This is one of the webpages of Libarid A. Maljian at the Department of Physics at CSLA at NJIT.

New Jersey Institute of Technology

College of Science and Liberal Arts

Department of Physics

The Earth in Space, Section 021

Phys 203-021

Summer 2025

Fourth Examination lecture notes

Introduction to the Atmosphere

An atmosphere is a thin layer of gas gravitationally held to a moon, a planet, or a star. The Earth’s atmosphere is roughly eighty percent nitrogen, roughly twenty percent oxygen, and tiny amounts of other gases. The tiny amounts of other gases are quite important, as we will discuss shortly. Every second of every day of our lives, we are breathing mostly nitrogen (roughly eighty percent) and a fair amount of oxygen (roughly twenty percent). This roughly twenty-percent abundance of oxygen is an enormous fraction; other planets have nowhere nearly this much oxygen in their atmospheres. Other planetary atmospheres have only tiny amounts of oxygen with a large abundance of carbon dioxide, as is the case with the atmospheres of planets Venus and Mars for example. The Earth’s atmosphere has a large fraction of oxygen but only a tiny amount of carbon dioxide. To understand why the Earth’s atmosphere is so different from other planetary atmospheres, we must discuss the history of the Earth’s atmosphere. When the Earth formed roughly 4.6 billion years ago, its atmosphere was almost entirely hydrogen gas and helium gas; this is called the Earth’s primary atmosphere. The primary atmosphere was almost entirely hydrogen and helium because the Earth together with the entire Solar System was born from a nebula, an enormous cloud of gas composed of mostly hydrogen and helium. Indeed, most of the universe is composed of hydrogen and helium. The more massive (or heavier) an atom or molecule, the slower it moves; the less massive (or lighter) an atom or molecule, the faster it moves. This is rather remarkable. Suppose all the air in a room is at the same temperature, which means that all the air molecules in the room have the same average energy. Nevertheless, the oxygen molecules are moving slower on average since they are more massive (or heavier), while the nitrogen molecules are moving faster on average since they are less massive (or lighter), even though all of the air is at the same temperature, which means both the nitrogen molecules and the oxygen molecules have the same average energy! Hydrogen is the least massive (lightest) atom in the entire universe, and helium is the second least massive (second lightest) atom in the entire universe. Hydrogen and helium are so light that they move so fast that they can escape from the Earth’s gravitational attraction. Thus, the Earth lost its primary atmosphere because its own gravity was too weak to hold onto hydrogen and helium. This occurred with all four of the inner planets orbiting the Sun (Mercury, Venus, Earth, and Mars). These four inner planets have weaker gravity since they are smaller with less mass as compared with the four outer planets orbiting the Sun (Jupiter, Saturn, Uranus, and Neptune). These four outer planets have stronger gravity since they are larger with more mass; thus, they have retained their primary (hydrogen and helium) atmospheres to the present day. Even the gravity of the outer planets is weak compared with the gravity of the Sun; therefore, the Sun has certainly retained its primary (hydrogen and helium) atmosphere to the present day. To summarize, the Sun and the four outer planets have retained their primary (hydrogen and helium) atmospheres, but the four inner planets have lost their primary (hydrogen and helium) atmospheres. After the Earth lost its primary atmosphere, this left behind a secondary atmosphere composed of an abundance of water vapor, nitrogen, carbon dioxide, methane, and other gases. These gases came from volcanic outgassing. Since the Earth was born almost entirely molten, volcanic eruptions everywhere on its surface ejected not just lava but gases as well, as we discussed earlier in the course. These gases are significantly more massive (or heavier) than hydrogen and helium. Therefore, they did not move fast enough to escape from the Earth’s gravitational attraction. As the Earth cooled, the water vapor condensed into liquid water which precipitated back down onto the planet for such a long period of time that most of the surface of the Earth became flooded, thus forming the oceans. At this point, the Earth may be regarded as having a normal atmosphere with an abundance of carbon dioxide similar to other planets such as Venus and Mars. However, roughly one billion years after the Earth formed (roughly 3.6 billion years ago), something extraordinary occurred in the oceans that to our knowledge did not occur anywhere else in the entire universe: life appeared. The first lifeforms were primitive unicellular microorganisms, such as bacteria and blue-green algae. Some of the carbon dioxide in the atmosphere dissolved into the oceans, which these primitive lifeforms converted to oxygen. Over the next roughly one billion years, the rock at the ocean floor was oxidized by the oxygen that these primitive microorganisms continually synthesized. When nearly all the rock at the ocean floor was oxidized, the oxygen that these primitive lifeforms continued to synthesize then began to accumulate within the oceans. Some of this accumulating oxygen then dissolved back into the atmosphere. After an additional roughly two billion years, these microorganisms actually succeeded in extracting almost all of the carbon dioxide from the atmosphere, replacing it with oxygen. Thus, as of roughly 600 million years ago, planet Earth attained its tertiary atmosphere that we enjoy to the present day: roughly eighty percent nitrogen, roughly twenty percent oxygen, and tiny amounts of other gases. Again, the tiny amounts of other gases are quite important, and we will discuss these trace gases shortly.

The pressure of the Earth’s atmosphere is typically a maximum at mean sea level and decreases exponentially with increasing elevation. The equation that describes this decreasing pressure with increasing elevation is called the law of atmospheres, but we do not need this equation to understand why this is the case. The Earth’s gravity pulls air downward; therefore, the air becomes thinner as we climb the atmosphere, making the air pressure less at higher elevations. The average air pressure at mean sea level is called one atmosphere of pressure, equal to 101325 pascals of pressure. One pascal of pressure is one newton of force per square-meter of area. This average air pressure of 101325 pascals is close enough to one hundred thousand pascals that meteorologists have defined another unit of air pressure: the bar. One bar of air pressure is exactly one hundred thousand pascals of air pressure. Thus, the average air pressure at mean sea level is equal to 1.01325 bars of pressure; this is also 1013.25 millibars of pressure. When meteorologists report the air pressure on any given day, they may report that the air pressure is several millibars above average or several millibars below average. A device that measures air pressure is called a barometer. To build a primitive barometer, we insert a long, narrow container inverted into any liquid. The air pressure will push downward onto the liquid, thus forcing the liquid upward into the long, narrow inverted column. If the air pressure is greater than average, it will push downward more strongly onto the liquid, thus forcing the liquid further upward the inverted column, making the column of liquid taller. If the air pressure is less than average, it will push downward less strongly onto the liquid, thus forcing the liquid not as far upward the inverted column, making the column of liquid shorter. Thus, by measuring the height of the column of liquid and performing a calculation, we can determine the air pressure that has pushed downward onto the liquid. Most barometers use the element mercury as the liquid; at average air pressure at mean sea level, liquid mercury will be pushed 760 millimeters (or 29.9 inches) up the narrow column. Thus, the average air pressure at mean sea level is also equal to 760 millimeters of mercury (or 29.9 inches of mercury). When meteorologists report the air pressure on any given day, they may report that the air pressure is several millimeters of mercury higher than average or several millimeters of mercury lower than average. Barometers almost always use liquid mercury because mercury is between thirteen and fourteen times more dense than water. In other words, mercury is between thirteen and fourteen times heavier than water; thus, gravity pulls mercury thirteen or fourteen times more strongly than water, making the column of mercury only 760 millimeters (or 29.9 inches) tall. If a barometer used water instead of mercury, the column of water would be between thirteen or fourteen times taller; this would make barometers more than ten meters (almost thirty-four feet) tall! It is not convenient to carry such a tall device; it is much more convenient to carry a barometer that is only 760 millimeters (or 29.9 inches) tall. This is why almost all barometers use mercury instead of water.

Meteorologists have defined layers of the Earth’s atmosphere based on the variation of the temperature of the Earth’s atmosphere with elevation. The lowest layer of the atmosphere is the troposphere. With increasing elevation, the troposphere is followed by the stratosphere, then the mesosphere, and finally the thermosphere. Beyond the thermosphere is the exosphere, where the air smoothly transitions from the Earth’s atmosphere to the surrounding outer space, as we will discuss shortly. The temperature typically cools with increasing elevation within the troposphere, the lowest layer of the atmosphere. However, we reach a certain elevation at which the temperature stops becoming cooler and begins instead to become warmer with increasing elevation. This elevation defines the end of the troposphere and the beginning of the stratosphere. This precise elevation is called the tropopause. We may regard the tropopause as the boundary between the troposphere and the stratosphere, but the tropopause is more correctly defined as the end of the troposphere. The temperature then typically becomes warmer with increasing elevation within the stratosphere. The reason for this warming is a heat source within the stratosphere that we will discuss shortly. However, we reach a certain elevation at which the temperature stops becoming warmer and begins instead to become cooler with increasing elevation. This elevation defines the end of the stratosphere and the beginning of the mesosphere. This precise elevation is called the stratopause. We may regard the stratopause as the boundary between the stratosphere and the mesosphere, but the stratopause is more correctly defined as the end of the stratosphere. The temperature then typically becomes cooler with increasing elevation within the mesosphere. However, we reach a certain elevation at which the temperature stops becoming cooler and begins instead to become warmer with increasing elevation. This elevation defines the end of the mesosphere and the beginning of the thermosphere. This precise elevation is called the mesopause. We may regard the mesopause as the boundary between the mesosphere and the thermosphere, but the mesopause is more correctly defined as the end of the mesosphere. The temperature then typically becomes warmer with increasing elevation within the thermosphere. The reason for this warming is a heat source within the thermosphere that we will discuss shortly. However, we reach a certain elevation at which the temperature stops becoming warmer and begins instead to become cooler with increasing elevation. This elevation defines the end of the thermosphere and the beginning of the exosphere. This precise elevation is called the thermopause. We may regard the thermopause as the boundary between the thermosphere and the exosphere, but the thermopause is more correctly defined as the end of the thermosphere. The temperature then typically becomes cooler with increasing elevation within the exosphere, smoothly transitioning into the very cold temperatures of the surrounding outer space. To summarize, the temperature typically becomes cooler with increasing elevation within the troposphere, the mesosphere, and the exosphere, while the temperature typically becomes warmer with increasing elevation within the stratosphere and the thermosphere.

