Extent Of The Atmosphere And Its Temperature And Pressure Profile

Roughly 5.1 x 1018 kg of atmosphere is distributed over the 5.1 x 1014 m2 of the earth's surface. This means that atmospheric pressure at sea level is about 104kg/m2, or 103 g/cm2. This is approximately equivalent to one standard atmosphere of pressure (1013 mbar). Most of the atmosphere is fairly close to the surface of the earth. Fifty percent of the atmosphere is within 5 km (3 mi) of sea level, that is, at a height of somewhat more than 5 km above sea level, atmospheric pressure is 0.5 atm. There are quite a few mountains that are higher than this. 0ne such mountain is Kilimanjaro in Tanzania, which rises nearly 6 km above sea level; Mount Whitney and the Matterhorn are just under 5 km in altitude.

Ninety percent of the atmosphere is within 12 km of sea level. By comparing 12 km with the radius of the earth, 6370 km, it is seen that 90% of the atmosphere exists in an extremely thin layer covering the earth's surface. The total extent of the atmosphere is much harder to specify, since there is no definite upper boundary. For most purposes, one can say that the atmosphere ends between 200 and 400 km above the earth's surface, but on occasion it is necessary to consider a few hundred or a thousand additional kilometers.

Nitrogen, oxygen, and carbon dioxide are reasonably well distributed at all altitudes in the atmosphere. Most of the water vapor and water droplets occur at altitudes below about 14 km, while most of the ozone is localized in the vicinity of 25 km above the earth's surface. There is, however, some water vapor at altitudes above 14 km, about 3 ppm in the stratosphere.

The exact manner in which temperature and pressure change with altitude in the atmosphere depends both on latitude and on the season of the year. Very close to the surface of the earth, temperature and pressure are extremely variable, even beyond the latitude and seasonal variations. For this reason, various national and international groups have proposed "standard atmospheres'' at various times. For illustrative purposes (see Table 2-4), we shall use the U.S. Standard Atmosphere, 1962, which depicts idealized year-round mean conditions for middle latitudes such as 45°N, for a range of solar activity that falls between sunspot minimum and sunspot maximum. Standard information for other latitudes and for various times of year can be found in the Additional Reading at the end of this chapter. Table 2-4 shows that the pressure drops off continuously with increasing altitude, but the temperature goes through some strange gyrations. The temperature of the atmosphere decreases from sea level

TABLE 2-4

Temperature and Pressure of the Standard Atmosphere

Altitude (km)

P (mbar)

T (K)

0

1013

288 (15°C)

1

899

282

2

795

275 (2°C)

5

540

256

10

265

223 (-50°C)

12

194

217

15

121

217 (-56°C)

20

55

217

25

25

222

30

12

227

40

3

250

50

0.8

271 (-2°C)

60

0.2

256

70

0.06

220

80

0.01

180

90

0.002

180 (-93°C)

100

0.0003

210

110

7 x 10-5

257

120

3 x 10-5

350 (77°C)

130

1 x 10-5

534

140

7 x 10-6

714

150

5 x 10-6

893 (620°C)

175

2 x 10-6

1130

200

1 x 10-6

1236

300

2 x 10-7

1432

400

4 x 10-8

1487

500

1 x 10~8

1500 (1227°C)

Source: Adapted from U.S. Standard Atmosphere, U.S. Government Printing Office.

Source: Adapted from U.S. Standard Atmosphere, U.S. Government Printing Office.

300-

200-

100-

300-

200-

100-

Ionosphere

(50-4000 km)

Thermosphere

-

(85-500 km)

Auroras

-----f----Mesopause

Mesosphere (50-85 km)

ice clouds -

--------V - Stratopause

Stratosphere

Meteors burn -

O3 formed

I I I

I I

10-1 1 10 100 1000

100 200 300 500 1000 2000

Temperature (K)

10-1 1 10 100 1000

100 200 300 500 1000 2000

Temperature (K)

FIGURE 2-4 Temperature and pressure profile of the U.S. Standard Atmosphere.

up to 12 km, remains constant up to 20 km (at least in the U.S. Standard Atmosphere, 1962), increases from 20 to 50 km, decreases again from 50 to 80 km, remains constant to 90 km, and then increases asymptotically to about 1500 K above 300 km. These variations are probably less confusing as depicted in Figure 2-4, which also shows the change in pressure with altitude. Note that the temperature scale in Figure 2-4 is logarithmic, to make it easier to see the temperature variations in the first 100 km of the atmosphere.

