Historical

A general historical introduction can be found in Chapter 1, but some additional background material related to the atmosphere is included here, while a more complete discussion is in West (1998). The notion that air has weight and therefore exerts a pressure at the surface of the earth eluded the ancient Greeks and had to wait until the Renaissance. Galileo (1981) was well aware of the force associated with a vacuum and therefore the effort required to “break” it, but he thought of this in the context of a force required to break a copper wire by stretching it, that is, the cohesive forces within the substance of the wire. It was left to Galileo’s pupil Torricelli to realize that the force of a vacuum is due to the weight of the atmosphere. In addition, he wondered whether the air pressure became less on the tops of high mountains where the air “begins to be distinctly rare” as he put it. Torricelli made the first mercury barometer, though barometers filled with other liquids had apparently been constructed previously, for example by Gaspar Berti in 1639. These had limitations because of the effect of the vapor pressure of the liquid.

A landmark experiment took place in 1648 when the French philosopher and mathematician Blaise Pascal (1623–62) suggested that his brother-in-law, F. Périer, take a barometer to the top of the Puy-de-Dôme (1463 m) in central France to see whether the pressure fell (Pascal 1981). The results were communicated to Pascal in a delightful letter by Périer in which he described how the level of the mercury barometer fell some three pouces (about 75 mm) during the ascent of “500 fathoms” of altitude (probably about 900 m). The experiment had elaborate controls. For example, the Reverend Father Chastin, “a man as pious as he is capable,” stood guard over one barometer in the town of Clermont while Périer and a number of observers (including clerics, counselors, and a doctor of medicine) took another to the top of the mountain. On returning, it was found that the first barometer had not changed, and Périer even checked it again by filling it with the same mercury that he had taken up the mountain. Another observation was made the next day on the top of a high church tower in Clermont, and this also showed a fall in pressure, though of much smaller extent.

A few years later, Robert Boyle carried out experiments with the newly invented air pump and wrote his influential book New Experiments Physico-Mechanicall Touching the Spring of the Air, and Its Effects. In the second edition of this book, published in 1662, he formulated his famous law, which states that at constant temperature, gas volume and pressure are inversely related (Boyle 1662). Recent commentaries on both the original book and Boyle’s law are available (West 1999b; West 2005).

An influential analysis of the relationships between altitude and barometric pressure was made by Zuntz et al. (1906). They pointed out the important effect of temperature on the pressure–altitude relationship noting that, on a fine warm day, the upcurrents carry air to high altitudes and thus increase the sea level barometric pressure. Indeed, this is the basis for weather prediction based on barometric pressure.

Zuntz et al. (1906) gave the following logarithmic relationship for determining barometric pressure at any altitude:

where h is the altitude difference in meters, t is the mean temperature (°C) of the air column of height h, B is the barometric pressure (mmHg) at the lower altitude, and b is the barometric pressure at the higher altitude. Note that this expression implies that the higher the mean temperature, the slower the barometric pressure decrease with altitude. In addition, if temperature were constant, log b would be proportional to negative altitude, that is, the pressure would decrease exponentially as altitude increased. Zuntz et al. cite Hann’s Lehrbuch der Meteorologie, where the pressure–altitude relationship is given in a slightly different form (Hann 1901).

The expression by Zuntz et al. was used by FitzGerald (1913) in her study of alveolar PCO₂ and hemoglobin concentration in residents of various altitudes in the Colorado mountains during the Anglo-American Pikes Peak expedition of 1911. She showed that barometric pressures calculated from the Zuntz formula agreed closely with pressures observed in the mountains when a sea level pressure of 760 mmHg and a mean temperature of the air column of 115°C were assumed. Kellas (2001) used the same expression to predict barometric pressures in the Himalayan ranges, obtaining a value of 251 mmHg for the summit of Mount Everest (8848 m), assuming a mean temperature of 0°C. This was almost the same as the pressure of 248 mmHg given by Bert (Bert 1878) in contrast to the erroneously low values used 70 years after Bert because of the inappropriate application of the standard atmosphere. However, a major difficulty with the use of the Zuntz formula is the sensitivity of the calculated pressure to temperature and the fact that the mean temperature of the air column is not accurately known. For example, the barometric pressure on the summit of Mount Everest was calculated by Kellas to be 267 mmHg for a mean temperature of 115°C, but only 251 mmHg for a mean temperature of 0°C.

Physical principles

Barometric pressure decreases with altitude because the higher we go, the less atmosphere there is above us pressing down by virtue of its weight. Various units for barometric pressure are available. In this book mmHg is used. One mmHg is equal to 0.133 kPa. The barometric pressure at sea level for the standard atmosphere is 760 mmHg or torr (0.9999998575337 mmHg = 1 torr) or 101.325 kPa. Other units are 1013.25 millibars (mbar) or 14.696 pounds per square inch (psi).

