & 2 account for how the wind impacts the face. The face is assumed to be a perfect cylinder of a given diameter whose centre is some height above the ground. The values chosen in the regression are a height of 1.5m above ground and a diameter of 18cm. This does broadly represent a decent average of the populace, but naturally your mileage may vary on how well you fit those values. The walking speed is assumed to be into the wind and is assumed to be 1.3m/s. So if you are standing still or running, the wind chill number produced by that equation is not valid for you.

The last value is the body thermal conductance and is perhaps the most contestable number in the entire thing. To create the wind chill equation a value of 11(frac{W}{m^2K}). This parameter is a measure of how effectively heat is transferred from the body’s core to the surface of the skin; the larger this number is the more heat is lost from the core. Obviously you could make this number very small by wearing some good Arctic issue winter wear, but in reality – as anyone who has been anywhere near a high school in winter has seen – people do not dress that well for cold weather. A lot of research has gone into this number from organizations all over the world and very reasonable acceptable values for it range from 4(frac{W}{m^2K}) all the way up to 100(frac{W}{m^2K}). This accounts for a dramatic range of heat loss.

These four parameters alone can substantially change the computed wind chill value, and there’s still the environmental parameters! The three that fit into that category are:

  1. Wind Power Exponent
  2. Wind Speed
  3. Air Temperature

The wind power exponent a number used to take a wind measurement at 10m off the ground and approximate the wind speed at the height of a person’s face. This number can vary quite a bit based on terrain, vertical stability profiles and other minor factors. The other two – wind speed and air temperature – are fairly self-explanatory.[2]

So now we’ve covered the 7 key parameters in calculating wind chill and some of the assumptions take with each one of them. To summarize each component and the assumed values are:

  • Face Height: 1.5m
  • Face Width: A cylinder with diameter of 18cm
  • Walking Speed: 1.3m/s
  • Body Thermal Conductance: 13(frac{W}{m^2K})
  • Wind Power Exponent: 0.21

These assumptions can be dangerous simply because not everyone’s face is 1.5m off the ground and we don’t all have perfect cylinder heads. Fortunately, we can account for those things by introducing error into our calculations; we can assume that the acceptable variance in a value is ±X, where X is some number that adequately captures an acceptable range in that parameter value. We can then calculate a simple graph called a probability distribution that depicts what the probability is of the end value being any one specific value (e.g. given all the variance, with these conditions how likely is it that the wind chill is actually -40).

Just A Little Off…

Great! We’ve assessed weaknesses in the assumptions and know that we can compensate for those by including variations on those values into the equations we use to calculate wind chill. Well, it would be great, but absolutely no error or variation is used in creating the wind chill equation. Even documented “guaranteed” error, such as the well-known ±4km/h attached to any wind speed reading from an anemometer has been ignored.

This has huge implications on the calculation of the wind chill. I’m going to skip a lot of small ones to target the big one:

Ignoring error in the calculation of wind chill has created a value that is conveyed as a number we have high confidence in; in reality, wind chill is one of the most uncertain weather parameters there is.

Here are two probability distributions for wind chill. The first one, in dark blue, follows the methodology used to create the wind chill equation and uses the assumed parameters while ignoring all variance. We see a very concise plot of a 100% certainty of a value of -40 for the wind chill. In a lighter blue, we’ve used the same parameter values but with reasonable variances included in the calculation. It’s easy to see that it tells a very different story.

Comparing the probability distribution for a -40 wind chill with error included vs. no error included. With no error, it states that there is 100% chance of the value being -40. With error included, that probability drops to just over 10% – a dramatic reduction in liklihood.
Comparing the probability distribution for a -40 wind chill with error included vs. no error included. With no error, it states that there is 100% chance of the value being -40. With error included, that probability drops to just over 10% – a dramatic reduction in liklihood.

The currently used linear regression for calculating wind chill is grossly over-confident in the actual wind chill value. In addition to that, its spread is very narrow (nothing), while the spread including standard deviation is quite large.

What does this mean in plain english? In reality, when you see that the wind chill is -40, it could actually be anywhere from -30 to -50 depending on a whole lot of small differences in our bodies and/or the environment.

