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Section 2.4 Structure of the atmosphere

Subsection 2.4.1 Pressure and density

NOAA Jetstream:

The atmosphere is bound to the Earth by gravity. As a result, atmospheric density and pressure are highest at surface and decreases (exponentially) with increasing altitude. The rate of change depends upon the force of gravity, temperature, the molecular weight of the gas(es).

Planetary atmospheres are in hydrostatic equilibrium. This means that gravity and pressure are in balance (in other words, the atmosphere does not escape into space nor does it collapse onto the surface of the planet).

Assuming hydrostatic equilibrium, we can determine the pressure at some altitude \(z\) by the relationship:

\(P(z)=P_o e^{(-z/H)}\)

where \(P_o\) is the initial pressure, \(z\) is the altitude, and \(H\) is the scale height defined as

\(H={RT}/{\mu g}\)

where \(R=8.314\) J/K-mol, \(g=9.8\) m/s\(^2\text{,}\) \(T=273\) K, and \(\mu=28.9\) g/mol (reflective of the molecular weights and proportions of nitrogen and oxygen). This yields a scale height of about 8 km in the troposphere. The scale height is a useful term in atmospheric science because it tells us how rapidly the pressure decreases with changes in altitude. A similar relation likewise tells us how the atmospheric density varies with altitude:

\(\rho = \rho_o e^{(-z/H)} \)

This pressure-altitude relation can also be used to estimate the fraction of the atmosphere above/below a certain level. For example, Denver has an elevation of 5280 ft above sea level (1.609 km), so we can estimate the average pressure at this elevation:

\(P(1.609 \textrm{ km})=(1 \textrm{ atm})(e^{(-1.609\textrm{ km}/8 \textrm{ km})}=0.82\) atm

In other words, the surface pressure at Denver is about 82% that at sea level. This explains (among other things) why water boils at a lower temperature in Denver than in Sioux Center. This relation can be used to explore other questions about pressure-related phenomena, as shown in the following examples.

Using an average tropospheric scale height of 8 km, how high would we have to go for 50% of the atmosphere to be below us?

The summit of Mt. Everest has an elevation of 8.8 km. Assuming an average tropospheric scale height of 8 km, what is the estimated pressure on the summit of Mt. Everest?

Note that different units are used for pressure. The units adopted are mostly a reflection of the instrument or method used for measurement:

Table 2.4.3. Units of pressure (1 atm is equal to...)
unit value
atmosphere (atm) 1
Pascal (Pa) 101325
bar 1.01325
mm of Hg (Torr) 760
inches of Hg (Torr) 29.92
meters of water 10.3

An instrument known as a barometer is used to measure the pressure.

Section 2.4.1 Atmospheric layers

Pressure or temperature can be used to divide the atmosphere into layers. Near the surface, the temperature also decreases with increasing altitude in the atmosphere. The rate of change is known as the lapse rate, defined as:

\(\Gamma=-\frac{\Delta T}{\Delta z}\)

A typical lapse rate is 6.5 K/km (3 F/1000 ft) but depends upon the presence of water (and latent heat released from condensation); a typical dry lapse rate is about 10 K/km (5 F/1000 ft).

NOAA Jetstream:

Troposphere: closest to the Earth, where the temperature generally decreases with altitude, from 288 K at surface to 217 K at tropopause

  • contains about 80% of the mass of the atmosphere

  • most “weather” occurs in troposphere

  • the top of the troposphere is the tropopause, a temperature inversion

  • the tropopause serves as upper lid on most weather patterns

  • the tropopause is typically 10 km in height, but varies and is generally higher in tropics (15-16 km) than at the poles (8-9 km)

If heat always rises, why does temperature decrease with height? Answer.
  • the atmosphere is heated from the surface

  • air is subject to adiabatic cooling as it ascends

Stratosphere: where temperature increases with altitude

  • ozone in the stratosphere absorbs incoming (primarily ultraviolet) solar energy; this absorption causes temperature increase

  • there is a relative lack of both mixing and turbulence - very stable with respect to vertical mixing because temperatures increase with altitude

  • the upper bound is known as the stratopause

Mesosphere: where temperature again decreases with altitude;

  • the upper bound is known as the mesopause

Thermosphere, where temperature increases with altitude again;

  • the tropopause to thermosphere is sometimes called the middle atmosphere, 100 km and above is upper atmosphere

  • At these upper layers, important distinction between temperature (average kinetic energy of gas particles) and heat (total thermal energy of the atmospheric gas)

  • Above 100 km, cosmic radiation, solar X-rays and ultraviolet radiation increasingly affect the atmosphere, which cause ionization (and hence ionosphere)

The atmosphere is a mixture of gases with constant proportions up to 80 km or more. The exceptions are ozone, which is concentrated in the lower stratosphere, and water vapor in the lower troposphere. The principal greenhouse gas is water vapor. Carbon dioxide, methane and other trace gases have increased since the Industrial Revolution, especially in the twentieth century due to the combustion of fossil fuels, industrial processes and other anthropogenic effects.