Comparison of Denali, K2, Everest, Chimborzo, Aconcagua, and Mt Vinson
Mountaineers are obsessed with physical altitude always creating lists such as the 8,000 meter peaks, the Seven Summits, the Colorado 14'ers, and countless others. However, just like wind and humidity affect the temperature that you feel; latitude, temperature, and weather affect the altitude that you really feel and the variances can be significant enough to move peaks in and out of various lists.
A previous post showed that geodists are able to calculate the physical height of mountains anywhere in the world within an accuracy of a meter. So why do mountaineers care about how high a mountain is?
- The human body needs oxygen to survive and lack of oxygen diminishes the body's ability to do work.
- In general, the higher you go the less oxygen there is and the harder it is to climb let alone survive.
- In particular there are factors, other than physical height above sea level, that affect oxygen deprivation and combined, give a better gauge as to how you truly feel climbing at a specific elevation, on a specific mountain, on a specific day.
The human body needs oxygen to survive:
Of the three main necessities of life (air, water, and food), oxygen is the most critical. It is air pressure, not air density, that forces air into the lungs and and allows it to assimilate into the blood stream. So from a mountaineer's perspective, we will focus on what has been termed "Pressure Altitude" as opposed to "Physical Altitude".
The higher you go, the less oxygen there is:
We get oxygen from the atmosphere which is a large mass of air that is several miles high. Air is compressible and has weight. The weight of all that air, at sea level, is roughly equivalent to 32 feet or ten meters of water. The weight of the air above you compresses the air around you, increasing the pressure. As you go up in altitude, there is less air above so the air around you becomes less compressed and is therefore thinner. As air gets thinner, it contains fewer gasses per unit of volume, and therefore less oxygen. (http://www.altitude.org/why_less_oxygen.php)
1976 International Standard Atmosphere Table
Other factors that affect oxygen deprivation:
Standard altitude-pressure tables allow mountaineers and aviators to determine their approximate height by measuring atmospheric pressure. Inversely, the height of a mountain approximately determines the pressure of the air on its summit. This general relationship usually works quite well; however, factors other than physical altitude, such as latitude, temperature, and weather also effect the air pressure and contribute to how you truly feel at a particular elevation. Think in terms of how wind chill can be significantly different than the actual temperature.
Just like there is no uniform sea level, there is no uniform atmospheric pressure throughout the world. The lowest portion of Earth's atmosphere, the troposphere, is wider at the equator (10 mi) than at the poles (5 mi). So the further north or south you go from the equator, the lower the air pressure will be at a given altitude. Contrary to popular belief, this variation in the troposphere is only slightly attributable to the gravitational shifts at higher latitudes due to the Earth's rotation and shape. The lower air pressure is caused almost exclusively by the lower temperatures encountered at more northern and southern latitudes. Please see "The Determination of Pressure Altitude and Implications for High Altitude Physiology" by Dr. Adam Helman, et al., 2006. This is an excellent paper and was the basis for all of my calculations.
Since cold air is more dense than warm air, at low temperatures the entire atmosphere is compressed downwards. Therefore, a specified air pressure will lie at a lower altitude in a cold environment compared to a warmer one. Temperature can change pressure by up to 15% from standard values. Using Dr. Helman's equation (13c), I compared perceived "Pressure Altitudes" for various well known peaks at high, mid, and zero latitudes including Denali (20,320 feet at 63° N), K2 (28,251 feet at 35° N), Everest (29,035 feet at 27° N), Chimborazo (20,702 feet at 01° S), Aconcagua (22,841 feet at 32° S), and Mt Vinson (16,050 feet at 78° S). I also included the 2 highest peaks in the lower 48 States Mt Whitney (14,505 feet at 36° N) and Mt Elbert (14,440 feet at 39° N) just for reference. I gathered historical average monthly temperature data from Wikipedia for towns near each mountain which served as the basis for the calculations and the results were surprising. (Note: the average monthly temperature data are rough approximations but the calculations are based on solid mathematical and physical principles. So the calculated pressure altitudes aren't absolutely accurate but should be accurate relative to one another.)
Click here for the spreadsheet with full data and calculations.
Insights from the Graph:
The first thing to note is that the pressure altitude on the summit of Everest is never as high as its physical altitude which is good for those of us who climb without supplemental oxygen. In conjunction, the pressure altitude on the summit of K2 is almost the same as that on Everest in January and December but then it just barely drops out of the 8,000 meter (26,246 feet) peak list in July. Next is the observation that Mt Vinson, where the average yearly temperature at Vostok Station is -65 F, has a pressure altitude at or above 20,000 feet (more than 4,000 feet higher than its physical altitude) for half of the year. Also note that both of the high latitude peaks (Denali and Mt Vinson) have pressure altitudes near or above their physical altitudes the entire year while Chimborazo, at the equator, is consistently at 19,500 which is 1,200 feet below its physical altitude. Finally, notice the indication that Mt Whitney (14,505 ft) in California and Mt Elbert (14,440 ft) in Colorado have virtually the same pressure altitude profile and that both drop below the coveted 14,000 foot mark during the normal climbing season of May through September.
Anyone who has ever owned an altimeter knows that you can gain or loose a few hundred feet just by sleeping in your tent overnight. This is due to high or low pressure weather systems. Because of thermal activity, air rises and falls within the atmosphere which changes the ambient pressure. Meteorologists measure the atmospheric pressure at the Earth's surface to help them predict weather patterns. High pressure usually means stable air and good weather, while low pressure can indicate instability and stormy weather. Therefore, if you wake up to bad weather, not only will you have to deal with the adverse conditions but you will feel like you are climbing at a higher altitude than you physically are.
Latitudinal temperature variances and area specific weather can have a noticeable effect on the real altitude that you feel. So when attempting a peak that you haven't climbed before, it is wise to consider factors other than physical height. Know the latitude of the peak and compare that to other peaks you have climbed. If you have climbed to 20,000 feet in South America, don't assume that is equivalent to 20,000 feet in Alaska. Choose an appropriate time of year and understand the effects of climbing outside of, or on the fringe of, the normal climbing season. Finally research the general weather patterns on or near the peak during your expedition window and plan accordingly. The more you know the better it will go.
Alan, I used Gilgit for K2. That was the closest city for which I could find climate data. Dr Helman’s paper gives an in depth analysis of his derivations of the equations but the bottom line is that temperature scales linearly with altitude in the troposphere. So to calculate the pressure altitude, you take the temp from a near by city extrapolate that to a sea level temp based on the city’s altitude and a standard lapse rate of 3.57 degrees per 1000 feet, convert it to Kelvin, and compare that to the International Standard Atmosphere sea level temp of 288.15 Kelvin. The ratio of those temps gives a good approximation the percent increase/decrease of the physical altitude.
So interesting. I had no idea that temperature on Denali is the reason it climbs “higher” than peaks lower on the face of the globe. Nice work 8kpeak.com!
Very nice article and graphs Jim. Curious what city you used fro K2’s annual temperature given it is so remote. Also, wouldn’t you need to consider the average air temperature from the earth’s surface to ??? the troposphere in order to accurately calculate the impact of the atmospheric weight?
In any event, excellent article.