With an average temperature of −63°C and winter lows of −120°C, Mars sounds far too cold for humans. However, thermometer readings from Mars are highly misleading to terrestrials who base their expectations of thermal comfort on their experience in Earth's much thicker atmosphere. The two-planet model of windchill described here suggests that Martian weather is much less dangerous than it sounds because in the meager atmosphere of Mars, convection is a comparatively feeble heat transfer mechanism. The windchill on Mars is expressed as the air temperature on Earth that produces the same cooling rate in still air, in Earth's much denser atmosphere. Because Earth equivalent temperature (EET) is identical to the familiar wind chill equivalent temperature (WCET) that is broadcast across much of North America in winter, it provides a familiar context for gauging the rigors of weather on another planet. On Earth, WCET is always lower than the air temperature, but on Mars the equivalent temperature can be 100°C higher than the thermometer reading. Mars is much colder for thermometers than for people. Some frontier areas of Earth are at least as cold as midlatitude Mars is, year round. Summer afternoons in the tropics of Mars might even feel as comfortable as an average winter day in the south of England. Sunshine on Mars should be about as warm as it is on Earth. Heat balance and clothing emissivity are also briefly discussed.
A two-planet model of windchill suggests that the weather on Mars is not nearly as cold as it sounds.
The groundbreaking book The Case for Mars (Zubrin 1996) advocates human exploration and colonization of the red planet. One of its themes is that Mars is beset by dragons of the sort that ancient mapmakers used to draw on maps in unexplored areas. The dragons of Mars are daunting logistical and safety challenges that deter human exploration. One such dragon must surely be its weather, for Mars sounds far too cold for human life.
No place on Earth experiences the low temperatures that occur every night on Mars, where even in the tropics in summer the thermometer often reads close to −90°C and, in midlatitudes in winter, as low as −120°C. The mean annual temperature of Mars is −63°C (Tillman 2009) compared to +14°C on Earth (NASA 2010). We can only try to imagine how cold the abysmally low temperatures of Mars might feel, especially when combined with high speed winds that sometimes scour the planet. This intensely bone-chilling image of Mars could become a psychological barrier to potential colonists, as well as to public support for such ventures. Fortunately, it is an alien cold. Thermometer readings from Mars are highly misleading to terrestrials, who base their expectations of thermal comfort on their experience with low temperatures in Earth's much denser atmosphere.
A visitor to an educational National Aeronautics and Space Administration (NASA) website (NASA 1997) noted that because the atmosphere of the planet is so thin, “a −20°C temperature on Mars would not feel as cold as −20°C air on Earth.” They went on to wonder what a person on Mars would feel the temperature to be and suggested that “It might be more relevant to many people to see the values shown on the website correlated to more human terms.” This paper provides that missing perspective by expressing the windchill on Mars as an Earth equivalent temperature (EET). EET is the air temperature on Earth, in still air and without sunshine, that would result in the same heat transfer rate and surface temperature as the very cold but insubstantial winds of Mars.
The mathematical model used for this calculation was developed in 2001 to calculate the values in the wind chill equivalent temperature (WCET) chart for North America (Osczevski and Bluestein 2005). In terms of heat loss rate, surface temperature, and cold sensation, EET is identical to the familiar WCET that is reported each winter across much of North America. It therefore provides a familiar context for assessing the rigors of weather on another planet, in this case Mars.
While it is highly improbable that anyone would ever directly experience the weather on Mars by exposing bare skin to the virtual vacuum that passes as its atmosphere, it is also unlikely that anyone on Earth would choose to face a WCET of −60°C without proper protection. Both EET and WCET are indices of the potential cooling power of the weather, whether or not anyone actually experiences it directly. They refer to the steady state heat transfer from the upwind sides of internally heated vertical cylinders having the same diameter, internal thermal resistance, and core temperature as the human head.
Air temperature alone is often a poor indicator of how cold the weather might feel. Wind, for example, makes a big difference to the thermal sensation at any temperature. The original “windchill index,” invented by Siple and Passel (1946), combined the cooling effects of low temperatures and wind in a number that was proportional to the rate of heat transfer from a small plastic cylinder. (Except when referring to specific products, this paper will follow the originators, Siple and Passel, in spelling windchill as one word, much as “rainfall,” “sunshine,” and “frostbite” are each one word.)
