#### xaktly | Meteorology

Earth's atmosphere

#### A thin wrapper around a pale blue dot

In this section, we'd like to understand the physical properties of Earth's gaseous atmosphere. It's worth putting the sizes of things in perspective first. The image below is known as the "pale blue dot" image. It was taken in 1990 by the Voyager 1 space probe as it left our solar system, from a distance of about 3.7 billion miles.

Image: NASA

In the image, the Sun is near the bottom. Prof. Carl Sagan, of Cornell University referred to this image in a speech that is well worth the few minutes it will take for you to listen to it. I highly recommend it. You can access that here. One thing is clear from this image: Everything we have ever experienced took place on this place that is tiny in the perspective of the solar system, our galaxy or the universe.

The image below was taken of our pale blue dot from orbit. It shows the thickness of the atmosphere in comparison to the size of the planet. The radius of Earth is about 6400 Km (about 4,000 miles). The atmosphere is no more than about 100 Km thick, and the part in which all living things live is thinner still. Humans can't generally survive for long above an altitude of about 20,000 feet, or roughly 4 miles. Viewed in this way, our atmosphere seems quite fragile.

Image: NASA

In this section we'll look at the physical properties of the atmosphere, its chemical composition, temperature and pressure profiles and some other properties.

### Composition

What we humans generally understand to be our atmosphere consists of layers called the troposphere, the lowest, in which we live, and the stratosphere, in which we can see high clouds from time to time. This diagram shows that there are other "layers" to it called the mesosphere, thermosphere and exosphere, but we should, with a couple of exceptions, think of it as a continuum of gas composition, pressure, temperature and other properties. Humans are classifiers; we need to "chunk" properties into categories so that they're easier to remember. This doesn't mean that there are distinct boundaries between these named atmosperic regions.

The properties of each layer depend mostly on the gravitational force that attracts gases toward the surface, and the penetrance of different wavelengths of sunlight through it. The composition of the lower layers also depends upon the mix of living things on the surface and in the oceans, and increasingly on the need for humans to extract and exploit substances like fossil fuels for energy and other conveniences.

#### 1. Gravity

The force of gravity between two objects with masses m1 and m2 is

$$F_g = \frac{G m_1 m_2}{r^2},$$

where G is the gravitational constant (just a number that gets the units right), and r is the distance between the centers of mass of the objects. So to calculate the gravitational force between Earth and a gas molecule, such as an O2 molecule, we'd need the mass of Earth (m1) and the mass of the molecule (m2), and the distance between them ( r ) would be approximately the radius of Earth. I meters, that's about 6,400,000 m.

We don't need to calculate any of those forces, only to compare them for different gases in the atmosphere. For example, most of the troposphere consists of nitrogen gas (N2). Any hyrogen gas (H2) has only 7% of the mass of N2, so all other things being equal, we expect it to be pulled toward Earth with only 7% of the force working on N2.

Thus lighter atoms and molecules experience less attractive force toward the planet, and are often found in more relative abundance higher in the atmosphere. Likewise, heavier atoms and molecules are more abundant near the surface. Of the major components of the troposphere, here are some molar masses (grams per mole) and relative abundances:

Component
Mass
(g/mol)
Abundance
(%)
Nitrogen (N2) 28 78.09
Oxygen (O2) 32 20.95
Argon (Ar) 40 0.9
Carbon dioxide (CO2) 44 0.04

Because of the high abundance of N2 in the atmosphere, the average molar mass per particle is close to 28 g/mol. So given that their masses are greater, we'd expect a slightly higher concentration of O2, Ar and CO2 near mean sea level. Indeed, anyone who has climbed high peaks understands very well the relative lack of oxygen compared to sea level.

Conversely, the upper atmosphere contains a higher proportion of lighter atoms and molecules like H2 and He, both of which are continuously lost from our atmosphere as they escape Earth's gravitational field. Indeed, many who use it regularly fear a global shortage of helium, mostly found in natural gas deposits, as it is released into the atmosphere. Liquid helium is an important cryogenic fluid used in cooling research and medical devices.

#### 2. Sunlight

Another crucial driver of atmospheric composition is the sun, and in particular, the penetrance of high-energy wavelengths of light into the atmosphere. In the stratosphere, for example, high-energy ultraviolet wavelengths strike oxygen molecules, breaking the O=O bond to form oxygen radicals (O·). In a series of interconnected steps, these form ozone, O3, which is, itself, a powerful UV absorber. Because of the ozone layer in the stratosphere, the living creatures of the troposphere are spared being irradiated with light of sufficient energy to break DNA bonds in skin and eye cells, which can cause cancers and other maladies. The stratospheric ozone layer is also the reason why, except for some human-caused ozone emission, there is no tropospheric ozone — a good thing because it's toxic to breathe.

Above the stratosphere, another region of highly ionized gases forms the ionosphere. It's in these upper regions that ionizing radiation, light in the ultraviolet bands and beyond to higher-energy wavelengths, is absorbed, forming ions. The ionosphere moves up and down with temperature, and is capable of reflecting some radio waves, particularly in the short-wave and AM bands. At night, when temperatures drop and the ionized gases of the ionosphere gain density and drop, these reflections lead to reception of long-wavelength radio signals over vast distances.

### Chemical composition

#### Troposphere

In the troposphere, where we live, and in which the entire height of Mt. Everest is included, is composed, on average, of

Component Formula Abundance
Nitrogen N2 78.08%
Oxygen O2 20.95%
Argon Ar 0.93%
Carbon dioxide CO2 0.04%
Water* H2O varies
Other gases ozone (O3), methane (CH4), NOx, neon, helium, SOx and others

*The components in this table other than water are called the components of dry air. Water vapor can compose up to about 2.5% of the atmosphere by mass; beyond that point (the dew point, which varies with temperature) it is no longer soluble in air and we get precipitation.

