The atmosphere is a mix of gases. The most important components
are:

**Constant gases (% of dry air):**

Nitrogen (N_{2})
78.08%

Oxygen (O_{2})
20.92%

Argon (Ar)
0.93%

**Variable gases:**

Water vapour (H_{2}O) 0-4%

Carbon dioxide (CO_{2}) 0.035%

Methane (CH_{4})
0.00017%

This composition has been profoundly influenced by Life, especially
photosynthesis by plants. The early atmosphere was created by outgassing
from volcanoes: 4 billion years ago it was predominantly Nitrogen and Carbon
Dioxide. The atmosphere became gradually enriched in oxygen by weathering,
the deposition of carbonate rocks, and photosynthesis, first by algae,
then by higher plants. The present atmospheric mix is maintained by ecosystems,
and the level of oxygen is optimum for life: a smaller proportion would
mean less available for animal respiration; and a larger (c. 25%) would
result in very extensive wildfires.

**Density** is the mass of air molecules per unit volume. Mass is
measured by the kilogram (kg), and volume in cubic metres (m^{3}),
so the unit of density is kilograms per cubic metre (kg m^{-3}).
We think of kilograms in terms of weight, but weight is the result of a
mass subjected to gravity. In classical physics, mass is independent of
gravity, and the kilogram measures a set mass of atoms, regardless of whether
these are on the Earth, on the moon, or freely floating in space. At sea
level, air density is around 1.2 kg m^{-3}. Air density decreases
with altitude, for reasons discussed below.

**Pressure** is the cumulative effect of the push exerted by each molecular
collision on its surroundings. Pressure is defined as force per unit area. Force
is defined as a mass subjected to an acceleration, or mass x acceleration. The
unit of mass is the kilogram (kg), and an acceleration is a change in velocity
through time, measured in metres per second (velocity) per second (m sec^{-1}
sec^{-1}, or m sec^{-2}). Thus the unit of force is kg m sec^{-2}
or Newton, named after **Sir Isaac Newton**, who formulated the basic laws
of force and motion (alongside major contributions to many other aspects of
science and mathematics). Pressure is a force distributed over an area. The
unit of Pressure is N m^{-2}, or Pascal. Atmospheric pressure is often
measured in millibars, 1 Millibar = 100 Pa (100 Pa = 1 hecaPascal or hPa). Mean
pressure at sea-level is 1013 mbar or approximately 100 kPa. This pressure is
exerted in all directions: up, down, and to all sides. For equilibrium, the
pressure exerted by an air parcel is exactly balanced by the downward force
exerted by the overlying air pulled by gravity. This balance is known as **hydrostatic
equilibrium**.

A pressure of 1000 mbar (100 kPa) results from the weight exerted by
10,000 kg of air overlying one square metre of surface, accelerated by
gravity (c. 10 m sec^{-2}). The huge pressure does not crush us
because it is exactly balanced by outward pressure from the inside of our
bodies. Ears popping due to change in altitude are the result of the pressure
difference between the inside of our heads and the surrounding air. Pressure
decreases with altitude, due to the reduction of the mass of overlying
air with height. Pressure is c. 700 mbar at 3,000m; 500 mbar at 5,500m;
300 mbar at 10,000m.

**Temperature** is a measure of the average speed of the moving molecules.
In meteorology and other branches of physics, temperature is measured on
the **Kelvin** scale, which begins at absolute zero, where there is
no molecular kinetic energy.

0^{°}K = - 273^{°} C.

The temperature of a mass of air depends on the average velocity of
the air molecules and their mass, and so temperature generally increases
with air density.