The windchill index was used successfully for decades until it was “improved” by expressing the cooling power of the weather as an equivalent temperature (i.e., the air temperature that would cause the same heat transfer rate when there is no wind). Although very popular, WCET is a deceptive simplification that only seems to be easier to understand. Over the years, many authors have criticized the original WCET and the windchill index on which it was based (Molnar 1960; Eagan 1964; Steadman 1971; Kessler 1993; Osczevski 1995, 2000; Bluestein and Zecher 1999). In 2001, the calculation model was updated (Bluestein and Osczevski 2002; Osczevski and Bluestein 2005) and a new WCET chart was produced for use in weather reports in Canada and the United States.
How cold it feels outside also depends on the physical properties of the medium in which one is immersed. Many have experienced the shock of discovering that immersion in 20°C water feels much colder than being in air at the same temperature. Water carries the heat away from the body much faster than air does at the same temperature. We do not often experience this nuance of windchill on Earth because atmospheric properties do not vary greatly from place to place or from day to day, but they do from planet to planet. Earth's atmosphere, being much denser than that of Mars, is analogous to the water in the above example.
THE ATMOSPHERE OF MARS.
Composition and pressure.
The air we breathe on Earth is mostly nitrogen, with significant oxygen, a bit of argon, and trace amounts of other gases. The atmosphere of Mars is almost entirely carbon dioxide (95%). The pressure at the surface is typically less than 1% of the sea level air pressure on Earth. At the Viking 1 and 2 landing sites of the 1970s the pressure averaged 8.5 mb (Tillman 2009). At the Viking 2 site it varied with season, being about 10 mb in the Northern Hemisphere winter and 7.5 mb in the late summer. On Earth, where the mean atmospheric pressure is 1,013 mb, pressures as low as those on Mars are only encountered in the stratosphere at an altitude of 32 km (110,000 ft) (ICAO 1993). This is two-and-a-half times the altitude at which commercial airliners fly and more than three times the height of Mount Everest.
Ambient temperatures on Mars.
Viking 2, which landed on Mars in 1976 at latitude 48°N, operated for over 1,000 sols (Martian days) and provided the longest and the most nearly complete record of weather conditions on Mars (Tillman 2009). Martian sols are 40 min longer than Earth days, and the solar year has 669 sols (Williams 2009). Wind and temperature data for the first 1,000 sols that Viking 2 operated are presented in Fig. 1. In summer, ambient temperatures, measured at 1.5 m above the surface, ranged from a low of −80°C at night to a comparatively balmy high of −30°C in during the day. In winter, they varied from roughly −120°C at night to −100°C during the daylight hours.
Winds on Mars.
Because of the physical size of robot landers like Vikings 1 and 2, wind speeds on Mars have never been measured 10 m above the ground, as they are by convention on Earth. The Viking landers measured the wind at a height of 1.5 m, which is convenient for modeling windchill as 1.5 m is about the height of the average adult's nose.
Winds speeds can exceed 100 km h−1 in global dust storms and briefly in dust devils, but they are usually much lighter. Because the atmosphere of Mars is very thin, even a 100 km h−1 wind would hardly be noticed, no more than a breeze of 10 km h−1 would be noticed on Earth (Zubrin 1996). Winds stronger than 60 km h−1 occurred in less than 1% of the observations at the Viking 2 site (Matz et al. 1998). Over a full year, the average of the archived data (Tillman 2009) was 16 km h−1. Winds stronger than 36 km h−1 occurred only during the fall, winter, and early spring at this site, when the average wind speed was 22 km h−1. In summer, the average was 10 km h−1.
HEAT TRANSFER CALCULATIONS.