It may seem reasonable to ask for the precise elevation at which the Earth’s atmosphere ends and outer space begins, but this is in fact an ill-defined question. The concentration of gases in the Earth’s atmosphere becomes thinner and thinner with increasing elevation until the concentration of gases matches the concentration of gases of the surrounding outer space. It is a common misconception that outer space is a perfect vacuum, but this is false. There is no such thing as a perfect vacuum; in fact, a perfect vacuum would violate the laws of physics. In actuality, the entire universe is filled with extremely diffuse gas. Therefore, the Earth’s atmosphere smoothly transitions into the gases of the surrounding outer space. We may actually interpret the Earth’s atmosphere as extending forever, filling the entire universe. The same interpretation can be applied to all other planetary atmospheres. In other words, there is no well-defined exopause. The tropopause is the end of the troposphere, the stratopause is the end of the stratosphere, the mesopause is the end of the mesosphere, and the thermopause is the end of the thermosphere. If there were an end of the exosphere (which would also be the end of the entire atmosphere), that end would be called the exopause, but there is no well-defined exopause. Nevertheless, if we insist upon a boundary between the Earth’s atmosphere and outer space, we may arbitrarily use the elevation of the tropopause, since the Earth’s gravity pulls most of the air in the entire atmosphere down into the troposphere. Indeed, the vast majority of all meteorological phenomena (commonly known as weather) occurs within the troposphere, the lowest layer of the atmosphere. The exceptions to this are rare. For example, the jet stream is a fast-moving current of air around the tropopause, much higher in elevation than most meteorological phenomena (weather). So, we may arbitrarily regard the thickness of the Earth’s atmosphere as the elevation of the tropopause as a rough estimate. The elevation of the tropopause is roughly ten kilometers above mean sea level. Using this as a rough estimate for the thickness of the Earth’s atmosphere, we conclude that the atmosphere is extremely thin as compared with the average radius of the Earth, roughly 6400 kilometers. To summarize, the Earth’s atmosphere extends indefinitely far according to strict interpretations, but the Earth’s atmosphere is only a few kilometers thick for all practical purposes. The Earth’s atmosphere keeps us alive in a variety of different ways. After we discuss all these ways the atmosphere keeps us alive, we will be humbled. In this vast universe, we are only able to survive within a very thin layer of air surrounding a single planet: the atmosphere of planet Earth.

The most obvious way the Earth’s atmosphere keeps us alive is with its abundance of oxygen. Humans and all animals must inhale oxygen to survive. This is because humans and animals must chemically react oxygen with glucose (a simple sugar) to extract the energy they need for their survival. Humans ingest various sugars as well as complex carbohydrates such as bread, rice, cereal, and pasta. Our bodies digest complex carbohydrates as well as sugars, breaking them down into glucose (a simple sugar). There is a tremendous amount of energy stored within the chemical bonds of the glucose molecule, which our bodies access by reacting it with oxygen. The human body is composed of roughly one hundred trillion cells. Within these cells, the following chemical reaction occurs: glucose plus oxygen yields energy plus carbon dioxide and water as waste products. This chemical reaction is called cellular respiration and is more properly written C₆H₁₂O₆ + 6 O₂ → energy + 6 CO₂ + 6 H₂O. When we inhale, the oxygen that enters our lungs is transferred to our blood; our blood then carries the oxygen to the trillions of cells of our bodies. The oxygen enters our cells and chemically reacts with glucose to yield energy. The carbon dioxide that is produced as a waste product from the reaction is transferred back into our blood; our blood then carries the carbon dioxide back to our lungs, and we then exhale. Cellular respiration not only explains why humans and animals must inhale oxygen; cellular respiration also explains why humans and animals must exhale carbon dioxide. Plants inhale carbon dioxide to use together with water as the raw materials to synthesize glucose. Plants use the energy of sunlight to initiate this reaction, which is why this chemical reaction is called photosynthesis. The photosynthesis reaction is more properly written 6 CO₂ + 6 H₂O + energy → C₆H₁₂O₆ + 6 O₂. Notice that the photosynthesis reaction is precisely the reverse of the cellular respiration reaction. Note also that oxygen is a waste product of this photosynthesis reaction. Plants inhale carbon dioxide and exhale oxygen, the precise reverse of humans and animals. Therefore, the relationship between animals (including humans) and plants is a symbiotic relationship. Animals (including humans) exhale carbon dioxide, which plants then inhale. Plants then exhale oxygen, which animals (including humans) then inhale. Animals (including humans) then exhale carbon dioxide, which plants then inhale, and so on and so forth.

Another way the Earth’s atmosphere keeps us alive is by maintaining a habitable temperature for life. Based on the Earth’s distance from the Sun, our planet should be too cold for life to exist. The temperature of our planet should be much colder than the freezing temperature of water; not only should all the oceans be frozen, but the continents should be frozen over as well. However, there are tiny amounts of gases within the Earth’s atmosphere that absorb and then emit some of the heat that our planet radiates. These gases are called greenhouse gases. The most important greenhouse gas is water vapor. Carbon dioxide, methane, and other gases are secondary greenhouse gases. These gases absorb some of the heat that the Earth radiates, and these gases then reradiate this heat themselves. Although these gases reradiate some of this heat into outer space, these gases also reradiate some of this heat back to the Earth. This causes the temperature of planet Earth to be significantly warmer than it would have been otherwise, based on its distance from the Sun. In fact, the Earth is sufficiently warmed that its average surface temperature is habitable for life. This warming is called the greenhouse effect, since it is rather like a greenhouse that is warm even in the wintertime. The Earth’s atmosphere is mostly nitrogen and oxygen, but neither of these gases can absorb or radiate heat efficiently. In other words, neither nitrogen nor oxygen are greenhouse gases. Primarily water vapor and secondarily carbon dioxide, methane, and other gases are able to absorb and radiate heat efficiently. The tiny amounts of water vapor, carbon dioxide, methane, and other gases in the Earth’s atmosphere warm the planet to a habitable temperature. This is a second way the Earth’s atmosphere keeps us alive.