The atmosphere is bombarded by shortwave radiation (including UV) from
above, and shortwave + longwave radiation from below, so the atmosphere
receives energy from above and below. Combined with the dependence of temperature
on air density, this gives the atmosphere a distinctive temperature profile.
From the surface, temperature decreases with altitude, as the air becomes
thinner. This zone is called the **troposphere** (from the Greek tropos
meaning 'change'): it is in this layer that the world's weather happens.
Then at altitudes of c. 10 - 15 km, the temperature stabilises, then rises
with altitude. This zone of rising temperature with altitude is called
the **stratosphere**. The high temperatures in the stratosphere are
due to the absorption of UV radiation by ozone. The stratospheric temperature
inversion creates a stable lid on the lower atmosphere (the **tropopause)**,
limiting the maximum thickness of weather systems to about 10-15 km. Above
the stratosphere (c. 50 km) the temperature again declines (the mesosphere),
then again rises above c. 85 km (the thermosphere). These higher levels
of the atmosphere do not concern us in this course.

The average temperature at the Earth's surface c. 15^{o} C (288^{o}
K), and generally decreases with height up to top of the Troposphere. The
average value of this vertical lapse rate is 6.6^{o} C km^{-1}.
However, temperature profiles in the lower atmosphere are actually very
variable, due to heating and cooling from the Earth's surface (sensible,
latent, and radiative heat transfer).

p = R r T

p is pressure,

r (Greek rho) is density

T is temperature (in degrees Kelvin),

R is the specific gas constant, which varies from gas to gas.

For dry air, R is 287 J K^{-1} kg^{-1}.

This very important relationship is known as the **Equation of State**,
and simply means:

(1) for constant density, pressure increases with temperature (that
is, if the molecules have a higher average kinetic energy, they exert a
greater push on their surroundings);

(2) for constant temperature, pressure increases with density (the
more molecules per unit volume, the greater the push exerted by collisions);

(3) for constant pressure, temperature and density are inversely related
(that is, if there are fewer molecules in a given volume, they need to
be travelling at a greater average speed to exert the same pressure).

Therefore, we can see that any change in any one variable is likely to cause
changes in the others. For example, if we heat a mass of air, we increase its
pressure, if the air is allowed to expand to equalise the pressure difference
with the surrounding air, the density will decrease. When this happens, it will
be lighter than the same volume of surrounding air, and will rise.

This is described by the equation p = R r T in the following way:

- Rearranging the equation to examine the effect of variations of pressure and density on temperature, we write: p/(r R) = T
- This says that pressure divided by (density multiplied by a constant) equals temperature
- In the demijohn experiment, we increase the air pressure and the density. As it turns out, the % increase in pressure is greater than the % increase in density, so the term p/rR increases. Hence, temperature increases.
- This explains the general reduction in temperature with altitude (a reduction in temperature due to decreasing pressure)

r = p / R T

This simply says that the air density is given by the pressure divided by (temperature x a constant). Therefore, for any given temperature, as pressure decreases, so does the air density. We have seen, however, that temperature decreases with reductions in pressure. A decrease in temperature will actually have the opposite effect on density, since density and temperature are inversely related in this equation. However, it turns out that this effect is outweighed by the pressure-density relationship, and as pressure decreases with height, so does air density.

We can see this effect with a worked example.

(1) The air pressure at sea-level is c. 1000 mbar, or 100,000 Pascals.
If the air is at 25^{o} C (298^{o} K), then:

r = 100,000 / (287 x 298) (recall that the gas constant
for dry air is 287)

= 1.17 kg m^{-3} (this figure is very close to the mean figure for sea-level
density quoted above)

(2) For 500 mbar (the air pressure at around 5,500 metres above sea-level),
the air temperature is typically -30^{o} C (243^{o} K)

thus:

r = 50,000 / (287 x 243)

= 0.72 kg m^{-3}

This is a little over half of the value for sea-level, showing that
the pressure is the overwhelming influence on the change in density.

Q: If there is a pressure gradient up though the atmosphere, why are there not constant upward-blowing winds?

A: Because the upward-directed pressure gradient force is exactly balanced
by the downward force of gravity acting on the air. This is called the
**hydrostatic
equilibrium**, and is expressed thus:

Dp / Dz = - r g

Dp (Greek delta p) is the difference in pressure,
and Dz is the change in height, so Dp
/ Dz is the vertical pressure gradient. r
is the local air density, g is gravity (9.8 m sec^{-2}), and the
minus sign on the right-hand side shows that gravity is directed downwards.