The two-planet model assumes that the atmosphere of Mars is pure CO2 at a constant pressure of 8.5 mb. The two hypothetical cylinders of the model are identical to those of Osczevski and Bluestein's (2005) windchill model, with the same diameter, constant internal temperature, internal thermal resistance, and emissivity. Both cylinders move into the wind at walking speed. Just what the walking speed on Mars might be (Hawkey 2005) has yet to be determined, so an average terrestrial walking speed of 1.34 m s−1 was used for both planets. Comparison of the Grashof number for free convection in still air or CO2 with the Reynolds number for forced convection in the same gas confirms that on both planets, free convection at this minimum relative wind speed is only about a tenth of the forced convection and so may be neglected (Incropera and DeWitt 1996). On Mars, forced convection accounts for only about a quarter of the total heat transfer at low wind speeds. Radiation is the dominant heat transfer mechanism on Mars at low to moderate wind speeds. To calculate radiant heat transfer, the two-planet model assumes that the ground temperature on Mars is equal to the ambient temperature, which is approximately true when averaged over the whole sol. The reference condition for calculating equivalent temperature is not still “air” (CO2) on Mars, but in still air on Earth, at night.
Physical properties of CO2.
The properties of CO2 gas at 8.5 mb, at the extremely low temperatures found on Mars, were extracted from an online calculator (MegaWatSoft 2009) for a series of temperatures down to −55°C, which was the low temperature limit of the calculator. Trend lines were fitted to the data to develop regression equations for thermal conductivity, k; kinematic viscosity, n; and the Prandtl number, Pr (Table 1). Atmospheric properties used in the model were evaluated at the mean film temperature (i.e., the average of the cylinder surface temperature and the ambient temperature). As in 2001, an iterative method was used to find the heat transfer rate and the surface temperature of a vertical cylinder on Mars and the equivalent still air temperature on Earth.
THE COLDNESS OF MARS IN TERRESTRIAL TERMS.
A windchill chart for Mars.
Earth equivalent temperatures were calculated for a range of air temperatures and wind speeds on the planet Mars (Table 2). Note that the equivalent temperatures in each column are always higher than the thermometer reading at the head of the column—sometimes more than 100°C higher.
In Fig. 2, the windchill curves for the two planets are compared at −40°C, with winds measured at face level. At this temperature, chosen because it occurs regularly on both planets, the windchill on Mars is about 50°C warmer than the windchill calculated for the same wind speed and air temperature on Earth. According to the 2001 model of windchill on Earth, at −40°C with no wind other than the relative motion of the cylinder as it moves through still air at walking speed (WCET = −40°C), the surface temperature of the cylinder (or cheek skin temperature) would be −12°C. The risk of frostbite exceeds 5% whenever the skin temperature is below −4.8°C (Danielsson 1996). Thus, there is a significant risk of frostbite at −40°C on Earth even when there is no wind. On both planets, a cylinder surface temperature of −4.8°C is reached at an equivalent temperature of −27°C. On Mars at −40°C, the cylinder surface temperature will often be well above Danielsson's critical skin temperature. Even with a wind speed of 100 km h−1, when EET is −20°C, the calculated cylinder surface temperature is just 0°C.
−20° on Mars.
We can now answer the question of what an ambient temperature of −20°C might feel like on Mars. Without wind, it should feel much like +2°C does on Earth in still air. With a 100 km h−1 wind, −20°C should only feel as cold as it does on Earth when the WCET is −9°C.
Viking 2 weather.
For convenience, an approximate equation was derived from the output of the model to calculate EET from wind speed and air temperature. The equation and the model agree within 0.4°C over a very wide range. Twenty-five “hourly” EET values were calculated for each of the first 1,000 sols of Viking 2 data. These values constitute the middle curve of Fig. 1. The upper and lower curves are the measured wind speeds and ambient temperatures, respectively. The calculated equivalent temperatures are much higher than the thermometer readings—75°C higher during the coldest part of the year with average winds. EET minimums for the first 1,000 sols ranged from −20°C in midsummer to −45°C in midwinter; maximum values ranged from 0°C in midsummer to −20°C in midwinter. The mean daily EET in winter was approximately −30°C.
Typical Mars summer weather.