The Sun not only radiates visible light; the Sun radiates all forms of electromagnetic radiation. The Electromagnetic Spectrum is a list of all the different types of electromagnetic waves in order as determined by either the frequency or the wavelength. Starting with the lowest frequencies (which are also the longest wavelengths), we have radio waves, microwaves, infrared, visible light (the only type of electromagnetic wave our eyes can see), ultraviolet, X-rays, and gamma rays at the highest frequencies (which are also the shortest wavelengths). All of these are electromagnetic waves. Therefore, all of them may be regarded as different forms of light. They all propagate at the same speed of light through the (near-perfect) vacuum of outer space for example. We now realize that whenever we use the word light in colloquial English, we probably mean to use the term visible light, since this is the only type of light that our eyes can actually see. The visible light band of the Electromagnetic Spectrum is actually quite narrow. Nevertheless, the visible light band of the Electromagnetic Spectrum can be subdivided. In order, the subcategories of the visible light band of the Electromagnetic Spectrum starting at the lowest frequency (which is also the longest wavelength) are red, orange, yellow, green, blue, indigo, and violet at the highest frequency (which is also the shortest wavelength). We now realize why electromagnetic waves with slightly lower frequencies (or with slightly longer wavelengths) than visible light are called infrared, since their frequencies (or wavelengths) are just beyond red visible light. In other words, infrared light is more red than red! We also realize why electromagnetic waves with slightly higher frequencies (or with slightly shorter wavelengths) than visible light are called ultraviolet, since their frequencies (or wavelengths) are just beyond violet visible light. In other words, ultraviolet light is more purple than purple! The Sun radiates all of these electromagnetic waves. For example, the near ultraviolet from the Sun causes suntans, and too much near ultraviolet from the Sun causes sunburns. The far ultraviolet has even more energy, and the Sun radiates sufficient far ultraviolet that we should be killed from its far ultraviolet radiation. X-rays have even greater energy; thus, the X-rays from the Sun should kill us in a fairly short amount of time. Something must be shielding us from the Sun’s far ultraviolet and from the Sun’s X-rays. Our atmosphere provides these shields. The symbol for the oxygen atom is O. Under ordinary temperatures and pressures, the oxygen atom will never remain by itself; it will always chemically bond with other atoms. The oxygen atom will even chemically bond with another oxygen atom. Two oxygen atoms chemically bonded to each other is called the oxygen molecule, which is written O₂. Molecular oxygen is also known as normal oxygen, since oxygen is always in this state under ordinary temperatures and pressures. Roughly twenty percent of the Earth’s atmosphere is molecular (normal) oxygen for example, and this is the form of oxygen that plants exhale as well as the form humans and all animals must inhale. Notice this is the form of oxygen appearing in both the cellular respiration reaction and the photosynthesis reaction written above. Whenever we use the simple word oxygen, we are not being clear. Do we mean atomic oxygen O or do we mean molecular oxygen O₂? We probably mean molecular oxygen, since this is normal oxygen. If molecular oxygen absorbs far ultraviolet, a chemical reaction will synthesize a strange form of oxygen: three oxygen atoms chemically bonded to each other. This strange form of oxygen is written O₃ and is called ozone. The synthesis of ozone is more properly written 3 O₂ + energy → 2 O₃. Ozone is toxic, since inhaling O₃ causes severe respiratory problems. This is ironic, since ozone also keeps us alive. The molecular oxygen in the Earth’s atmosphere absorbs the far ultraviolet from the Sun, synthesizing ozone. Therefore, the far ultraviolet from the Sun never reaches the surface of the Earth, since it is absorbed by molecular oxygen to synthesize ozone. In fact, there is a layer of ozone in the stratosphere below which far ultraviolet does not penetrate. This layer is commonly known as the ozone layer, but it is more correctly called the ozonosphere. The ozonosphere is the heat source within the stratosphere that is responsible for warming temperatures with increasing elevation within that atmospheric layer. Much higher in the atmosphere within the thermosphere, various atoms and molecules absorb X-rays from the Sun. X-rays have so much energy that absorbing them strips electrons completely free from an atom or molecule. In other words, atoms or molecules are ionized by X-rays. Therefore, the X-rays from the Sun never reach the surface of the Earth, since they are absorbed by atoms and molecules to synthesize ionized atoms and molecules. In fact, there is a layer of ionized atoms and molecules in the thermosphere below which X-rays do not penetrate. This layer is called the ionosphere, and it is the heat source within the thermosphere that is responsible for warming temperatures with increasing elevation within that atmospheric layer.

Let us summarize all the ways the Earth’s atmosphere keeps us alive. Firstly, humans and animals would not have oxygen to react with glucose to extract energy for their survival if unicellular microorganisms did not remove most of the carbon dioxide from the atmosphere, replacing it with molecular oxygen. Secondly, planet Earth would be too cold for life to exist without the presence of greenhouse gases that make the planet warm enough to be habitable for life. Thirdly, life on Earth would be killed from the far ultraviolet from the Sun if it were not for the ozonosphere. Fourthly, life on Earth would be killed from the X-rays from the Sun if it were not for the ionosphere. As we discussed earlier in the course, the atmosphere would be substantially ionized by the Sun’s solar wind without the Earth’s magnetic field deflecting most of these charged particles from the Sun that continually bombard our planet. This is a fifth way our planet keeps us alive. If only one of these were the case, we would not be here from the lack of the other four. If two were the case, we would not be here from the lack of the other three. If three were the case, we would not be here from the lack of the other two. If four were the case, we would not be here from the lack of the remaining one. The fact that all five of these are the case on the same planet is truly miraculous. Again, we are humbled. In this vast universe, we are only able to survive within a very thin layer of air surrounding a single planet: the atmosphere of planet Earth.

The surface temperature of the Earth causes the Earth to radiate heat from its surface. This explains why the troposphere becomes cooler with increasing elevation; as we climb the troposphere, we are further and further from the surface of the Earth and thus further and further from this source of heat. Air in the lower troposphere (near mean sea level) is often heated by the Earth’s surface. Since hot fluids rise, this hot air may rise to the upper troposphere (near the tropopause). This rising air may cool, as we will discuss shortly. Since cool air sinks, air in the upper troposphere (near the tropopause) may sink to the lower troposphere (near mean sea level), where it may be warmed again thus causing it to rise again. In summary, there is significant convection within the troposphere caused by continually circulating air within the troposphere. This convection (circulation) of air within the troposphere is ultimately responsible for meteorological phenomena (commonly known as weather), as we will discuss. This explains why the vast majority of all meteorological phenomena (weather) occurs within the troposphere, the lowest layer of the atmosphere. This also explains why the lowest layer of the Earth’s atmosphere is called the troposphere, since the Greek root tropo- means turning. The ozonosphere is in the upper stratosphere, near the stratopause. This explains why the temperature warms as we climb the stratosphere. After passing the tropopause, we approach the ozonosphere, which serves as a heat source, thus causing warming temperatures. After passing the stratopause, we are further and further from the ozonosphere. This explains why the temperature cools as we climb the mesosphere. Note that cooler air resides in the lower stratosphere while warmer air resides in the upper stratosphere. Since cool fluids do not rise, the cool air in the lower stratosphere does not rise to the upper stratosphere. Conversely, since warm fluids do not sink, the warm air in the upper stratosphere does not sink to the lower stratosphere. Therefore, there is no convection (circulation) of air within the stratosphere. The air in the stratosphere remains layered based on temperature. This explains why this layer of the atmosphere is called the stratosphere, since the air is stratified or layered. The word stratify is derived from a Latin word meaning layer. As we discussed earlier in the course, the word stratum (a layer of sedimentary rock) derives from the same Latin word. The air in the mesosphere cools as we climb the mesosphere, just as air in the troposphere cools as we climb the troposphere. This may lead us to conclude that there is significant convection (circulation) of air within the mesosphere just as in the troposphere, thus causing an abundance of meteorological phenomena (weather) within the mesosphere. However, the Earth’s gravity pulls most of the air in the entire atmosphere down into the troposphere. Although there is convection (circulation) of air within the mesosphere, the air within this layer is too thin for this convection (circulation) to result in an abundance of meteorological phenomena (weather) within the mesosphere. The Greek root meso- means middle. For example, Central America is sometimes called Mesoamerica, as in Middle America. Therefore, the word mesosphere simply means middle sphere or middle layer. The ionosphere is in the upper thermosphere, near the thermopause. This explains why the temperature warms as we climb the thermosphere. After passing the mesopause, we approach the ionosphere, which serves as a heat source, thus causing warming temperatures. After passing the thermopause, we are further and further from the ionosphere. This explains why the temperature cools as we climb the exosphere. Note that cooler air resides in the lower thermosphere while warmer air resides in the upper thermosphere. Since cool fluids do not rise, the cool air in the lower thermosphere does not rise to the upper thermosphere. Conversely, since warm fluids do not sink, the warm air in the upper thermosphere does not sink to the lower thermosphere. Therefore, there is no convection (circulation) of air within the thermosphere. The air in the thermosphere remains layered based on temperature. This is similar to the air in the stratosphere, but note that the air in the thermosphere is much thinner than the air in the stratosphere, since the Earth’s gravity pulls air downward. As we climb the exosphere, the air becomes cooler and cooler, smoothly transitioning into the very cold temperatures of the surrounding outer space. The Greek root exo- means outside or external. For example, an exoskeleton is a skeleton that is outside (surrounding) an organism. Therefore, the word exosphere simply means external sphere or external layer. The exosphere is a layer of gas that is not strictly part of the Earth’s atmosphere but is outside (surrounding) the Earth’s atmosphere that smoothly transitions into the gas of the surrounding outer space.

All of us have a basic understanding of the seasons: it is warmer in summertime and colder in wintertime. It is a common misconception that the seasons occur because of the varying distance of planet Earth from the Sun. Supposedly when our planet Earth is closer to the Sun, it is warmer causing summertime, and supposedly when our planet Earth is further from the Sun, it is colder causing wintertime. This argument seems reasonable, but it is completely wrong. The orbit of the Earth around the Sun is almost a perfect circle, meaning that the Earth is roughly the same distance from the Sun throughout the entire year. Of course, the true shape of the Earth’s orbit around the Sun is an ellipse; sometimes the Earth is closer to the Sun than average, and other times the Earth is further from the Sun than average. However, the eccentricity of the Earth’s elliptical orbit is so close to zero that the orbit is almost a perfect circle. The eccentricity of an ellipse quantifies the elongation of the ellipse. When the eccentricity is zero, the ellipse is a perfect circle. When the eccentricity is close to zero, the ellipse is almost a perfect circle. The eccentricity of the Earth’s elliptical orbit around the Sun is so close to zero that its orbit is almost a perfect circle. When the Earth is at perihelion (closest to the Sun), it is roughly 2.5 million kilometers (roughly 1.5 million miles) closer to the Sun than average. When the Earth is at aphelion (furthest from the Sun), it is roughly 2.5 million kilometers (roughly 1.5 million miles) further from the Sun than average. These closer or further distances may seem large, but the Earth is on average roughly 150 million kilometers (roughly 93 million miles) from the Sun. Therefore, these closer or further distances are less than two-percent variations from the average distance between the Earth and the Sun, and this is not enough of a difference to cause the seasons. There is a spectacular piece of evidence that will forever bury the misconception that the varying distance of the Earth from the Sun causes the seasons: the Earth is closest to the Sun in wintertime and furthest from the Sun in summertime! The Earth is at its perihelion on roughly January 03rd every year, but early January is in wintertime! The Earth is at its aphelion on roughly July 03rd every year, but early July is in summertime! Therefore, it is absolutely not the Earth’s varying distance from the Sun that causes the seasons. Caution: we do not argue that distance from the Sun is completely irrelevant. Obviously, if we were to move the Earth fifty million kilometers closer to the Sun, of course the planet would become so hot that it would no longer be habitable for life (all life, including all of us, would die). Obviously, if we were to move the Earth fifty million kilometers further from the Sun, of course the planet would become so cold that it would no longer be habitable for life (all life, including all of us, would die). However, if we were to move the Earth only a couple million kilometers closer to or further from the Sun, this would not be enough to affect the Earth’s average temperature. The proof of this assertion is that this already occurs; every year as the Earth orbits the Sun on its elliptical orbit, the Earth moves roughly 2.5 million kilometers closer to the Sun at perihelion and roughly 2.5 million kilometers further from the Sun at aphelion, and these variations do not affect the average temperature of the planet. In fact, planet Earth is closest to the Sun in wintertime and furthest from the Sun in summertime!

