AMREE 1981 · 790 weather-balloon stations · the alveolar gas equation

The Mountain Stands in Thicker Air

By the standard atmosphere, the air pressure on the summit of Everest is 236 Torr, so low that a person breathing the way they do at sea level would have no oxygen left in their lungs at all. The barometer carried to the top in 1981 read 253. The difference is where the mountain stands. Everest is in the subtropics, where the air beneath the summit is warm and there is more of the atmosphere still overhead at 8,849 m, and the people who climb it without bottled oxygen pant their carbon dioxide down to a fifth of its normal level. Below, 790 weather-balloon stations are asked what the summit air would be if Everest stood above them, month by month. At Denali's latitude, its best month would be thinner than its worst month is over Tibet.

The arithmetic that says no

The air you breathe is about 21% oxygen at any height; what thins with height is the air itself. How much oxygen reaches the air sacs of the lungs, where the blood picks it up, is set by three numbers, and physiologists write them into one line called the alveolar gas equation:

P_AO₂ = 0.2093 × (P_B − 47) − P_ACO₂ × 1.139

P_B is the barometric pressure. The 47 is water vapour: the airway saturates every breath at body temperature, and at 37 °C water vapour takes 47 Torr of whatever pressure there is, first. What is left, times oxygen's share of dry air (0.2093), is the oxygen you breathe in. The last term is what carbon dioxide costs: the lungs are also where it leaves the blood, and the more of it sits in the air sacs, the less room there is for oxygen. The factor 1.139 comes from assuming the body gives off 0.85 molecules of carbon dioxide for each molecule of oxygen it takes up, the value the 1981 expedition's summit paper used.

At sea level, with the ordinary 40 Torr of carbon dioxide in the air sacs, the equation gives about 104 Torr of oxygen. Now put in the summit. The standard atmosphere (the 1976 U.S. edition: one fixed profile of pressure against height, the same everywhere) gives 236.2 Torr at 8,848.86 m. Water vapour takes 47 of it, and the oxygen breathed in is 39.6 Torr. Ordinary breathing charges 45.6 Torr for carbon dioxide. The equation comes out below zero. Breathing as you do at sea level, it runs out at 264.8 Torr, which is higher than the summit's pressure by either reckoning. Nobody reaches the top of Everest breathing like that. Anyone who reaches it without bottled oxygen has done two things: gone to a mountain whose air is thicker than the table says, and breathed so hard that the carbon dioxide term nearly vanishes. Try both.

Set the pressure to the measured summit and slide the carbon dioxide down. The oxygen comes back only as the carbon dioxide goes: every Torr of it you breathe off returns 1.139 Torr of oxygen. The expedition's summit samples held 7.5 Torr of carbon dioxide, which the equation turns into 34.6 Torr of oxygen (the paper gives 35). The same breathing at the standard atmosphere's 236.2 would leave 31.1.

What the barometer said

On 24 October 1981, Chris Pizzo, a physician on the American Medical Research Expedition to Everest, reached the summit at about half past twelve with Sherpa Yong Tenzing, read a light hand-held barometer with a digital output, and collected samples of expired air, which were carried back to San Diego in gas-tight cans. The expedition's leader, the physiologist John West, and four colleagues reported the reading in the Journal of Applied Physiology in 1983:

“The mean daily pressures were 400.4 +/- 2.7 (SD) Torr (n = 35) at 5,400 m, 351.0 +/- 1.0 Torr (n = 16) at 6,300 m, 283.6 +/- 1.5 Torr (n = 6) at 8,050 m, and 253.0 Torr (n = 1) at 8,848 m. All these pressures are considerably higher than those predicted from the ICAO Standard Atmosphere.”

J. B. West, S. Lahiri, K. H. Maret, R. M. Peters Jr and C. J. Pizzo, “Barometric pressures at extreme altitudes on Mt. Everest: physiological significance”, J. Appl. Physiol. 54 (1983), 1188 to 1194, abstract.

The standard atmosphere's 236.2 is 16.8 Torr below that. The gap had been predicted before anyone measured it: Griffith Pugh, the 1953 expedition's physiologist, “predicted a pressure of 250 Torr for the summit of Mt. Everest in 1957”, West and Wagner wrote in 1980, and their own paper, using weather-balloon data from New Delhi (and Gauhati) that Charles Stidd of Scripps analysed for them, put it at 249 to 250 Torr in May and October; the standard atmosphere, they wrote, “gives a value of about 235 Torr”, and the difference “results in a doubling of predicted maximal oxygen uptake.” Of the summit samples, the expedition's gas-exchange paper, also of 1983, reported:

“Alveolar CO2 partial pressure (PCO2) fell approximately linearly with decreasing barometric pressure to a value of 7.5 Torr on the summit. For a respiratory exchange ratio of 0.85, this gave an alveolar O2 partial pressure (PO2) of 35 Torr.”