Viking 2 sol 100 appears to have been an unremarkable summer sol. It had an average temperature of −60°C and average wind speed of 9.6 km h−1. During the daylight hours, EET reached −7°C. The mean for the sol was −13°C. Most summer sols were unremarkable. At any hour the temperature was almost the same as it had been the day before at that same hour—slightly warmer as solstice approached and slightly cooler afterward.
Inland areas on Earth have an average wind speed of 14 km h−1 (NASA 2004). In order that the WCET be −13°C with an average wind, the air temperature need only be −7°C. That is, at −60°C, the tenuous winds of Mars should feel about as cold as winds usually do on Earth when the air temperature is −7°C (+19°F). Many people thrive on this planet in such conditions during winter.
A typical winter day on Mars.
According to the two-planet model, at −100°C on Mars, with an average Viking 2 winter wind of 22 km h−1, the EET is −29°C. On Earth, with an average terrestrial wind, a WCET of −29°C occurs when the air temperature is −20°C. This temperature is typical of winter lows in midlatitude areas of Earth with continental climates.
COMPARING THE WEATHER ON MARS AND EARTH.
Example 1: Minneapolis/St. Paul, United States, 45°N.
Three million people live in the metropolitan area of Minneapolis/St. Paul, a midlatitude urban area with a continental climate. The average winter (December, January, February) temperature is −8.1°C (14°F) and the average winter wind speed is 16.5 km h−1 (University of Minnesota 2005). These combine to produce an average WCET of −15°C. Mars, with a mean annual EET of −16°C, is only a degree colder on average than the “Twin Cities” in winter.
Example 2: Resolute, Canada, 75°N.
Approximately 250 people live in the hamlet of Resolute, which is not far from the Haughton-Mars Project research station. The average annual temperature at Resolute is −16°C and the average wind speed is 20 km h−1 (Environment Canada 2012). The annual average WCET is therefore −25°C, which is 9°C colder than the mean annual EET of Mars. In summer, the average WCET at Resolute is −12°C, much like a typical summer day in the midlatitudes of Mars, except that the sun does not set.
During winter, the air temperature at Resolute averages −32°C, and the average WCET is −45°C. The latter is 15°C colder than the average EET during winter at the Viking 2 site on Mars and is close to the record low EET for this site. The lowest temperature ever recorded in Resolute was −52.2°C and the lowest WCET was −72°C (−98°F). For comparison, the lowest EET for the Viking 2 site on Mars is just −46°C, while the record low WCET for Minneapolis/St. Paul is a cool −55°C (−67°F).
In shade or heavy overcast, summer in the High Arctic probably feels much like a summer sol in the midlatitudes of the Northern Hemisphere of Mars. However, when the temperature drops after sunset on Mars, its weather probably feels colder than the High Arctic does in the continuous daylight of summer. In winter, the weather on Mars will generally feel more comfortable than the challenging, dark winter typical of Earth's High Arctic—more comfortable but, as Lowell (1908) put it, still having “a polar complexion to it not wholly pleasing to contemplate.”
Example 3: The south of England.
In 1907, American astronomer Percival Lowell calculated a mean global temperature for Mars of +8°C (Lowell 1907)—warm enough for liquid water to flow in the network of canals that he and other astronomers thought they could see on its surface. Wallace (1907) challenged Lowell's calculation and pointed out that an average temperature of +8°C was “almost exactly the same as that of mild and equable southern England,” which he thought was impossible for a planet so far from the sun. He noted that in 1904 J. H. Poynting had calculated the average temperature of Mars to be −38°C (Wallace 1907).
To Lowell, the canals were evidence that a race of intelligent beings inhabited Mars and had probably constructed the canals to convey meltwater from the seasonally melting polar caps to arable land at lower latitudes in response to catastrophic global climate change (Lowell 1908). For ice to melt and water to flow, the temperatures on Mars had to be much higher than Poynting's estimate.
“Canals” continued to be observed, discussed, and drawn on authoritative maps of Mars for at least another half-century (e.g., NASA 1962). However, as we now know, they were an illusion. Wallace was correct; Mars is much colder than Lowell hoped, and colder still than Poynting thought.