This is described by the equation p = R r T in the following way:

- The rapid equalisiation of pressure means that we can regard the pressure as constant.
- Since the term R is also a constant for any gas, we can write: r x T = constant
- In turn, this means that for higher temperatures, the density is lower.

The lower density of a heated mass of air means that the downward
force - r g (the mass of air accelerated by the
downward force of gravity) is reduced, relative to that exerted by the
vertical pressure gradient. As a result, there is a net upward force on
the air mass, and it rises. Thus, the increase in temperature and reduction
in density disturbs the local hydrostatic equilibrium and the air mass
rises. The opposite happens when an air mass is chilled relative to the
surrounding air. The reduction of temperature reduces the average velocity
of the consitituent molecules, reducing the force they exert on the surrounding
air. As a result, the chilled air mass contracts, increasing its density.
The consequent increase in downward force upsets the local hydrostatic
balance, and the air mass sinks.

The magnitude of the **buoyant force** is given by a minor modification
to the right-hand side of the hydrostatic equation:

buoyant force = -((r_{0} - r_{f})/r_{0})g

where r_{0} is the density of the
air parcel, and r_{f }is the density
of the surrounding air. Thus if r_{0}
= r_{f} the air is neutrally buoyant,
if r_{0} > r_{f}
the buoyant force is more negative and the air sinks, and if r_{0}
< r_{f} the buoyant force increases
and the air rises.

**Rocket experiment**: the dramatic effects of air pressure differences
are demonstrated by a compressed-air powered rocket! Pumping air into the
rocket increases its pressure. The seal fails when the pressure inside
the bottle is c. 180 kPa, or 180% of atmospheric pressure. This rapidly
forces water out of the base, sufficient to cause spectacular take-off.

**Where to get a rocket:**

Rokit, Hinterland Ltd. Stanstead Rd., Hertford SG13 7AY, UK.

(1) differences in potential temperature

(2) air motions, especially convergence and divergence.

The influence of potential temperature can be understood in terms of the equation of state discussed above. Air with lower potential temperature will become more dense, reducing the vertical thickness of a given mass of atmosphere. Thus a given pressure (say, 500 mbar) will occur at lower altitude than for air with a higher potential temperature. Conversely, air with a higher potential temperature will tend to expand, so in regions where the air has a relatively high potential temperature, a given air pressure (again, say, 500 mbar) will occur at a higher altitude. The altitude at which the pressure of 500 mbar is encountered will thus be higher for warm air masses than for cool air masses. We therefore say that the 500 mbar surface is higher or lower, depending on the potential temperaure of the atmosphere. The 500 mbar surface is lower at high latitudes than nearer the equator. In weather forecasting, the altitude of the 500 mbar surface is a valuable indicator of the position of different air masses, and in the mid-latitudes it varies on a daily basis with the passage of weather systems. Thus the instantaneous position of the surface is highly irregular, due to the presence of waves in the atmosphere. These will be discussed in greater detail later in the course.

**The 500 millibar surface on 17th January 2001. The surface altitudes
are in tens of metres (dam). Note the decline in altitude of the surface
with latitude: over the Sahara, it is at 5,880 metres, whereas over Greenland
it is only 4,920 metres: almost 1 kilometre lower. The red and blue coloring
denotes vorticity, or rotation of air. This will be discussed in Lecture
6.**

The influence of divergence and convergence on air pressure arises because convergence imports air into a region, increasing the local mass of the atmosphere, and conversely, divergence exports air from a region, reducing the mass of the atmosphere.

Meteorological maps for the all parts of the world (current analyses and forecasts)
can be viewed at the COLA-IGES web
pages. Of special relevance to this lecture are the "500 mbar geopotential
height" maps in the Northern Hemisphere MRF forecasts. Also well worth checking
out, if you are using a reasonably fast computer, is the one-month Java animation
of Northern Hemisphere circulation: viewing the 500 mbar surface in motion gives
a vivid impression of the varying pressure waves on the planet.