Wind Chill Parameter Variance
ParameterVariance
Face Height (m)1.5 ± 0.05
Face Width (cm)18 ± 0.006
Walking Speed (m/s)1.3 ± 0.27
Body Thermal Conductance13 ± 4.5
Wind Power Exponent0.21 ± 0.06
Wind Speed (km/h)15 ± 1.85
Air Temperature (°C)-29 ± 0.25

And this is why wind chill, in its current form, is such a poor parameter to be using. Undoubtedly wind chill is a very real phenomenon that can have a dramatic impact on our bodies. It is, however, a parameter which has huge variation from person to person and depends significantly on how we dress, what our environment is like and on many factors where there will always be some level of uncertainty or variation. While we have gotten used to explicit declarations of the wind chill value, reality is far more fuzzy.

Warn On The Temperature

The significant problems with the calculations of wind chill and some of the curiosities regarding how Environment Canada warns a wind chill event leads us back to the changes being made to the warnings for extreme cold in the winter time.

As I’ve shown above, there are some egregious assumptions made that oversimplify the reality of how wind chill can be measured. In addition to that, there are fundamental parameters that can be dramatically altered by body type and clothing. The idea that there’s a “one size fits all” solution to wind chill simply isn’t rooted in reality.

Because of that, I can only applaud Environment Canada for moving back towards using the temperature to warn for extreme cold. The temperature is nothing but itself and is the baseline for heat loss. We are very good at measuring it and its variability across an area is far smaller than the wind.

This makes temperature a far more favourable parameter to use when talking about extreme cold; it is more representative over an area, has a more uniform affect on our bodies and requires no external assumptions. Hopefully, the next time you hear the “feels like” temperature in the winter time, you’ll now know that number isn’t all it’s cracked up to be.

For further reading on how the cold affects the body, check out this excellent article by Outside Magazine. I’ve attached my references below.

References

  1. Bluestein, M. and J. Zecher, 1999: A new approach to an accurate wind chill factor. Bull. Amer. Meteor. Soc., 80, 1893-1899.
  2. Bluestein, M. and R. Osczevski, 2002: Wind chill and the development of frostbite in the face. Preprints, 15th Conf. on Biometeorology and Aerobiology, Kansas City, MO, Amer. Meteor. Soc., 168-171.
  3. Tikuisis, P. and R. Osczevski 2002: Facial Cooling During Cold Air Exposure. Bull. Amer. Meteor. Soc. July 2003, p. 927–934
  4. Osczevski, Randall and Maurice Bluestein. The New Wind Chill Equivalent Temperature Chart. Bulletin of the American Meteorological Society, Oct. 2005, p. 1453–1458.
  5. Osczevki, R. J., 1994: The thermal resistance of the cheek in cold air. Defence and Civil Institute of Environ- mental Medicine Rep., 94–47.
  6. Stolwijk, J. 1971: A Mathematical Model of Physiological Temperature Regulation in Man. NASA Contractor Report, August 1971

  1. Most wind chill warnings occur at night.  ↩
  2. Remember that wind speed, when talked about with regards to calculating wind chill, is the speed measured 10m above the ground.  ↩

Weather Education: Low Pressure Systems

Low pressure systems are the “engine” that drive weather. They are what interact with warm and cold fronts, and they function to convert and dissipate the energy stored within the fronts. These systems have a “traditional” or “classical” progression that can be observed.

Frontal Wave

A simple schematic of a developing frontal wave. The blue line represents a cold front and the red line represents a warm front.

The first sign of the development of a low pressure system is the appearance of a frontal wave. This is a slight bend in an area of high thermal contrast. This is the beginnings of the warm and cold fronts.

Surface Low Appearance

A representation of a maturing surface low. The frontal wave has tightened into a near 90° angle at the intersection point of the warm and cold front, a sign that an occlusion will soon form.

As the wave tightens, and the cold front becomes more perpendicular to the warm front, the low pressure center appears on the inflection point of the warm and cold fronts (where the two fronts attach to each other). The low will then move with the mean flow aloft, following the troughs of upper-level waves (more on that later). As the low moves, the fronts move along with it. And naturally, the weather associated with those fronts moves along as well.

Mature Low

Analysis of a mature low. Convection is visible along the cold front over the Eastern United States. The warm front extending from Southern Quebec southeastwards into the Atlantic Ocean has a large cloud shield ahead of it. A trowel is visible arcing backwards around the low from Southern Quebec through Central Ontairo and bad around the Low in Minnesota into Michigan.