J. B. West, P. H. Hackett, K. H. Maret, J. S. Milledge, R. M. Peters Jr, C. J. Pizzo and R. M. Winslow, “Pulmonary gas exchange on the summit of Mount Everest”, J. Appl. Physiol. 55 (1983), 678 to 687, abstract.

West, looking back in 2019 on the 7.5: “This was an almost unbelievably low value since the sea level value is about 40 mm Hg.” His plainest statement of what the two findings mean together is in a 1982 review, written once the expedition was home: “It is apparent that the mountain can be climbed without supplementary oxygen only because the barometric pressure at the summit is not as low as has often been predicted, and because of the extreme hyperventilation that man develops under these conditions.”

Why the air is thicker there

The pressure at any height is the weight of the air still above it. How much air is above a given height depends on how far the air below has expanded, and warm air expands: the hydrostatic equation makes this exact, and says that for the same pressure at the ground, the pressure at 8,849 m is higher wherever the column of air underneath is warmer. Everest is at 28° north, under the warm, tall troposphere of the subtropics. A 2020 study put it this way: “Mt. Everest is, along with all other peaks over 8,000 m, located in the warmth of the subtropics.” West's 1983 abstract gave a different reason, from the top: pressures at these heights are “higher near the equator because of the large mass of cold air in the stratosphere of that region.” (His 1980 paper with Wagner gave a third, the “oblate spheroid shape of the atmosphere”.) What the balloons below weigh, either way, is how much air is still overhead at 8,849 m, and the hydrostatic arithmetic this page uses needs only the ground pressure and the temperature of the column beneath.

You do not have to take that on trust, because the atmosphere has been measured, twice a day, for decades. NOAA's Integrated Global Radiosonde Archive gathers weather-balloon soundings from stations around the world, and its monthly means give, for each station, the height and temperature of the standard pressure levels. At each station and month, this page finds the pressure at the height of Everest's summit: 8,848.86 m, converted to the geopotential metres balloons report in (about 8,823 over Tibet, about 8,850 over Alaska, because gravity is weaker near the equator), and interpolated between the two levels that bracket it, normally 400 and 300 hPa, assuming temperature changes linearly with height between them. Keep the stations with at least ten Januaries, ten Februaries and so on in 1991 to 2020, and you have 790 of them. Choose a month, and put Everest anywhere.

Over the whole year the stations draw an arch: highest across the tropics, where it barely moves with the seasons (the mean over every station from 10°S to 10°N is 254.5 Torr for the year), falling toward the poles, and swinging hard with the seasons in between. The standard atmosphere's 236.2 is close to what the balloons give for the band from 40 to 50°N over a year, 238.0. Everest's own latitude sits on the shoulder of the arch.

Then move Everest north. Denali, in Alaska, is at 63.07° north. The long Alaskan radiosonde record closest to that latitude is McGrath's, at 62.96°, about 230 km west of the mountain, and above it the summit of an Everest would sit in air of 238.4 Torr in its warmest month, July, and 217.6 in December. Over Tibet and northern India, the worst month of the year is January, at 242.7 to 243.1. At Denali's latitude, Everest's best month would be thinner than its worst month is where it stands. West, in 1984, did not hedge: “It seems certain that if Everest were located at the latitude of Mount McKinley, for example, it would be impossible to climb it without supplementary oxygen because the barometric pressure would be so low.” The page cannot test “impossible”. It can say what the equation does with the number: at the summit samples' 7.5 Torr of carbon dioxide, December air over McGrath leaves 27.2 Torr of oxygen in the air sacs, against 34.6 at the 1981 reading.

The mountain's own seasons

Three balloon stations stand close enough to Everest to say what its summit air does through the year. Lhasa is about 450 km east, on the Tibetan plateau, with flights from 1957 to now. New Delhi is about 950 km west, on the plains, one of the two stations West and Wagner relied on. Tingri is about 70 km north of the summit and flew from 1973 to 2000, too early and too sparse for the 1991 to 2020 climatology, so it is shown over its whole record.