After discussing in tremendous detail what does not cause the seasons, we must finally discuss what does cause the seasons. The Earth’s rotational axis is tilted from the vertical, the vertical being defined as perpendicular to the plane of the Earth’s orbit around the Sun. The tilt of any planet’s rotational axis is called the obliquity of the planet. The seasons are caused by the Earth’s obliquity, the tilt of its rotational axis. The obliquity of planet Earth is roughly 23½ degrees. As the Earth orbits the Sun, this 23½ degrees of obliquity remains fixed to an excellent approximation. Thus, as the Earth orbits the Sun, sometimes the Earth’s northern hemisphere will be tilted toward the Sun, causing that hemisphere to receive more direct sunlight thus causing warmer summertime. The warmer summertime is also caused by daytime being longer than nighttime, as we will discuss shortly. At the same time the Earth’s northern hemisphere is tilted toward the Sun, the Earth’s southern hemisphere is tilted away from the Sun, causing that hemisphere to receive less direct sunlight thus causing colder wintertime. The colder wintertime is also caused by nighttime being longer than daytime, as we will discuss shortly. Six months later when the Earth is on the opposite side of its orbit, the Earth’s northern hemisphere will be tilted away from the Sun, causing that hemisphere to receive less direct sunlight and causing that hemisphere to have longer nighttime than daytime, thus causing colder wintertime. At the same time the Earth’s northern hemisphere is tilted away from the Sun, the Earth’s southern hemisphere is tilted toward the Sun, causing that hemisphere to receive more direct sunlight and causing that hemisphere to have longer daytime than nighttime, thus causing warmer summertime. This is remarkable; the seasons are reversed in the two hemispheres at the same time! As another example, when it is springtime in the northern hemisphere, it is autumntime in the southern hemisphere at the same time. This means that the Earth is at perihelion (closest to the Sun) during the southern hemisphere’s summertime, and the Earth is at aphelion (furthest from the Sun) during the southern hemisphere’s wintertime. We may be tempted to conclude that the southern hemisphere’s summertime is especially hot, and the southern hemisphere’s wintertime is especially cold. This is false; the opposite is true! Summers are typically hotter in the northern hemisphere as compared with summers in the southern hemisphere, and winters are typically colder in the northern hemisphere as compared with winters in the southern hemisphere! In other words, both summers and winters are more mild in the southern hemisphere as compared with the northern hemisphere, where both summers and winters are more severe. As we discussed earlier in the course, this is because the continents are presently somewhat crowded together in the northern hemisphere, making the southern hemisphere mostly covered with ocean (water). Water has a large heat capacity, meaning that it is difficult to change the temperature of water. Therefore, the abundance of water in the southern hemisphere stabilizes temperatures, causing smaller temperature variations in the southern hemisphere as compared with larger temperature variations in the northern hemisphere. This spectacularly emphasizes that variations in the distance from the Sun do not determine seasonal temperatures. Again, summers are more mild (less hot) in the southern hemisphere, even though the Earth is closest to the Sun during summertime in the southern hemisphere, while summers are more severe (more hot) in the northern hemisphere, even though the Earth is furthest from the Sun during summertime in the northern hemisphere! Similarly, winters are more mild (less cold) in the southern hemisphere, even though the Earth is furthest from the Sun during wintertime in the southern hemisphere, while winters are more severe (more cold) in the northern hemisphere, even though the Earth is closest to the Sun during wintertime in the northern hemisphere! The large heat capacity of liquid water is also responsible for moderating the temperature difference between daytime and nighttime on our planet Earth. The daytime side of any planet faces toward the Sun, while the nighttime side of any planet faces away from the Sun. For most planets, nighttime is much colder than daytime, but the nighttime side of planet Earth is only slightly cooler than its daytime side, thanks to the stabilizing effect of all the water that covers most of the planet. Extraordinarily, the nighttime side of planet Earth may at times become warmer than the daytime side depending upon weather patterns, as we will discuss. As another example of how water stabilizes temperatures on our planet Earth, other planets have north poles and south poles that are much colder than their equators. Although the Earth’s poles are cold and the Earth’s equator is hot by human standards, the difference in temperature is nevertheless moderate as compared with other planets. Without the abundance of water that covers our planet Earth, our poles would be too cold and our equator would be too hot to be habitable for life.

The moment when the Earth’s northern hemisphere is tilted the most toward the Sun is called the summer solstice. This occurs on average June 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later. Since the northern hemisphere is tilted the most toward the Sun on the summer solstice, the Sun appears to be highest in the sky, since the northern hemisphere receives the most direct sunrays. This is also the longest daytime and the shortest nighttime of the year in the northern hemisphere. The precise duration of daytime and nighttime depends upon our latitude. At the midlatitudes, there are roughly fifteen hours of daytime and only roughly nine hours of nighttime on the summer solstice. Note that the sum of fifteen hours and nine hours is twenty-four hours. Six months later when the Earth is on the other side of its orbit around the Sun, there is a moment when the Earth’s northern hemisphere is tilted the most away from the Sun. This moment is called the winter solstice, occurring on average December 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later. Since the northern hemisphere is tilted the most away from the Sun on the winter solstice, the Sun appears to be lowest in the sky, since the northern hemisphere receives the least direct sunrays. This is also the longest nighttime and the shortest daytime of the year in the northern hemisphere. The precise duration of nighttime and daytime depends upon our latitude, but it will always be the reverse of the summer solstice. At the midlatitudes for example, there are roughly fifteen hours of nighttime and only roughly nine hours of daytime on the winter solstice. Note again that the sum of fifteen hours and nine hours is twenty-four hours. Halfway in between the solstices are two other moments called the equinoxes when the Earth’s axis is not tilted toward or away from the Sun, resulting in equal amounts of daytime and nighttime (twelve hours each). This is why they are called equinoxes, since there are equal amounts of daytime and nighttime. Roughly three months after the summer solstice (roughly three months before the winter solstice) is the autumn equinox, occurring on average September 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later. Roughly three months after the winter solstice (roughly three months before the summer solstice) is the vernal equinox (or the spring equinox). The vernal equinox (spring equinox) occurs on average March 21st every year; some years it could occur one or two days earlier, while other years it could occur one or two days later. It is a common misconception that since every day is twenty-four hours, supposedly every day has twelve hours of daytime and twelve hours of nighttime. This is false for almost every day the entire year. In fact, there are only two days of the entire year when this is the case: the equinoxes. Once we pass the vernal equinox (spring equinox), every day for the next six months there is more daytime than nighttime, with maximum daytime on the summer solstice. Once we pass the autumn equinox, every day for the next six months there is more nighttime than daytime, with maximum nighttime on the winter solstice.

The term summer solstice has at least two different yet interrelated meanings. We may interpret the summer solstice as the location on the Earth’s orbit where its northern hemisphere is tilted the most toward the Sun. We may also interpret the summer solstice as the moment in time when the Earth’s northern hemisphere is tilted the most toward the Sun, occurring on average June 21st every year. Obviously, the Earth is located at its orbital summer solstice at the moment of the temporal summer solstice. The terms winter solstice, vernal equinox, and autumn equinox have similar interpretations. The term winter solstice has at least two different yet interrelated meanings. We may interpret the winter solstice as the location on the Earth’s orbit where its northern hemisphere is tilted the most away from the Sun. We may also interpret the winter solstice as the moment in time when the Earth’s northern hemisphere is tilted the most away from the Sun, occurring on average December 21st every year. Obviously, the Earth is located at its orbital winter solstice at the moment of the temporal winter solstice. The term vernal equinox (spring equinox) has at least two different yet interrelated meanings. We may interpret the vernal equinox (spring equinox) as the location on the Earth’s orbit where its axis is not tilted toward or away from the Sun as it journeys from the orbital winter solstice toward the orbital summer solstice. We may also interpret the vernal equinox (spring equinox) as the moment in time occurring on average March 21st every year when the Earth’s axis is not tilted toward or away from the Sun after the temporal winter solstice but before the temporal summer solstice. Obviously, the Earth is located at its orbital vernal equinox at the moment of the temporal vernal equinox. Finally, the term autumn equinox has at least two different yet interrelated meanings. We may interpret the autumn equinox as the location on the Earth’s orbit where its axis is not tilted toward or away from the Sun as it journeys from the orbital summer solstice toward the orbital winter solstice. We may also interpret the autumn equinox as the moment in time occurring on average September 21st every year when the Earth’s axis is not tilted toward or away from the Sun after the temporal summer solstice but before the temporal winter solstice. Obviously, the Earth is located at its orbital autumn equinox at the moment of the temporal autumn equinox.