A satellite image depicting a mature low pressure system. The cold front is represented by the blue line, the warm front by the red line, and the trowel by the blue/red half-arrows. The center of the low circulation is marked by the large L.

One characteristic of cold fronts is that they are often faster moving that warm fronts. This can result in the warm front moving “along” the warm front and lifting the warm air up. This is called an occlusion process. The warm air aloft then is pulled towards the low and around it, rising in height. This warm air aloft is called an occlusion, or more frequently today, a trowel.

A mature low will have 4 distinct areas and kinds of precipitation: warm front precipitation, cold front precipitation, occlusion/trowel precipitation, and “wrap around” precipitation. Wrap-around precipitation is the weather that occurs in extremely close proximity.

Low Dissipation

Eventually, the warm and cold fronts pull themselves off the low pressure system. It can be likened that the “gas” for a low pressure system is the temperature contrast present in the fronts. When the fronts leave the low, warm air wraps around it and soon there is no more sharp temperature contrasts. When this happens, the low will “fill in” and dissipate.

Why Is It Called A Low Pressure System?

A cross-section schematic of the air flow through a low pressure system.

When a low pressure system begins to form, air is pulled in towards the center of it. We have discovered that, more or less, air in the atmosphere doesn’t like to compress. So instead of compressing as all this air meets in one place, it pushes air upwards. This creates a circulation where air moves in towards the low at the surface, rises some height, then flows out and away from the low. This results in low pressure near the surface, where the air is rising, and higher pressure somewhere above, where the air is moving outwards. Thus, a low pressure system is called such because the surface pressure is actually lower than the areas around it. As it “dies,” the surface pressure will return to the normal pressure around the low.

I should mention that this is an extremely brief overview of low pressure systems. If you would like to learn more, there are entire books written on the subject, and to this day it is still an area of active research.

What Happened To Winter?

Winnipeg has been enjoy a wonderful winter, quite a surprise given that a lot of forecasts had called for colder than normal temperatures, a common occurance when La Nina is in full swing. This winter has been stellar so far, but just how warm has it been? Lets take a closer look, and then a special announcement!

For full disclosure, I’m using numbers from January 1981 to now from the Winnipeg Richardson Int’l Airport (1981-2007) and the Winnipeg Richardson AWOS (2007-Current). The numbers are gathered from the daily summary provided on the Weather Office Climate Archive site. The data used is “current” to January 25, 2012.

Looking first at daytime highs. We know that December was well above normal, as was the start to January. How much above normal?

December 2011 Temperatures vs. Climatology

December 2011 daytime highs compared to 30 year means. Maximum and minimum extrema included (these are the warmest and coolest daytime highs for those days in the last 30 years).

We can see that this year (yellow bold line), much of December was spent above our average daytime high. In fact, 84% of the days in December had daytime highs above normal, with a streak of 17 days with above normal temperatures. We were, on the days we were above normal, on average 10°C above our normal daytime highs for each respective day in December.

January 2012 Temperatures vs. Climatology

January 2012 daytime highs compared to 30 year means. Maximum and minimum extrema included (these are the warmest and coolest daytime highs for those days in the last 30 years).

So far this January, we’ve been off to a great start as well, with 71% of our days above normal for daytime highs, which isn’t bad for having quite a cold snap in the middle of the month. We had a nice streak at the beginning of the month with 11 days in a row with above normal temperatures. On the days this month that we’ve been above our normal temperatures, we’ve been, on average, 6.5°C above normal for each respective day in January.

So the days have been warm. This only tells half the story, however. An interesting story emerges when we look at overnight lows…

December 2011 Temperatures vs. Climatology

December 2011 overnight lows compared to 30 year means. Maximum and minimum extrema included (these are the warmest and coolest overnight lows for those days in the last 30 years).

When we look at December of this winter, we see a compelling argument unfold. 23 nights (74%) of the monthhad temperatures, on average, 8.4°C above normal. We had 11 nights in a row with overnight lows above normal by as much as 13.5°C! And January is an equally compelling story…

January 2012 Temperatures vs. Climatology

January 2012 overnight lows compared to 30 year means. Maximum and minimum extrema included (these are the warmest and coolest overnight lows for those days in the last 30 years).

