- Temperature
- Pressure
- The Troposphere
- The Stratosphere
- The Thermosphere
- Molecular Temperature
- The Ionosphere
- Density

Meteorologists are concerned largely with the troposphere because it is within this layer that storms and clouds reside. In our discussions, we will used data from the Standard Atmosphere for the tropospheric layer. Within the troposphere the density of the atmosphere, atmospheric pressure and temperature all decrease systematically with altitude.

(T in degrees C)

In the illustration above it is clear that everywhere below the tropopause temperatures decline with altitude at all latitudes (Figure 20). It is also evident that above the troposphere temperatures are nearly constant with height. It is significant that at around 20 km it is quite cold over the low latitudes compared to the polar regions. This pattern will prove to be very important in our study of the jet stream, which is located at the tropopause in the middle latitudes.

The rate of change of temperature with height is called the lapse rate and is symbolized as dT/dz. Often the upper case greek letter gamma (G) is used to denote a lapse rate. The change in temperature with height in the troposphere is rather linear and has a lapse rate of 6.4 *o*C/km using Standard Atmosphere data. So for every 1000 meters in elevation you should expect temperatures fall 6.4 *o*C. A graph of temperature against altitude is presented in Figure 21.

Temperature as a function of height may be determined by calling upon the Hydrostatic Equation ( Eq. 12), the Equation of State ( Eq. 13 and Eq. 15)and the First Law of Thermodynamics ( Eq. , Eq. 17 and Eq. 20).

The relationship between specific volume (a) and density (r) is given in Eq. 14 and in conjunction with Eq. 13 can be used to derive a second expression for the equation of state ( Eq. 15).

The First Law of Thermodynamics states that

The specific heat at constant volume (C*v*) or at constant pressure (C*p*) of one gram of a specific gas is the heat required to raise its temperature 1*o*C. The specific heat at constant volume is presented in Eq. 18, and the specific hear at constant pressure is presented in Eq. 19.

Using the expression for the specific heat at constant pressure, the first law of thermodynamics may be expressed in more specific terms for dU and dW ( Eq. 20).

If now we assume that there is not heat added to or removed from our gas we have defined adiabatic condition ( Eq. 21).

With the adiabatic assumption we can write the first law of thermodynamics as

With the hydrostatic equation ( Eq. 12) substituted into Eq. 22 we derive the following expression

(EQ 23)

Now solving for the rate of change of temperature with respect to height (dT/dz) we find the following relationship

As both gravity (g) and the specific heat at constant pressure are constants, we find that the rate of change of temperature with height under adiabatic conditions is also a constant (-9.8*o*C/km). If we calculate the temperature expected at 15,000 m using Eq. 24 we estimate the temperature there to be about -150*o*C. Actual measurements at 15,000 m indicates that a temperature of about -75*o*C is closer to reality. Why the difference between the calculation and the observation?

FIGURE 21

Density, Pressure and Temperature Vs. Altitude (Standard Atmosphere data).

Pressure may be treated as a function of height in terms of atmospheric density:

FIGURE 22 A Column of Air Through the Atmosphere

By putting Eq. 29 into Eq. 30 we obtain

(EQ 32)

and

Eq. 33 tells us that the acceleration of gravity that attracts mass downward toward the earth is balanced by the acceleration of the decline in pressure with altitude. If we take a simple case of temperature constant with height (an isothermal atmosphere) we can integrate the above equation (recall that P = rRT).

(EQ 34)

(EQ 35)

(EQ 36)

Atmospheric pressure decreases exponentially with height in an isothermal atmosphere. Some comparisons of elevations and the pressures at those elevations is presented below.

- 0 km = ~1000 mb
- 5.5 km = ~500 mb
- 10.0 km = ~250 mb
- 15.5 km = ~125 mb
- 20.0 km = ~62.5 mb

Cumulonimbus clouds (thunderheads) penetrate the entire troposphere and often penetrate into the stratosphere. Present day aircraft operate mostly in the upper troposphere at altitudes between 10 and 13 km. The temperature at the boundary between the troposphere and the stratosphre is around -50*o*C but may be significantly colder or warmer depending on geographic location and time of year.