As we discussed earlier in the course, the latitude of any location on planet Earth is defined as its angle north or south from the equator. The colatitude of any location on planet Earth is defined as its angle from the north pole. Since there are ninety degrees of latitude from the equator to the north pole, this makes the colatitude equal to ninety degrees minus the latitude. For example, if our latitude is ten degrees north, this means we are ten degrees of latitude north of the equator, making us eighty degrees from the north pole; therefore, our colatitude is eighty degrees. Indeed, ninety minus ten equals eighty. As another example, if our latitude is seventy degrees north, this means we are seventy degrees of latitude north of the equator, making us twenty degrees from the north pole; therefore, our colatitude is twenty degrees. Indeed, ninety minus seventy equals twenty. The only location on planet Earth where our latitude and our colatitude equal the same number is at forty-five degrees north latitude, since that would place us halfway between (equidistant from) the equator and the north pole. Indeed, ninety minus forty-five equals forty-five. The altitude of the Sun at noon on the summer solstice equals our colatitude plus the obliquity. The altitude of the Sun at noon on the winter solstice equals our colatitude minus the obliquity. The altitude of the Sun at noon on either equinox equals our colatitude. Everything we have discussed applies not just to planet Earth but also to any other planet orbiting the Sun. The obliquity of any planet is the angular tilt of its rotational axis from the vertical direction that is perpendicular to its own orbital plane around the Sun. The poles of any planet are where its own rotational axis intersects the planet. The equator of any planet is halfway between the two poles of the planet. Our latitude on that planet would be our angle north or south from that planet’s equator. The planet’s equator would be 0° latitude on that planet. The planet’s north pole would be 90°N latitude on that planet, and the planet’s south pole would be 90°S latitude on that planet. Our colatitude on that planet would be our angle from that planet’s north pole, which would again be ninety degrees minus our latitude. The summer solstice of any planet is the moment when its northern hemisphere is tilted the most towards the Sun. The winter solstice of any planet is the moment when its northern hemisphere is tilted the most away from the Sun. The equinoxes of any planet is halfway between the solstices when its rotational axis is not tilted toward or away from the Sun. The altitude of the Sun at noon on each of these dates would be the same equations: colatitude plus obliquity on the summer solstice, colatitude minus obliquity on the winter solstice, and colatitude on the equinoxes. The only difference in this analysis for other planets are the actual dates of the solstices and the equinoxes. For any planet orbiting the Sun, the time from one solstice to the next solstice (which is also the time from one equinox to the next equinox) is one-half of the planet’s orbital period around the Sun. The time from one solstice to the next equinox (which is also the time from one equinox to the next solstice) is one-quarter of the planet’s orbital period around the Sun. As an example, consider a hypothetical planet with an obliquity of thirty degrees, and suppose we live at fifty degrees north latitude on this hypothetical planet. Since our latitude is fifty degrees north, our colatitude is forty degrees, since ninety minus fifty equals forty. Hence, the altitude of the Sun at noon on the summer solstice would be seventy degrees, since the colatitude plus the obliquity is forty plus thirty, which equals seventy. The altitude of the Sun at noon on the winter solstice would be ten degrees, since the colatitude minus the obliquity is forty minus thirty, which equals ten. The altitude of the Sun at noon on either equinox would be forty degrees, since that is our colatitude.

It is a common misconception that the Sun is directly overhead at noon. This misconception comes from the phrase high noon. Of course, the Sun is highest in the sky at noon, giving this phrase some validity. Nevertheless, the Sun is never ever directly overhead at most locations on Earth. For example, suppose we live at forty degrees north latitude. Our colatitude would be fifty degrees, since ninety minus forty equals fifty. The highest the Sun would ever be at this location is on the summer solstice, when its altitude at noon is 73½ degrees, since our colatitude plus obliquity is fifty plus 23½, which is indeed 73½ degrees. Although 73½ degrees is a high altitude, it is not directly overhead. Directly overhead would be ninety degrees of altitude. If the Sun is not directly overhead at noon on the summer solstice, it would only be lower in the sky every other day of the year. This shows that the Sun is never ever directly overhead at most locations on Earth. Is there anywhere on planet Earth where the Sun is directly overhead at noon on the summer solstice? Yes, at a latitude equal to the same number of degrees north of the equator as the obliquity of planet Earth. To prove this, suppose we live at 23½ degrees north latitude, then our colatitude would be 66½ degrees, since ninety minus 23½ equals 66½. Thus, the altitude of the Sun at noon would be our colatitude 66½ degrees plus the obliquity of planet Earth 23½ degrees, but 66½ plus 23½ equals ninety degrees of altitude, directly overhead! This location of 23½ degrees north latitude is so important that it deserves a special name: the Tropic of Cancer, as we discussed earlier in the course. There is only one location on planet Earth where the Sun is directly overhead at noon on the winter solstice: 23½ degrees south latitude. This location is so important that it deserves a special name: the Tropic of Capricorn, as we discussed earlier in the course. The words Cancer and Capricorn refer to astronomical constellations of the zodiac; the reason these lines of latitude are named for astronomical constellations of the zodiac is beyond the scope of this course. There is only one location on planet Earth where the Sun is directly overhead at noon on the equinoxes: the equator at zero degrees latitude. Thousands of years ago, primitive humans did not understand that the Earth is a planet with a tilted rotational axis orbiting the Sun. For thousands of years, humans believed that the motion of the Sun was responsible for the seasons. Although today we understand that it is actually the Earth that is orbiting the Sun, we must also confess that when we look up into the sky, it does appear as if the Sun is moving. Therefore, we should understand the seasons from the frame of reference of the Earth, which was the only understanding of humans for thousands of years. From the frame of reference of the Earth, the Sun appears to be directly on top of the Tropic of Cancer on the summer solstice. For the next six months, the Sun appears to move south, arriving on top of the equator three months later on the autumn equinox and arriving on top of the Tropic of Capricorn three months after that on the winter solstice. For the following six months, the Sun appears to move north, arriving on top of the equator three months later on the vernal equinox (spring equinox) and arriving on top of the Tropic of Cancer three months after that on the summer solstice. Again, it is not the Sun that is actually moving north and south; in actuality, the Earth is orbiting the Sun. Nevertheless, we live on planet Earth, and so we must understand the seasons from the frame of reference of the Earth. To summarize, it is only possible for the Sun to appear directly overhead at noon if we live somewhere between the Tropic of Cancer and the Tropic of Capricorn. If we live north of the Tropic of Cancer or south of the Tropic of Capricorn, the Sun never ever appears to be directly overhead.

The Arctic Circle is 66½ degrees north latitude, making its colatitude 23½ degrees, since ninety minus 66½ equals 23½. The altitude of the Sun at noon at the Arctic Circle on the winter solstice would be zero degrees, since our colatitude minus the obliquity would be 23½ minus 23½, which is obviously zero. An altitude of zero degrees means the Sun is on the horizon, such as during sunrise. At even more northern latitudes, the altitude of the Sun on the winter solstice will be a negative number, which means it is below the horizon. In other words, we cannot see the Sun, making it nighttime even though the clock time is noon! Before noon or after noon, the Sun will be even further below the horizon. Thus, the entire day is in perpetual nighttime! The same occurs on the Antarctic Circle at 66½ degrees south latitude: the altitude of the Sun at noon on the summer solstice is zero degrees, meaning that it is on the horizon. At even more southern latitudes, the altitude of the Sun on the summer solstice will be a negative number, which means it is below the horizon. Again, we cannot see the Sun, making it nighttime even though the clock time is noon! Before noon or after noon, the Sun will be even further below the horizon. Thus, the entire day is in perpetual nighttime! These extreme northern latitudes and extreme southern latitudes are the only places on Earth where the Sun may never rise on some days of the year and may never set on other days of the year. At the north pole, six months of continuous nighttime occurs from the autumn equinox all the way to the vernal equinox (spring equinox), and then six months of continuous daytime occurs from the vernal equinox (spring equinox) all the way to the autumn equinox. The reverse occurs at the south pole: six months of continuous nighttime occurs from the vernal equinox (spring equinox) all the way to the autumn equinox, while six months of continuous daytime occurs from the autumn equinox all the way to the vernal equinox (spring equinox). Even when the clock time is midnight, the Sun may still be in the sky causing daytime at these extreme latitudes. This is the origin of the phrase midnight Sun.