Decades later, Carl Sagan (Sagan 1985) confused the issue when he commented that Lowell had imagined the Martian temperatures “a little on the chilly side, but still as comfortable as the ‘South of England.’” Sagan did not say who he was quoting, but since Lowell does not seem to have mentioned either England or comfort in connection with the temperature of Mars, it could not have been him. Whatever its origins, the seemingly implausible notion that Mars might ever be as “comfortable” as the South of England can now be tested.
In December, January, and February, the mean temperature of a large area of southern England, one degree of longitude wide and one degree of latitude high, centered on 51.5°N, 1.5°W (approximately midway between London and Bristol) is +4.4°C, which is 67°C higher than the mean temperature of Mars. However, temperature is only one factor in thermal comfort. The average wind speed during this period is 23 km h−1 (NASA 2004). The average WCET in south England in winter is therefore 0°C, which is 16°C warmer than the average EET of Mars. On average then, south England is much more comfortable for humans than Mars—but perhaps not always.
If we compare the summer conditions on Mars to winter in south England, there is some similarity. At the Pathfinder landing site at 19°N latitude, the mean daily high temperature in early summer was −14°C (Tillman 2009). A typical wind speed at this location was 14 km h−1. EET calculated for this combination of wind speed and temperature is +1°C, which is one degree warmer than the mean winter WCET of south England. Thus, in midafternoon in summer, the tropics of Mars were about as comfortable as an average winter day in south England. Even much farther north at the Viking 2 site, the EET in summer equaled the average winter WCET of south England on several occasions (Fig. 1).
Mars receives much less heat from the sun than Earth does because it is much farther away from it. The irradiance at the top of the atmosphere of Mars averages 590 W m−2, which is 43% of the irradiance in Earth orbit (Matz et al. 1998). In the south of England, cloud cover in winter averages 70%, so bright sunshine is not the norm, but on Mars, it is.
In the area of south England defined earlier, the radiation incident on a horizontal surface at midday during December, January, and February averages just 150 W m−2 (NASA 2004). At the same latitude in the summer hemisphere of Mars, the solar load can exceed 500 W m−2 at midday, even when there is dust in the air (Justus Duvall and Johnson 2003). With the same geometry, the solar heat absorbed by the cylinder on Mars is likely to be about three times what it would be at midday in winter in cloudy south England. This difference in solar heating increases the likelihood that some regions of Mars might be as comfortable as the south of England in winter.
Radiant heat transfer to the sky and ground.
The model assumes that the sky temperature on Mars is constant at −110°C and that ground temperature is equal to air temperature. On both planets, ground temperatures often differ significantly from the temperature of the atmosphere a meter or so above it, depending on the time of day, wind speed, and solar radiation. On Mars, ground temperature departures from ambient temperature are largest in the afternoon, when they can be 25°C warmer than ambient temperature (Matz et al. 1998). To see what effect this might have on calculated values of EET, the ground temperature in the Mars portion of the model was first set to 25°C above an ambient temperature of −60°C and then to 25°C below it. EET differed by less than 3°C from the value in Table 2 at any wind speed.
The constant sky temperature of −110°C is the average of the summer and winter daily maximum and minimum values of sky temperature taken from in Fig. 3 of Matz et al. (1998); thus, it is an estimate of the annual average sky temperature at 22°N latitude (Viking 1 landing site) in both clear and dusty skies. It is thought to vary by ±10°C during the daylight hours (Matz et al. 1998), and to be as high as −70°C during dust storms (Justus Duvall and Johnson 2003). When a sky temperature of −70°C was used in the model instead of −110°C, with an ambient temperature of −60°C, EET was less than 3°C warmer at any wind speed.
The radiant heat transfer to the sky (and ground) is proportional to the difference between the fourth powers of the cylinder surface temperature and the sky (or ground) temperature. At absolute zero there is no radiant heat from the sky. It increases slowly at first as sky temperature warms. Even at a sky temperature of −70°C, sky radiation received at the vertical surface of the cylinder is small compared to the total heat transferred from it when its temperature is around 0°C. Thus, on Mars, the net radiant heat transfer from the cylinder to the sky is relatively insensitive to errors in sky temperature. This is also why excursions in ground temperature do not have a large effect on radiant heat transfer and EET. The potential errors incurred by assuming that the ground temperature equals the ambient temperature, and that the sky temperature is a constant −110°C, seem acceptable for the limited purposes of this study.