If the atmospheric air were incompressible, as is very nearly the case for a liquid, barometric pressure would decrease linearly with altitude, just as it does in a liquid. However, because the weight of the upper atmosphere compresses the lower gas, barometric pressure decreases more rapidly with height near the earth’s surface. If temperature were constant, the decrease in pressure would be exponential with respect to altitude, but because the temperature decreases as we go higher (at least, in the troposphere), the pressure falls more rapidly than the exponential law predicts.

The relationships between pressure, volume, and temperature in a gas are governed by simple laws. These derive from the kinetic theory of gases that states that the molecules of a gas are in continuous random motion and are only deflected from their course by collision with other molecules, or with the walls of a container. When they strike the walls and rebound, the resulting bombardment results in a pressure. The magnitude of the pressure depends on the number of molecules present, their mass, and their speed:

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  Boyle’s law states that, at constant temperature, the pressure (P) of a given mass of gas is inversely proportional to its volume (V), or PV = constant (at constant temperature). This can be explained by the fact that as the molecules are brought closer together (smaller volume), the rate of bombardment on a unit surface increases (greater pressure).

  
  
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  Charles’ law states that at constant pressure, the volume of a gas is proportional to its absolute temperature (T), or V/T = constant (at constant pressure). The explanation is that a rise in temperature increases the speed and therefore the momentum of the molecules, thus increasing their force of bombardment on the container. Another form of Charles’ law states that at constant volume, the pressure is proportional to absolute temperature. (Note that absolute temperature is obtained by adding 273 to the Celsius temperature. Thus 37°C = 310 K.)

  
  
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  The ideal gas law combines the above laws; thus: PV = nRT, where n is the number of gram molecules of the gas and R is the “gas constant.” When the units employed are mmHg, liters, and Kelvin, then R = 62.4. Real gases deviate from ideal gas behavior to some extent at high pressures because of intermolecular forces, which are neglected in the derivation of the ideal gas law.

  
  
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  Dalton’s law states that each gas in a mixture exerts a pressure according to its own concentration, independently of the other gases present. That is, each component behaves as though it were present alone. The pressure of each gas is referred to as its partial pressure. The total pressure is the sum of the partial pressures of all gases present. In symbols: P_x = PF_x, where P_x is the partial pressure of gas x, P is the total pressure, and F_x is the fractional concentration of gas x. For example, if half the gas is oxygen, Fo₂ = 0.5. The fractional concentration always refers to dry gas.

  
  
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  The kinetic theory of gases explains their diffusion in the gas phase. Because of their random motion, gas molecules tend to distribute themselves uniformly throughout any available space until the partial pressure is the same everywhere. Light gases diffuse faster than heavy gases because the mean velocity of the molecules is higher. The kinetic theory of gases states that the kinetic energy (0.5 mv²) of all gases is the same at a given temperature and pressure. From this it follows that the rate of diffusion of a gas is inversely proportional to the square root of its density (Graham’s law).

Based on different rates of diffusion, one might expect that very light gases such as helium would separate and be lost from the upper atmosphere. This does happen to some extent at extreme altitudes. However, at the altitudes of interest to us, say up to 10 km, convective mixing maintains a constant composition of the atmosphere.

Vertically, the atmosphere can be divided based on temperature variations into the troposphere, the stratosphere, and regions above that. The troposphere is the region where all the weather phenomena take place and is the only region of interest to high altitude medicine. Here, the temperature decreases approximately linearly with altitude until a low of about −60°C is reached. The troposphere extends to an altitude of about 19 km at the equator but only to about 9 km at the poles. The average upper limit is about 10 km.

Above the troposphere is the stratosphere where the temperature remains nearly constant at about −60°C for some 10–12 km of altitude. The interface between the troposphere and stratosphere is known as the tropopause.

Beyond the stratosphere, temperatures again vary with altitude. One of the important components of this region is the ionosphere where the degree of ionization of the molecules makes short-wave radio propagation possible.

Standard atmosphere

With the development of the aviation industry in the 1920s, it became necessary to develop a barometric pressure–altitude relationship that could be universally accepted for calibrating altimeters, low pressure chambers, and other devices. Although it had been recognized for many years that the relationship between pressure and altitude was temperature-dependent and, as a result, latitude-dependent, there were clear advantages in having a model atmosphere that applied approximately to mean conditions over the surface of the earth. This is often referred to as the ICAO Standard Atmosphere (ICAO 1964) or the US Standard Atmosphere (NOAA 1976). These two are identical up to altitudes of interest to us.

The assumptions of the standard atmosphere are a sea level pressure of 760 mmHg, sea level temperature of +15°C, and a linear decrease in temperature with altitude (lapse rate) of 6.5°C km⁻¹ up to an altitude of 11 km (Table 2.1). Haldane and Priestley (1935, p. 323) gave the following expression for the pressure–altitude relationship of the standard atmosphere in the second edition of their textbook Respiration:

where P₀ and P are the pressures in mmHg at sea level and high altitude, respectively, and H is the height in thousands of feet. A more rigorous description is given in the Manual of the ICAO Standard Atmosphere (ICAO 1964).