There are several religious holidays that have their origins in the solstices and the equinoxes. For example, Christmas Day is observed on December 25th every year. Notice that this is shortly after the winter solstice. Before Christmas Day became the celebration of the birth of Jesus Christ, this was a pagan holiday celebrating the winter solstice. Why would pagans celebrate the day when the Sun appeared to be lowest in the sky at noon with the most number of nighttime hours? Primitive humans observed the Sun appear lower and lower in the sky after the summer solstice; many primitive humans were probably terrified that the Sun would continue to move downward until it disappeared below the horizon. However, by simply paying attention every year, we observe that the Sun stops moving downward on the winter solstice, and then begins to move upward. This was a reason to celebrate for many ancient pagans. This pagan celebration became the celebration of the birth of Jesus Christ, since early Christians saw the birth of Jesus Christ as bringing more and more light into a spiritually dark world. In actuality, Jesus was not born on December 25th. We will never be certain of the exact day of the birth of Jesus. Most of the details of the vast majority of persons throughout human history, including Jesus, were never recorded. We will also never be certain of the exact year of the birth of Jesus. Although it is commonly believed that the year of the birth of Jesus was anno Domini 1, in actuality no one recorded the year that Jesus was born. Again, most of the details of the vast majority of persons throughout human history, including Jesus, were never recorded. The people of the world did not declare the year to be anno Domini 1 when Jesus was born. The ancient Romans designated years using a few different numbering schemes, among which was the number of years since the founding of the city of Rome, which was more than seven centuries before the birth of Jesus. Using this particular convention, the ancient Romans designated years using either of the Latin phrases “ab urbe condita” or “anno urbis conditae,” meaning “in the year since the founding of the city.” Either Latin phrase was abbreviated AUC. This numbering scheme continued to be used by Europeans even after the fall of the Western Roman Empire. More than five centuries after the birth of Jesus and roughly fifty years after the Western Roman Empire fell, the Christian monk Dionysius Exiguus tried to determine the year that Jesus was born. This monk declared that the year AUC 1278 should be redesignated A.D. 525, where A.D. is the abbreviation for the new Latin phrase “anno Domini” meaning “in the year of our Lord,” effectively meaning the number of years since the birth of Jesus. Over the next few centuries, Europeans retroactively changed the years of historical dates from AUC to A.D. based on this declaration by Dionysius Exiguus. Europeans even changed the years of historical dates before the birth of Jesus from AUC to B.C., which is simply an abbreviation for “before Christ.” Modern scholarship has revealed that the year that Jesus was born as determined by Dionysius Exiguus is probably a few years in error. Modern scholarship estimates that 6 B.C. is a more accurate estimate for the year of the birth of Jesus. Many students are offended by this assertion. Students claim that it would be contradictory for Jesus to have been born in the year 6 B.C., since B.C. is the abbreviation for before Christ and no one can be born before the year of their own birth! Again, we must remember that no one recorded the date that Jesus was born. We must remember that the belief that the year of the birth of Jesus was A.D. 1 is based upon an estimate by a monk who lived roughly five centuries after Jesus was born. In fact, we should marvel that the estimate made by Dionysius Exiguus for an unrecorded event that occurred roughly five centuries earlier was only a few years in error! As another example of a religious holiday that has its origin in the solstices and the equinoxes, Easter is always the first Sunday after the first Full Moon after the vernal equinox (spring equinox) every year. Since Jesus was Jewish, what is traditionally called the Last Supper was in actuality a Passover celebration. The Jewish calendar is a lunar calendar, and hence Jewish holy days are determined by the cycles of the Moon. Placing Easter on the first Sunday after the first Full Moon after the vernal equinox (spring equinox) is an attempt to keep the date of Easter as close as possible to the date of Passover.

A thermometer is a device that measures temperature. The operation of a thermometer is based on the principle of thermal expansion and thermal contraction. Most substances expand when they become warmer, and most substances contract when they become colder. To build a primitive thermometer, we take any object and measure its length at one temperature, and we measure its different length at a different temperature. We draw marks at each of these lengths, and we draw other marks between these two marks. To determine the temperature, we simply read off whichever mark the end of the object meets based on its length at that temperature. Unfortunately, most substances expand and contract by only tiny amounts when their temperature changes. Hence, the marks are often too close together, making differences in length difficult to measure. However, the element mercury expands by quite a noticeable amount as it becomes warmer and contracts by quite a noticeable amount as it becomes colder. Therefore, most thermometers use liquid mercury, since the marks are then well separated and easy to read. An actinometer is a device that measures solar radiation. To build a primitive actinometer, we take any object and use a thermometer to measure its initial temperature. Then, we place the object in sunlight for a certain amount of time, perhaps one hour. As the object absorbs solar radiation, it becomes hotter. We use a thermometer to measure its hotter temperature afterwards, and from the difference in temperature between its hotter final temperature and its colder initial temperature, we can calculate the amount of solar radiation the object absorbed. Note that we must wrap the object in black cloth to ensure that it absorbs all of the solar radiation. Otherwise, the object will only become hotter by some of the solar radiation that it absorbed, since the object will reflect the rest of the solar radiation. It is convenient to use a bucket of water as the object, since we know the heat capacity of water. An actinometer would measure the greatest amount of solar radiation on the summer solstice, and an actinometer would measure the least amount of solar radiation on the winter solstice. However, the summer solstice is almost never the hottest day of the year; a thermometer measures the hottest air temperature roughly a month later, in late July in the northern hemisphere. Similarly, the winter solstice is almost never the coldest day of the year; a thermometer measures the coldest air temperature roughly a month later, in late January in the northern hemisphere. These delays occur because the Earth is mostly covered with water, which has a large heat capacity. In other words, it is difficult to change the temperature of water. The northern hemisphere receives the most direct sunrays on the summer solstice around June 21st, but it still takes another month for the air to warm to maximum temperature sometime in late July. In fact, it takes yet another month for the ocean waters to warm to maximum temperature, in late August in the northern hemisphere. This is why most people in the northern hemisphere take their summer vacations in August, so that they may enjoy swimming in the ocean when it is warmest. The northern hemisphere receives the least direct sunrays on the winter solstice around December 21st, but the oceans have retained so much heat from the summertime that it still takes another month for the air to cool to minimum temperature sometime in late January. In fact, it takes yet another month for the ocean waters to cool to minimum temperature, in late February in the northern hemisphere.

Local (Small-Scale) Meteorological Dynamics

Aside from the seasonal temperature variations we have discussed, many other variables affect the air temperature on a daily basis, on an hourly basis, and even shorter timescales. These variations in air temperature cause variations in air pressure. These variations in air pressure cause the meteorological phenomena (commonly known as weather) that we will discuss. Air pressure is the force that the air exerts per unit area. This pressure (force per unit area) is ultimately caused by molecular collisions. Therefore, we may interpret air pressure as a measure of how frequently air molecules collide with each other. Warm air is at a lower pressure, while cold air is at a higher pressure. This is because the molecules of warm air are moving faster, enabling them to move further from one another; hence, they collide with each other less frequently since they are further apart from one another. Conversely, the molecules of cold air are moving slower; they cannot move far from one another and hence they collide with each other more frequently. Suppose all the air in a certain room is at the same pressure, and consider a parcel of air in the middle of the room. Since the air pressure on either side of the parcel of air is the same, it will suffer equal molecular collisions from either side of itself. These equal molecular collisions will balance each other, and the parcel of air will not move. Now suppose instead that the air on one side of the room is at a higher air pressure for whatever reason, and suppose the air on the other side of the room is at a lower air pressure for whatever reason. Again, consider a parcel of air in the middle of the room. This parcel of air will now suffer greater molecular collisions from the higher-pressure side of the room, and the parcel of air will suffer fewer molecular collisions from the lower-pressure side of the room. The net result is that the parcel of air will be pushed from the higher pressure toward the lower pressure. The parcel of air will move, since it is pushed by a pressure imbalance. This pressure imbalance is so important that it deserves a name; it is called the pressure gradient force. If the air pressure throughout the room were the same, there would be no pressure gradient and hence no force; the air would not move. If there are variations in pressure, the pressure gradient force pushes air from higher pressure toward lower pressure. Moving air is called wind. Hence, the pressure gradient force causes wind to blow.

A geometrical curve connecting locations of equal air pressure is called an isobar. The pressure gradient force is always zero along any isobar, since every point on an isobar is at the same pressure. Since the pressure gradient force is always zero along any isobar, the pressure gradient force must point directly perpendicular to isobars. If the pressure gradient force did not point directly perpendicular to isobars, then we would be able to break the force into two components: one component directly perpendicular to the isobars and the other component along the isobars. However, the component along the isobars must be zero, as we just argued. Therefore, the pressure gradient force can only have one component: the component directly perpendicular to the isobars. The pressure gradient force does not have two components; it only has one component that is directly perpendicular to the isobars. Every point on an isobar is at the same air pressure, but two different isobars will of course be at two different pressures. Suppose as we move from one isobar to a neighboring isobar, the pressure always drops by a definite amount, perhaps ten millibars. If isobars are closely spaced to each other, this means that the pressure drops by ten millibars over a narrow distance. In other words, the pressure gradient will be steep, thus causing strong winds. If the isobars are widely spaced from each other, this means that the pressure drops by ten millibars over a wide distance. In other words, the pressure gradient will be shallow, thus causing light winds. This is remarkable, since the pressure drop from one isobar to the neighboring isobar is always a fixed amount: ten millibars in these examples. Nevertheless, the ten-millibar pressure drop is steep if the isobars are closely spaced to each other, while the ten-millibar pressure drop is shallow if the isobars are widely spaced from each other. Again, this is remarkable: the same ten millibar pressure drop is steep causing strong winds to blow in one case, while the same ten millibar pressure drop is shallow causing light winds to blow in another case.