Starting at the earth's surface, at sea level, the temperature of the standard atmosphere decreases steadily in the troposphere (sometimes referred to as the lower atmosphere) up to the tropopause. We shall see in Chapter 3 how temperature inversions, (i.e., regions where the temperature increases with increasing altitude) can sometimes occur in the troposphere. The troposphere contains most of the mass of the atmosphere, it is the only continuously turbulent part of the atmosphere, and it contains most of our weather systems. Atmospheric pressure drops off logarithmically with altitude near the earth's surface, but more slowly at higher elevations, and there are no pressure inversions.5

5The thermodynamic concept of an equilibrium temperature may not be valid at elevations above 350 km where the pressure is less than 10~7 mbar. The very few molecules present, seldom collide, and thus they probably are not at equilibrium. Thus, the temperature at altitudes above

300 km should be considered to be a mean kinetic temperature, having to do with the average kinetic energy of the molecules present.

Wherever the temperature rises with an increase in altitude in the atmosphere, there must be one or more exothermic (i.e., solar-energy-absorbing) chemical reactions involved. Without such processes, the temperature of the atmosphere would vary smoothly from warm at the earth's surface to very cold, close to absolute zero, at very high altitudes. Radiant energy from the sun is absorbed in various photochemical processes both in the stratosphere and in the thermosphere, thus increasing the temperature with increasing altitude as shown in Figure 2-4.

The photochemical processes of the thermosphere will be fully discussed in Chapter 5. At this point, let us simply note that atmospheric oxygen and nitrogen in the thermosphere above 100 km absorb virtually all the ultraviolet radiation having wavelengths below 180 nm (1800 A). This circumstance is very fortunate for two reasons. First, this high-energy radiation would initiate chemical reactions in all complex molecules, with the result that life as we know it would be impossible if this radiation reached the earth's surface. Second, the large variations in the intensity of the sun's radiation at these short wavelengths have very little effect on the troposphere where our weather originates, since all these wavelengths are removed at much higher altitudes.

Radiation with wavelengths between 180 and 290 nm would also be destructive to life, but these wavelengths are absorbed in the stratosphere by oxygen and ozone. The maximum absorption of ozone is at 255 nm (see Section 5.2.3.1). The major reactions in the stratosphere, much simplified from the more complete discussion to be found in Section 5.2.3.1, are as follows:

Reaction (2-2) also occurs at higher altitudes, but does not lead to reaction (2-3) because the pressure is too low to allow termolecular collisions to occur with any reasonable frequency. A third atom or molecule M is needed for reaction (2-3), so that both energy and momentum can be conserved in the reaction. The symbol M* refers to the increase in the energy of M while 02 is combining with O to form 03.

0zone is formed down to about 35 km altitude, below which the ultraviolet radiation necessary for its formation (X < 240 nm) has been fully absorbed. Most of the ozone in the atmosphere, however, exists at altitudes between 15 and 35 km, so that mixing processes must occur in the stratosphere as well as in the troposphere. Also, ozone concentrations are low over the equator, where, on the average, most of the sun's radiation impinges, and high near

the poles, at latitudes greater than 50°, where less radiation comes in from the sun. Consequently, it is obvious that there are mechanisms for the transport of ozone from the equator to the poles. Furthermore, there are transitory losses of ozone over the Antarctic and (sometimes) Arctic regions during their early springtimes (see Sections 5.2.3.3 and 5.2.3.4, respectively). This ozone appears to be replenished during the Antarctic summer by transport from the stratosphere over the temperate regions of the southern hemisphere. Transport of gases through the tropopause and from one region of the stratosphere to another occurs readily; this transport has seasonal aspects and the mechanism is quite complicated and is still being studied.

Solar radiation with wavelengths greater than 290 nm (2900 A) is transmitted to the lower stratosphere, the troposphere, and the earth's surface. We shall see that this remaining radiation, including UV with wavelengths exceeding 290 nm, visible and infrared, comprises more than 97% of the total energy from the sun.

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