This month, we’ve spent 16 nights with above normal temperatures (65% of the month), which have been 10.6°C above normal on average. We had a wondeful streak of 11 nights at the beginning of the month with above normal overnight lows, including January 9th, whose overnight low was a whopping 17.5°C above the 30-year mean.

So not only have we been nowhere close to as cold as it can be, we haven’t even really spent any signifigant time being anywhere near as cold as we ought to be! But there’s one way to make this even more succinct…

December 2011 Means vs. Climatology

December 2011 mean temperatures compared to 30 year means.

What I’ve done here is a crude approximation of the mean daily temperature. While it would be nice to properly integrate the hourly observations to calculate a true time-weighted mean temperature for each day, I have weather stripping to install, shelves to build, and many other things that would also like my time. So I’ve done a quick average of each day’s maximum and minimum temperatures ( [Max + Min]/2 ). I’ve calculated the 30 year mean by taking the mean of the mean daily temperatures.

What this shows us is a “combined” look at how much warmer the entire day was, instead of singular values. We can see that once we shifted into a warmer patter around the 10th of December, we cruised without looking back. A total of 26 days (84% of the month) above the normal mean daily temperature, with many days as high as 10-15°C above normal. We had 17 days in a row with above normal temperatures in December, and for all the days above normal, we were on average 6.9°C warmer.

December 2011 Means vs. Climatology

January 2012 mean temperatures compared to 30 year means.

January tells a similar story with 17 days so far above normal, on average by 10°C! What these mean values tell us is that not only have our days been warm this winter, but the entire 24-hour cycle has been significantly wamer than normal as well. Save for one day, we were above normal in hour temperatures from December 10th to January 11th, 32 days in a row. We spent a month with temperatures 6-10°C above normal on average, with many days near or warmer than 0°C during a time of the year when it’s not uncommon to be hiding inside while it’s -35°C outside! What a winter indeed!

And with ensembles predicting above normal temperatures into the middle of February, our odds of getting an entrenched arctic deep freeze in Winnipeg are starting to look mighty, mighty slim. Something I’m sure not too many people will complain about.


And Now For Something Different…

So, what if you want to make your own temperature forecast? Or precipitation forecast? What if you need to make your own decision on whether or not you should take your sailboat out on the South Basin tomorrow?

Fortunately for the public, most government agencies make their model data freely available for use. Getting at it can be difficult and time-consuming though. Everybody has their own tools for viewing data; often they are bulky and slow server-side PHP solutions. That jargon means that it’s not very fast and you spend a lot of time waiting for pages to reload.

Well, it doesn’t have to be that way! A Weather Moment is excited to introduce our model viewer! We’ve built a comprehensive tool that lets you view model data from several models, including Environment Canada’s GEM-Regional and GEM-Global models, the NWS NAM and GFS models, as well as the UKMET model and ECMWF. Over time, we plan on adding more publically accessible data to the viewer.

A Weather Moment Presents the Model Viewer

A Weather Moment Presents the Model Viewer!

You can easily switch models and load new products without ever having to refresh the page. We have convenient keyboard shortcuts to control everything from animation to mangification to removing frames from the loop or jumping back to the beginning or end. Our Frame Omitter gives you the control to view exactly the images you want. All of this is part of a lightning-fast backbone that lets you view model data quicker than anywhere else on the internet.

We are providing this to let you begin to see what goes into making a forecast. Please note that model data is not the “answer” to the weather. It is a computer’s opinion, and is wrong just as often as anyone else is. It can be very helpful guidance, and can often give you a good idea of what to expect.

We hope that this tool can help anybody who views our site access weather forecasting information quickly and easily! The only limitation is that, unfortunately, the viewer does not currently support Internet Explorer. There are a lot of technical reasons for this, but ultimately it’s because I’ve coded the tool to W3C standards for optimal compatibility, and Internet Explorer does not yet conform to those standards. The tool may or may not render and/or operate correctly on any version of Internet Explorer. Any other browser will work great, though (e.g. Mozilla Firefox, Google Chrome, Apple’s Safari). You can check it out by hitting the Model Viewer link at the top menu of the site, so go check it out!