An anemometer is a device that measures the velocity of wind, meaning that an anemometer measures both the speed and the direction of wind. An anemometer is essentially a wind vane together with a flag. As the wind blows, the wind vane turns with a certain angular speed. From that angular speed, we can calculate the speed with which the wind blows. A wind vane shaped like a rooster is called a weathercock. The flag reveals the direction with which the wind blows; whichever way the flag flutters is the direction the wind is blowing. The Beaufort scale is a wind scale, named for the Irish oceanologist/oceanographer Francis Beaufort. The Beaufort scale uses numbers from zero (for no winds) to twelve (for hurricane-speed winds). A low number on the Beaufort would be a light wind, which is called a breeze. A middle number on the Beaufort scale would simply be called a wind. A high number on the Beaufort scale would be a strong wind, which is called a gale.

We have already discussed enough basic meteorology to analyze some simple weather patterns. Suppose we are at the beach in the daytime when the Sun warms the Earth. Since water has a large heat capacity, the ocean does not become as warm as the continent. All of us have experienced this while at the beach in the daytime; no matter how hot the daytime temperature, the ocean water is not as warm as the sand. Therefore, the air above the continent is warmer than the air above the ocean. Thus, the air above the continent is at a lower pressure as compared with the air above the ocean, which is at a relatively higher pressure. Since the pressure gradient force pushes air from high pressure toward low pressure, wind will blow from the ocean toward the continent. This is called the sea breeze. In meteorology, we always name wind based on the direction it is blowing from, which is the opposite of the direction the wind is blowing toward. For example, a wind blowing from the north (which means it is blowing toward the south) is called a north wind. As another example, a wind blowing from the southwest (which means it is blowing toward the northeast) is called a southwest wind. The sea breeze is blowing from the ocean toward the continent; hence, it is called the sea breeze. We often feel this sea breeze while at the beach in the daytime. The sea breeze is a steady wind blowing from the ocean toward the continent during the daytime. In the nighttime, the opposite occurs. Suppose we are at the beach in the nighttime when the Earth cools. Since water has a large heat capacity, the ocean does not become as cold as the continent. Perhaps some of us have experienced this while at the beach in the nighttime; no matter how cool the nighttime temperature, the ocean water is not as cold as the sand. Therefore, the air above the continent is colder than the air above the ocean. Thus, the air above the continent is at a higher pressure as compared with the air above the ocean, which is at a relatively lower pressure. Since the pressure gradient force pushes air from high pressure toward low pressure, wind will blow from the continent toward the ocean. This is called the land breeze. Again, we always name wind based on the direction it is blowing from, which is the opposite of the direction the wind is blowing toward. The land breeze is blowing from the continent toward the ocean; hence, it is called the land breeze. Perhaps some of us have felt this land breeze while at the beach in the nighttime. The land breeze is a steady wind blowing from the continent toward the ocean during the nighttime. If we are facing the ocean, we feel the land breeze upon our backs; if we turn our backs to the ocean, we feel the land breeze upon our fronts. Similar to the sea breeze and the land breeze is the valley breeze and the mountain breeze. In the daytime, the Sun warms the air. Hot air is less dense, and so hot air will be buoyed upward by the surrounding air. This is why hot air rises. Therefore, daytime winds will blow from a valley up toward a mountain. This is called the valley breeze. Again, we always name wind based on the direction it is blowing from, which is the opposite of the direction the wind is blowing toward. The valley breeze is blowing from the valley up toward the mountain; hence, it is called the valley breeze. Perhaps some of us have felt this valley breeze while on a mountain in the daytime. The valley breeze is a steady wind blowing from the valley up toward the mountain during the daytime. In the nighttime, the opposite occurs. The air cools in the nighttime. Cold air is more dense, and so cold air will descend into the surrounding air. This is why cold air sinks. Therefore, nighttime winds will blow from a mountain down into a valley. This is called the mountain breeze. Again, we always name wind based on the direction it is blowing from, which is the opposite of the direction the wind is blowing toward. The mountain breeze is blowing from the mountain down into the valley; hence, it is called the mountain breeze. Perhaps some of us have felt this mountain breeze while in a valley in the nighttime. The mountain breeze is a steady wind blowing from the mountain down toward the valley during the nighttime. To summarize, during the daytime the sea breeze blows from the ocean toward the continent, while during the nighttime the land breeze blows from the continent toward the ocean. During the daytime the valley breeze blows from the valley up toward the mountain, while during the nighttime the mountain breeze blows from the mountain down toward the valley.

Fictitious forces or pseudoforces are forces that do not actually exist; they only seem to exist in certain frames of reference. For example, suppose we are in a stationary car waiting at a red traffic light. When the red traffic light turns green, we place our foot upon the car’s accelerator pedal. As the car accelerates forward, everyone and everything in the car feels a backward force. We actually feel ourselves pulled backward into the backrest of our chair. Anything hanging from the rearview mirror also swings backward. This backward force is a fictitious force or a pseudoforce. It does not exist; it only seems to exist within the car as the car accelerates forward. Although everyone and everything within the car feels this backward force, it nevertheless does not actually exist. In actuality, everyone and everything within the car remains stationary for a moment as the car and its chairs accelerate forward, and hence the backrests of the chairs accelerate forward and collide with our own backs. This is amusing: within the car we feel pulled backward into the backrests of the chairs, but in actuality we remain stationary while the backrests of the chairs accelerate forward into our backs! Although we feel a backward force within the car, we nevertheless conclude that this backward force is a fictitious force or a pseudoforce. It does not actually exist; it only seems to exist within the car as the car accelerates forward. As another example, suppose we are in a moving car when we see a green traffic light turn yellow, and so we place our foot upon the car’s brake pedal. As the car slows down, everyone and everything in the car feels a forward force. We actually feel ourselves pulled forward off of the backrest of our chair. Anything hanging from the rearview mirror also swings forward. In extreme cases, we may feel pulled forward so strongly that our heads may collide with the windshield. This forward force is a fictitious force or a pseudoforce. It does not exist; it only seems to exist within the car as the car slows down. Although everyone and everything within the car feels this forward force, it nevertheless does not actually exist. In actuality, everyone and everything within the car remains in motion for a moment as the car and its chairs and its windshield slow down, and hence the backrests of the chairs move away from our own backs while the windshield moves toward our heads. This is amusing: within the car we feel pulled forward off of the backrests of the chairs and toward the windshield, but in actuality the backrests of the chairs move away from our backs and the windshield moves toward our heads! Although we feel a forward force within the car, we nevertheless conclude that this forward force is a fictitious force or a pseudoforce. It does not actually exist; it only seems to exist within the car as the car slows down. As yet another example, suppose we are in a moving car when we see that the highway ramp ahead curves to the left, and so we turn the steering wheel to the left so that the car will remain on the highway ramp. As the car turns left, everyone and everything in the car feels a rightward force. We actually feel ourselves pulled rightward away from the driver’s side of the car and toward the passenger’s side of the car. Anything hanging from the rearview mirror also swings rightward and continues to remain suspended rightward in apparent defiance of the Earth’s downward gravity as the car turns left! This rightward force is a fictitious force or a pseudoforce. It does not exist; it only seems to exist within the car as the car turns left. Although everyone and everything within the car feels this rightward force, it nevertheless does not actually exist. In actuality, everyone and everything within the car remains in forward motion as the car turns left, and hence the driver’s side of the car turns away from us while the passenger’s side of the car turns toward us. This is amusing: within the car we feel pulled rightward toward the passenger’s side of the car, but in actuality we remain in forward motion while the passenger’s side of the car turns leftward toward us! Although we feel a rightward force within the car, we nevertheless conclude that this rightward force is a fictitious force or a pseudoforce. It does not actually exist; it only seems to exist within the car as the car turns left. As a fourth example, projectiles will appear to suffer from deflections within a rotating frame of reference. This deflecting force is a fictitious force or a pseudoforce. It does not exist; it only seems to exist within the rotating frame of reference. In actuality, the projectiles are not deflected; the projectiles in fact continue moving along straight paths. The frame of reference is rotating, and the rotation of the entire frame of reference seems to cause projectiles to deviate from straight trajectories. This particular fictitious force or pseudoforce is called the Coriolis force, named for the French physicist Gaspard-Gustave de Coriolis who first derived the mathematical equations describing this particular fictitious force or pseudoforce. The Coriolis force appears to cause rightward deflections in frames of reference rotating counterclockwise, and the Coriolis force appears to cause leftward deflections in frames of reference rotating clockwise. The Coriolis force appears to cause stronger deflections if the frame of reference is rotating faster and appears to cause weaker deflections if the frame of reference is rotating slower. The Coriolis force appears to vanish if the frame of reference stops rotating. The Coriolis force only appears to cause deflections; it does not cause projectiles to speed up or slow down.