Solar heating on Earth and on Mars.
To see if solar heating might be more effective on Mars a small amount of external heat (10 W m−2) was mathematically added to the vertical surfaces of the cylinders in both the 2001 terrestrial model and the new two-planet model. Air temperatures in this experiment were set at −40°C. No extra heat was added in either reference still air condition. The cylinders were mathematically exposed to the same wind speeds at cylinder level.
Over a wide range of wind speeds, the average increase in the calculated equivalent temperature due to the extra heating was 2.8 times as great on “Mars” as it was on “Earth” (Fig. 3). Thus, the lower irradiance at the orbit of Mars might be completely offset by the greater heating effectiveness of sunshine in the thin Martian atmosphere (i.e., 2.8 × 43% > 100%). On Earth, bright sunshine is thought to add about 10°C to the WCET in average winds (Environment Canada 2012). On Mars, sunshine should add at least that much, significantly enhancing the thermal comfort of individuals during daylight hours.
Internal thermal resistance.
WCET and EET are not calculated for the average person, but for those most susceptible to facial cooling and frostbite. If windchill equivalent temperatures on both planets were calculated for the average person, the windchill on Mars might sound even less frightening.
Changing the internal thermal resistance of the cylinders used in the 2001 terrestrial WCET model from the 95th percentile value to the 50th percentile value (Ducharme et al. 2002) shifts the WCET for any given wind and temperature combination on Earth a few degrees lower (Osczevski and Bluestein 2005). That is, it makes Earth windchill sound colder, but any given WCET would now feel warmer to everyone than it did prior to that change.
Making the same changes to the internal resistances of the cylinders of the two-planet model shifts EET a degree or two higher, making Mars sound warmer than Table 2 now suggests. Not only would the number increase, but the WCET it equated to would feel warmer than it does now.
Cylinder emissivity, EET, and heat balance.
Changing the surface emissivity of the model cylinder on Mars has an interesting effect on EET. The model assumes that its emissivity is 1, which is close to the emissivity of skin, many plastics, and most fabrics. An emissivity of 0.2 could be easily attained with a clean metal surface. Using an emissivity of 0.2 increases the calculated value of EET at −60°C by a whopping 27°C with no wind and by 17°C with a wind speed of 100 km h−1.
On Earth, where convection dominates, the popular wisdom is to dress in layers so that clothing can be added or removed to maintain comfortable skin temperatures when activity level or ambient temperature changes. Because radiant heat transfer is the dominant heat transfer mechanism on Mars, significant adjustments to heat balance might be conveniently accomplished by varying the emissivity of the outer surface of the pressure suit or of some garment worn over it.
The tenuous winds of Mars are clearly far less challenging than those we face on Earth. Because of its thin atmosphere, Mars should prove to be much warmer for people than it is for thermometers. Those of us who live where the winter is colder than the winter in south England regularly experience weather that feels colder than the midlatitudes of Mars during the afternoon of an average summer sol. This includes much of Asia, North America, and northern Europe. Some sparsely populated frontier areas of Earth feel at least as cold as much of Mars does, year round.
Regardless of how one regards the thermal comfort of winter in England, or of summer in Resolute, they suggest a much improved prospect for summer on Mars than the one rendered up to now by raw temperature readings transmitted from its surface. The image of winter on Mars has also been enhanced, for it is not as fiercely cold as spacecraft weather reports have made it seem, but might actually seem warmer than the winter in some frontier areas of our home planet.
There may very well be good reasons why Mars is not suited for humans, but extremely cold air is not one of them. Mars simply does not have enough of it to be an insurmountable problem. Scratch one dragon.
Defence Research and Development Canada provided financial support for the publication of this paper. Some solar and meteorological data were obtained from the NASA Langley Research Center Atmospheric Science Data Center. Also, my thanks go to David Phillips, Senior Climatologist at Environment Canada, for wondering if I could tell him what the windchill was on Mars.