#### Upper layers

The chemical composition of the atmosphere above the troposphere is altered in two ways. First, heavier atoms and molecules thin out in the upper layers because they are pulled more strongly toward Earth by gravity. Likewise, lighter atoms and molecules like hydrogen (H2) and helium (He) are more abundant. Second, because ionizing radiation from the Sun can penetrate the upper layers, ionized atoms and molecules and ozone are abundant in those regions.

The chemistry of the upper atmosphere is a complex one because of constant irradiation by sunlight at wavelengths capable of removing electrons and breaking bonds. The reactive species – ions and free radicals – formed in this way lead to a variety of complex and branching chain reactions that are still an area of major research.

### Pressure

The concentration, or relative abundance of oxygen is roughly constant throughout the troposphere. Yet it is well known that it becomes more difficult to breathe (that is, to sufficiently oxygenate ones blood so that the tissues are adequately perfused) as one climbs up a high peak. What's happening is that the total pressure of the gases in the atmosphere decreases as we move upward. Here is a rough graph of pressure (measured in atmospheres – atm.) vs. altitude in kilometers (Km).

Notice that at the top of the highest mountain in the lower 48 states of the U.S., Mt. Whitney, California (14,505 ft.), the pressure is about 60% of what it would be at mean sea level. While the proportion of oxygen to all of the other atmospheric gases is the same there, it's also true that the molecules are less dense, so that every breath takes in proportionally fewer of all gas atoms and molecules, oxygen included. So a human just has to take more breaths per unit time in order to keep up. And if you've climbed that high, you'll understand. It takes a lot of heavy breathing. Few people have climbed as high as the summit of Mt. Everest (29,028 ft.) without using supplemental compressed oxygen.

What accounts for the difference in pressure as we go up? It's the same reason that the pressure on a diver increases as she dives deeper under water.

The pressure on the diver is the weight (downward force) of the water column above the diver divided by the area over which it is measured. The more water above, the greater that force. The SI pressure unit of Pascals has units of Newtons per square meter (N/m2).

So too, the weight of the column of air above a person produces pressure on him. The difference is that the density (mass per volume) of the column of air decreases as the altitude increases*, so we need a somewhat more complicated formula to calculate it, but the idea is the same.

*Water is nearly incompressible, so its density doesn't change too much as we go deeper.

From a fit of experimental pressure vs. altitude data to a decaying exponential function $C(h) = C_0 (1 - kh)^m,$ where Co, k and m are parameters calculated using the data, we can calculate the approximate pressure (P) in Pascals (1 atm. = 101,325 Pa) at height h using this equation:

$$P = 101325 [1 - (2.25577 \times 10^{-5})\cdot h]^{5.25588}$$

### Temperature

The temperature of the atmosphere varies across a range of about 110˚C. The temperature at any given altitude is a complicated consequence of solar gain at various wavelengths, chemical composition, density of the gases and winds that mix warmer and cooler air masses.

#### Troposphere

In the troposphere, carbon dioxide (CO2) and water (H2O) are heat trapping ("greenhouse") gases. They partially trap infrared radiation from the sun and reflect it back toward the surface. This effect, combined with the abosorption of heat by water and land masses keeps the surface temperatures relatively warm. As we move up into the stratosphere, both of these effects diminish and the temperature declines, to about -60˚C at the tropopause, a region where the temperature stabilizes and eventually warms in the stratosphere. The tropopause is generally considered to be the top of the troposphere. Its altitude varies with latitude. Near the poles the troposphere is thin because the ground is cold and the rays of the sun strike at low angles (far from perpendicular or normal to the planet surface), and near the equator it is thicker, often by a factor of 3 or 4.

#### Stratosphere

As we move past the tropopause into the stratosphere, temperatures warm considerably. There is still sufficient mass in the stratosphere for UV and visible radiation to interact with. The formation of ions and radicals in this region is an energy-absorptive process, causing atmospheric heating.

Atmospheric scientists can fly planes, balloons and soundign rockets into the stratosphere to collect data, so its composition and chemistry, while still an area of study, is reasonably well-understood.

#### Mesosphere

The mesosphere and stratosphere are separated by a change in temperature, called the stratopause, largely caused by the relative lack of matter above. Only about 1% of the mass of the atmosphere is above the stratopause. While there's plenty of solar radiation in this region, not much of it interacts with the sparse matter there, thus there is little warming and the atmosphere cools as altitude increases.

Because we can't fly aircraft or balloons into the mesosphere, we can't collect much data there, thus the region isn't as well understood as the troposphere and stratosphere.

#### Thermosphere

There isn't really much atmosphere in the thermosphere. In fact, the international space station (ISS) orbits within it, so we'd generally consider it to be "space."

Gases in the thermosphere are hot because they are the first encountered by the full energy of the sunlight that hit Earth. "Hot" in this sense means that they have a lot of translational kinetic energy — they're moving fast. That's what heat is. But if you could survive in the thin atmosphere of the thermosphere, you wouldn't necessarily feel hot. There just aren't that many atoms and molecules buzzing about to bang into you and transfer that energy to the vibration of the molecules that compose you. Spacecraft exposed to the direct light of the sun in the thermosphere need to be cooled, however, to accommodate human passengers. The direct radiation of the sun there, unimpeded by any real atmosphere, can heat spacecraft beyond livability.

X

### normal

A normal is a line that is perpendicular to a surface or to a tangent plane to that surface at a given point. It is more than a perpendicular line. It is perpendicular to a surface or tangent plane when viewed at any angle.

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