West's 1983 paper, from the balloons of its day: “Data from weather balloons show that the pressure at the altitude of the summit of Mt. Everest varies considerably with season, being about 11.5 Torr higher in midsummer than in midwinter.” The New Delhi balloons, forty years on, give 11.6 from January to August; Lhasa's give 12.6. Most ascents without bottled oxygen are made in May and October, when these monthly means are 250 to 252. That is not the whole story of a climbing day. Single flights scatter widely around the mean: over Lhasa, the middle 90% of May flights runs from 248.1 to 254.2. The 2020 study reconstructed the summit pressure on the days of all 208 oxygenless ascents from 1979 to 2019 and found them “on days with relatively high oxygen availability for the time of year”, near the 70th percentile of May days and the 80th of October's. West, in 1999, with a second summit reading and a season of data from the South Col: “on days when the mountain is usually climbed, during May and October, the summit pressure is 251-253 Torr.”

Two days, from the balloons

Because the archive keeps the individual flights, the two days this story turns on can be looked up. Nobody was measuring the air for the climbers' sake; the balloons flew at their routine hours, 00 and 12 UTC. This is what they found at the summit's height, by the same method as everything above.

On 8 May 1978, Reinhold Messner and Peter Habeler went from the South Col to the summit without supplemental oxygen, the first to do so; the Austrian expedition's report says they “took about eight hours to the summit”. Lhasa's balloons that day read 249.6 at 00 UTC and 253.4 at 12 UTC. On 24 October 1981, the day of Pizzo's reading, Lhasa's two flights read 252.9 and 253.3, bracketing his 253 in time and in value. New Delhi, on the plains, read four to five Torr lower that day; which station better stands for the air over the summit is a question the page cannot settle (Tingri's flights on and around that day lack the 400 hPa level the method needs). The agreement with Lhasa is a coincidence of weather as much as a confirmation of anything. But the balloons and the barometer were independent instruments, 450 km apart, and they agree to within half a Torr.

What the blood does with it

The equation gives the oxygen in the air sacs. The blood gets less, and near the top of Everest it can be measured how much less. A team from the Caudwell Xtreme Everest expedition drew arterial blood from climbers high on the mountain, and published in 2009. From the abstract:

“In four samples taken at 8400 m (27,559 ft)--at which altitude the barometric pressure was 272 mm Hg (36.3 kPa)--the mean PaO(2) in subjects breathing ambient air was 24.6 mm Hg (3.28 kPa), with a range of 19.1 to 29.5 mm Hg (2.55 to 3.93 kPa). The mean PaCO(2) was 13.3 mm Hg (1.77 kPa), with a range of 10.3 to 15.7 mm Hg (1.37 to 2.09 kPa).”

M. P. W. Grocott et al., “Arterial blood gases and oxygen content in climbers on Mount Everest”, N. Engl. J. Med. 360 (2009), 140 to 149, abstract.

Put 272 and 13.3 into the instrument and it gives 31.9 Torr in the air sacs; the blood they drew held 24.6 on average, and as little as 19.1. (Their own calculated alveolar-to-arterial difference was 5.4 Torr, with assumptions about the exchange ratio that are in the paper's methods, which we could not read.) Those four samples were taken about 450 m below the summit, at a pressure 19 Torr higher than Pizzo's. Why the gap is as wide as it is, the authors left open: it “may represent a degree of subclinical high-altitude pulmonary edema or a functional limitation in pulmonary diffusion.”

What this page does not know

• The summit itself, day by day. Everything here but the two direct readings is inferred from balloons launched between 70 and 950 km away, and Lhasa and New Delhi can differ by several Torr on the same day (on 24 October 1981, by four to five). Weather stations have since been installed on Everest's upper slopes; their papers report weather-driven swings of about 10 hPa in a few days, which this page's monthly means smooth away.
• Two small approximations in the method. The balloons' monthly means are averages of heights at fixed pressures; turning them into a pressure at a fixed height treats the two as interchangeable, which is very nearly but not exactly true. And the interpolation ignores water vapour, which is scarce at 8 to 10 km. Log-linear interpolation, a different assumption between the same two levels, never differs from the one used by more than 1.7 hPa (1.3 Torr) on any of about a million station-month-hours, and the difference is usually far smaller. Station-month-hours whose reported heights and temperatures disagree by more than 30 m of thickness were dropped (7,700 of them).
• The balloons themselves. Radiosondes have changed makes and methods over the decades these records span, which can shift a station's long record, so the page does not use the long records to claim a trend. (The 2020 study estimates that 2 °C of warming above pre-industrial could raise the summit's pressure by 4 to 5 hPa; this page has not checked it.)
• The one reading. Pizzo's is a single reading from a single instrument. The expedition's report in the American Alpine Journal (1982), written before the barometer's final calibration, gave it as “between 250 and 253 mmHg”; the published figure is 253.0. A second summit reading, in May 1997, was “within approximately 1 Torr of 253 Torr”, West wrote in 1999.
• The body. The equation's 0.85 is an assumption; any exchange ratio from 0.8 to 1 moves the summit's alveolar figure by about a Torr or less. Nothing here says at what alveolar oxygen a person stops being able to climb. West wrote that the summit is “at the limit of man's tolerance”, and the page leaves the word “impossible”, for Everest at Denali's latitude, as his.