The tropopause is the boundary between the troposphere and the stratosphere and may be as low as 7 km in altitude in polar regions and as high as 17 km in tropical latitudes. The stratosphere may be isothermal (no change in temperatuare with height) or may be characterized by an inversion in temperature (temperature increasing with height). Vertical motions in the stratosphere are inhibited owing to the fact that the stratosphere is a gaseous layer and not a material surface. Thus the stratosphere is a stable layer. Air motions in the stratosphere are largely horizontal rather than vertical. This lack of vertical motion allows pollutants (gas and dust particles) to become traped within the stratospheric layer. However, the pollutants may be brought to the surface by a process known as folding. folding is a process by which particulate matter subsides into the troposphere. Occassionally this particulate mater may reach the ground surface.

FIGURE 23 Folding or the downwelling of stratospheric air into the troposphere

Photo-dissociation of O*2* requires energy at a wavelength of 0.2424 mm or less. The absorption of photons of ultraviolet radiation from the sun by the oxygen molecule results in the production of atomic oxygen

(EQ 37)

where hv represents a photon of ultraviolet radiation. The atomic oxygen then may participate in two additonal chemical reactions.

(EQ 38)

(EQ 39)

These reactions require 3-body collisions, (represented by M) and may be any particle capable of absorbing the extra energy released by the reaction. O + O collide and unite. Howeve, the product (O*2*) is unstable and will dissociate unless it can release its energy to a 3rd particle in short time.

Mother of Pearl clouds (Nacreous clouds) are of unknown composition and are observed mainly in high latitudes (Scotland, Scandinavia). These clouds occur in the stratosphere and can be observed from the diffraction of sunlight from the spherical particles of which they are composed. The Mesosphere

The mesosphere is the layer of the atmosphere above the stratrosphere and extends from 50 to 100 km in altitude. The mesosphere is characterized by a strong temperature decrease with altitude. Clouds also may form in this layer. These clouds are called noctilucent clouds and are typically seen between 75-90 km altitude. They are bluish-silver in color and are most often seen around twilight at 5*o* to 13*o* below the horizon. These clouds are most common in summer at 50-75*o* N or S latitudes.

(EQ 40)

T*m* is the kinetic temperature of the molecules arising from their velocities, M*o*is molecular weight of air at sea level (28.966), and M is the molecular weight of air at the altitude considered. Below 90 km T*m* = T (i.e., M*o* = M).Above 90 km T*m* becomes increasingly greater than T, and T*m* = 400 to 2000*o*C (note: temperature of sun = 6000*o*C). Above 90 km the diurnal variation is between 500 and 800 *o*C and the mean path length between molecular collisions is as much as 100 km. The heat transfer at these altitudes is very low owing to the fact that the pressure is very low. The temperature of the molecules at these elevations, like the temperatures on the surface of satellites, depends on the radiative balance.

(EQ 41)

Given the gravity of a planet and the rate of change of pressure with height, a specific density is required.

The relationships between temperature, pressure and density in the troposphere are shown in Figure 24. In Figure 24 the pressure axis is presented with highest pressure at the bottom and lowest at the top. In this way pressure serves as a surrogate for altitude in meters. In the troposphere temperature declines with pressure and altitude as detailed earlier. Density also declines with altitude and pressure. In addition, we find that density is highest at highest temperature. As we will see in later chapters atmospheric scientists often assume linear changes in temperature, pressure and density with height. The errors in making these assumptions of linearity are small and are ignored. The complexity of the equations we use is minimized in the assumjption of linearity without significant loss of information or precision. Simplicity in specifying equations is a pedological and practical necessity.

FIGURE 24 Temperature, Pressure and Density Co-variations

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