Table 2.1 Barometric pressures (in mmHg) from the standard atmosphere (ICAO 1964) and a model atmosphere (West 1996): The latter is a better fit for most sites where high altitude physiology and medicine are studied

It should be emphasized that this standard atmosphere was never meant to be used to predict the actual barometric pressure at a particular location. Rather, it was developed as a model of more or less average conditions within the troposphere with full recognition that there would be local variations caused by latitude and other factors. Nevertheless, the standard atmosphere has assumed some importance in respiratory physiology because it is universally used as the standard for altimeter calibrations, and it has frequently been inappropriately used to predict the pressure at various specific points of the earth’s surface, particularly on high mountains.

Haldane and Priestley (1935) clearly understood that the standard atmosphere predicted barometric pressures considerably lower than those given by the expression of Zuntz et al. (1906), which had been shown by FitzGerald to predict accurately pressures in the Colorado mountains when a mean air column temperature of +15°C was assumed.

Nevertheless, some physiologists have used the standard atmosphere for predicting the pressure at great altitudes, for example on Mount Everest (Houston and Riley 1947; Houston et al. 1987; Rahn and Fenn 1955; Riley and Houston 1951). The barometric pressure calculated in this way for the Everest summit (8848 m) is 236 mmHg, which is far too low. In retrospect, one of the reasons for the indiscriminate use of the standard atmosphere was undoubtedly its very frequent employment in low pressure chambers during the very fertile period of research on respiratory physiology during World War II.

Climbers using altimeters, including those on some wristwatches, should be aware that these use the standard atmosphere to convert barometric pressure to altitude. The difference between the readings given by these altimeters and the true altitude up to about 3000 m is unimportant for navigation in the mountains. From 4000 to 5000 m a climber should add 3% to the altimeter reading to get a truer altitude. From 5000 to 6000 m the change is 4%, from 6000 to 8000 m the change is about 5%, and above 8000 m it is 6% to 7%. Of course, if the altimeter also measures and reads pressure, the best solution is to relate this to altitude using the model atmosphere equation. Many modern-generation watches and navigation devices circumvent these issues by measuring altitude using GPS technology.

Variation of barometric pressure with latitude

The limited applicability of the standard atmosphere is further clarified when we look at the relationship between barometric pressure and altitude for different latitudes (Figure 2.1). This shows that the barometric pressure at the earth’s surface and at an altitude of 24 km is essentially independent of latitude. However, in the altitude range of about 6–16 km, there is a pronounced bulge in the barometric pressure near the equator both in winter and summer. Since the latitude of Mount Everest is 28°N, the pressure at its summit (8848 m) is considerably higher than would be the case for a hypothetical mountain of the same altitude near one of the poles.

The cause of the bulge in barometric pressure near the equator is a very large mass of very cold air in the stratosphere above the equator (Brunt 1952). In fact, paradoxically, the coldest air in the atmosphere is above the equator. This is brought about by a combination of complex radiation and convective phenomena, which result in a large up-welling of air near the equator. Another corollary of the same phenomenon is that the height of the tropopause is much greater near the equator than near the poles. These latitude-dependent variations of pressure are of great physiological significance for anyone attempting to climb Mount Everest without supplemental oxygen, because they result in a barometric pressure on the Everest summit which is considerably higher than that predicted from the model atmosphere. By the same token, a climber at a high latitude such as Denali (Mt. McKinley, 63°N latitude) is at a considerable disadvantage because of the low barometric pressure, especially in the winter months. It is for this reason that climbers feel that Denali behaves as a taller mountain than its true altitude.

Variation of barometric pressure with season

Not only does barometric pressure change with latitude, there is also marked variation according to the month of the year. For example, Figure 2.2 shows the mean monthly pressures for an altitude of 8848 m as obtained from radiosonde balloons released from New Delhi, India, which has about the same latitude as Everest, over a period of 15 years. Note that the mean pressures were lowest in the winter months of January and February (243.0 and 243.7 mmHg, respectively) and highest in the summer months of July and August (254.5 mmHg for both months). The monthly standard deviation showed a range of 0.65 mmHg (July) to 1.66 mmHg (December). The daily standard deviation was as low as 1.54 in the summer and as high as 2.92 in the winter. The standard deviation shown in Figure 2.2 is the mean of the monthly standard deviation for the 12 months of the year. Similar seasonal variation in barometric pressure was demonstrated in a more recent study in which in situ data on barometric pressure, as well as temperature and wind speed, were measured over a seven-month period by an automatic weather station installed at the South Col on Mount Everest (7896 m). Pressure was lowest in the pre- and postmonsoon period and varied significantly during passages of major weather systems (Figure 2.3) (Moore et al. 2012). Premonsoon data were limited in scope, however, because of a lack of data prior to the middle of May, likely due to the fact that this is the time period at which climbers first begin to access the South Col during the spring climbing season.