Sources

1. J. B. West, S. Lahiri, K. H. Maret, R. M. Peters Jr and C. J. Pizzo, “Barometric pressures at extreme altitudes on Mt. Everest: physiological significance”, Journal of Applied Physiology 54 (5) (1983), 1188 to 1194. doi:10.1152/jappl.1983.54.5.1188; abstract at PubMed 6863078.
2. J. B. West, P. H. Hackett, K. H. Maret, J. S. Milledge, R. M. Peters Jr, C. J. Pizzo and R. M. Winslow, “Pulmonary gas exchange on the summit of Mount Everest”, Journal of Applied Physiology 55 (3) (1983), 678 to 687. doi:10.1152/jappl.1983.55.3.678; PubMed 6415007.
3. J. B. West, “Man at extreme altitude”, Journal of Applied Physiology 52 (6) (1982), 1393 to 1399. doi:10.1152/jappl.1982.52.6.1393; PubMed 7050056.
4. J. B. West and P. D. Wagner, “Predicted gas exchange on the summit of Mt. Everest”, Respiration Physiology 42 (1980), 1 to 16. doi:10.1016/0034-5687(80)90100-0. Read from a copy hosted at web.njit.edu.
5. J. B. West and J. Evans, “American Medical Research Expedition to Everest”, American Alpine Journal (1982), publications.americanalpineclub.org: the summit day, Pizzo and Yong Tenzing, the time, the barometer.
6. J. B. West, “‘Oxygenless’ Climbs and Barometric Pressure”, American Alpine Journal (1984), publications.americanalpineclub.org.
7. J. B. West, “Barometric pressures on Mt. Everest: new data and physiological significance”, Journal of Applied Physiology 86 (3) (1999), 1062 to 1066. doi:10.1152/jappl.1999.86.3.1062; PubMed 10066724.
8. W. Nairz, “Mount Everest, Austrian Expedition”, American Alpine Journal (1979), publications.americanalpineclub.org: Messner and Habeler, 8 May 1978.
9. M. P. W. Grocott, D. S. Martin, D. Z. H. Levett, R. McMorrow, J. Windsor and H. E. Montgomery, for the Caudwell Xtreme Everest Research Group, “Arterial blood gases and oxygen content in climbers on Mount Everest”, New England Journal of Medicine 360 (2009), 140 to 149. doi:10.1056/NEJMoa0801581; PubMed 19129527.
10. T. Matthews, L. B. Perry, T. P. Lane et al., “Into Thick(er) Air? Oxygen Availability at Humans' Physiological Frontier on Mount Everest”, iScience 23 (12) (2020), 101718. doi:10.1016/j.isci.2020.101718 (open access).
11. G. W. K. Moore, J. L. Semple, P. Cristofanelli, P. Bonasoni and P. Stocchi, “Environmental conditions at the South Col of Mount Everest and their impact on hypoxia and hypothermia experienced by mountaineers”, Extreme Physiology & Medicine 1 (2012), 2. doi:10.1186/2046-7648-1-2 (open access).
12. J. C. Tremblay and P. N. Ainslie, “Global and country-level estimates of human population at high altitude”, PNAS 118 (18) (2021), e2102463118. doi:10.1073/pnas.2102463118: inspired oxygen as (P_B − 47) × 0.2093.
13. U.S. Standard Atmosphere, 1976, NOAA, NASA and USAF, Washington, October 1976, NTRS 19770009539: sea-level pressure, temperature and lapse rate, equation 33a. The exponent 5.25588 is computed from its constants.
14. NOAA National Centers for Environmental Information, Integrated Global Radiosonde Archive (IGRA) version 2.2; data at ncei.noaa.gov/data/integrated-global-radiosonde-archive.
15. Natural Earth, 1:110m land, public domain, naturalearthdata.com.