If the Earth were not rotating, the study of the Earth’s atmosphere would be relatively simple. The pressure gradient force would simply push wind perpendicular to isobars from high pressure toward low pressure. However, the Earth is rotating, and the rotation of the Earth causes gross complications in the Earth’s atmosphere. The Earth rotates from west to east. Therefore, the northern hemisphere rotates counterclockwise when viewed from above the north pole, while the southern hemisphere rotates clockwise when viewed from above the south pole. We conclude that there is a Coriolis force on planet Earth that appears to cause rightward deflections in the northern hemisphere and appears to cause leftward deflections in the southern hemisphere. The Coriolis force would appear to be stronger if the Earth were rotating faster, while the Coriolis force would appear to be weaker if the Earth were rotating slower. The Coriolis force would appear to vanish if the Earth were to stop rotating altogether. The Coriolis force only appears to cause deflections; it does not cause projectiles to speed up or slow down. Finally, the Coriolis force is weak near the equator (the Coriolis force is in fact zero at the equator), and the Coriolis force becomes stronger and stronger as we move away from the equator toward the poles (the Coriolis force is in fact strongest at the poles). The pressure gradient force still pushes air perpendicular to isobars from high pressure toward low pressure, but in addition the Coriolis force causes deflections to the right in the northern hemisphere and deflections to the left in the southern hemisphere. Since the Coriolis force appears to cause these deflections, wind will not blow directly perpendicular to isobars; wind will not blow directly from high pressure toward low pressure.

A thermal is a parcel of air in the Earth’s atmosphere. If we have a low-pressure thermal surrounded by high pressure, the pressure gradient force will push wind from the surrounding high-pressure air inward toward the low-pressure thermal. At the same time, the Coriolis force will cause deflections to the right in the northern hemisphere and to the left in the southern hemisphere. The net result of the pressure gradient force together with the Coriolis force is an inward circulation of wind. Winds will blow inward while circulating counterclockwise in the northern hemisphere, and winds will blow inward while circulating clockwise in the southern hemisphere. If we instead have a high-pressure thermal surrounded by low pressure, the pressure gradient force will push wind from the high-pressure thermal outward toward the surrounding low-pressure air. At the same time, the Coriolis force will cause deflections to the right in the northern hemisphere and to the left in the southern hemisphere. The net result of the pressure gradient force together with the Coriolis force is an outward circulation of wind. Winds will blow outward while circulating clockwise in the northern hemisphere, and winds will blow outward while circulating counterclockwise in the southern hemisphere. The weather pattern around a low-pressure thermal is called a cyclone. Tornadoes and hurricanes are extreme examples of cyclones, as we will discuss. The weather pattern around a high-pressure thermal is called an anticyclone. A beautiful clear day is an extreme example of an anticyclone, as we will also discuss. In summary, a cyclone is the weather pattern around a low-pressure thermal, where winds blow inward while circulating counterclockwise in the northern hemisphere and clockwise in the southern hemisphere; an anticyclone is the weather pattern around a high-pressure thermal, where winds blow outward while circulating clockwise in the northern hemisphere and counterclockwise in the southern hemisphere.

At the center of a cyclone is a low-pressure thermal; this low-pressure thermal has a low density and is therefore buoyed upward by the surrounding air. As an alternative argument, the low pressure is caused by hot temperatures, and hot air must rise. Either argument leads us to conclude that the low-pressure thermal at the center of a cyclone rises. At the center of an anticyclone is a high-pressure thermal; this high-pressure thermal has a high density and therefore sinks downward into the surrounding air. As an alternative argument, the high pressure is caused by cold temperatures, and cold air must sink. Either argument leads us to conclude that the high-pressure thermal at the center of an anticyclone sinks. As the low-pressure thermal at the center of a cyclone rises, the surrounding air pressure at higher elevations decreases in accord with the law of atmospheres. Therefore, the rising low-pressure thermal expands as its own pressure pushes the surrounding lower-pressure air. As the high-pressure thermal at the center of an anticyclone sinks, the surrounding air pressure at lower elevations increases in accord with the law of atmospheres. Therefore, the high-pressure thermal contracts as the surrounding high-pressure air compresses the sinking thermal. In summary, a cyclone is the weather pattern around a low-pressure thermal, where winds blow inward while circulating counterclockwise in the northern hemisphere and clockwise in the southern hemisphere; the low-pressure thermal then rises to higher elevations and expands. Conversely, an anticyclone is the weather pattern around a high-pressure thermal that sinks to lower elevations and contracts, then the winds blow outward while circulating clockwise in the northern hemisphere and counterclockwise in the southern hemisphere.

The most obvious way to change the temperature of a gas is through the addition or extraction of heat. If we add heat to a gas, we expect it to become warmer; if we extract heat from a gas, we expect it to become cooler. However, it is possible to change the temperature of a gas without adding or extracting heat. If a gas expands, it must become cooler even if no heat was extracted. This is because the expanding gas must push the surrounding gas. This requires work, and work is a form of energy. The gas extracts this energy from its own internal energy content, and so the gas becomes cooler. Conversely if a gas contracts, it must become warmer even if no heat was added. This is because the surrounding gas performs work on the gas while compressing the gas. This work is added to the internal energy content of the gas, and so the gas becomes warmer. This is remarkable; we can actually change the temperature of a gas without adding or extracting any heat. We can demonstrate this by performing all of these experiments while the gas is wrapped within a thermal insulator, which will not permit any heat to be added or extracted. Nevertheless, the gas becomes warmer when we compress it, and the gas becomes cooler when we expand it. We are forced to conclude that heat and temperature are two completely different physical concepts. Most people naïvely believe that heat and temperature are essentially the same thing. After all, when we add heat to an object it often becomes warmer, and when we extract heat from an object it often becomes cooler. Nevertheless, we have just discussed circumstances where we can actually change the temperature of a gas without the addition or extraction of any heat. In fact, it is possible for a gas to become warmer under certain circumstances when we have extracted heat from the gas! It is also possible for a gas to become cooler under certain circumstances when we have added heat to the gas! These extraordinary examples persuade us that heat and temperature are indeed two completely different physical concepts. Therefore, we must use different terms to describe one process where there is no temperature change and another process where there is no heat exchanged, since heat and temperature are two completely different physical concepts. A process where there is no temperature change is called an isothermal process. A process where there is no heat exchanged is called an adiabatic process. These are two different processes. Simply because a process is adiabatic (no heat exchanged) does not mean that it is necessarily isothermal (no temperature change). Simply because a process is isothermal (no temperature change) does not mean that it is necessarily adiabatic (no heat exchanged). We just discussed two examples of adiabatic processes that are not isothermal. A gas that expands adiabatically (no heat exchanged) becomes cooler; since the temperature is changing, this is not an isothermal process. A gas that contracts adiabatically (no heat exchanged) becomes warmer; since the temperature is changing, this is not an isothermal process either. These are two examples of processes that are adiabatic yet not isothermal, meaning the temperature changes even though no heat was exchanged. There are other examples of processes that are isothermal yet not adiabatic, meaning heat was exchanged even though the temperature did not change. Obviously, there are processes that are neither adiabatic nor isothermal. Also note that a process where there is no pressure change is called an isobaric process.

Air is a poor conductor of heat. A spectacular illustration of the poor conduction of heat through air is the moderate heat we feel from the intense temperature of charcoal during a barbecue. When a piece of charcoal begins glowing red, its temperature is a couple thousand degrees! Yet, we can place our hand within just a few inches of the charcoal; although we feel moderate heat, our hand is not in danger from the extreme temperature of the charcoal. How can our hand be within a few inches of an object at a couple thousand degrees of temperature and yet not be in any danger? We conclude that the air between our hand and the hot charcoal is a poor conductor of heat. Since air is such a poor conductor of heat, we always assume thermals in the Earth’s atmosphere neither gain heat from their surroundings nor lose heat to their surroundings. That is, we always assume thermals in the Earth’s atmosphere do not exchange heat with their surroundings. This is called the adiabatic approximation, since an adiabatic process involves no exchange of heat. Of course, thermals do exchange some heat with their surroundings, but air is such a poor conductor of heat we can ignore the small amounts of heat that are exchanged between a thermal and its surroundings. In other words, the adiabatic approximation is an excellent approximation for analyzing most meteorological processes. As we discussed, the air at the center of a cyclone rises and expands. As an excellent approximation, the rising thermal expands adiabatically, by the adiabatic approximation. If the thermal expands adiabatically, then it must cool. As we discussed, the air at the center of an anticyclone sinks and contracts. As an excellent approximation, the sinking thermal contracts adiabatically, by the adiabatic approximation. If the thermal contracts adiabatically, then it must warm. In summary, a cyclone is the weather pattern around a low-pressure thermal where winds blow inward while circulating counterclockwise in the northern hemisphere and clockwise in the southern hemisphere; the low-pressure thermal then rises, expands adiabatically, and cools. Conversely, an anticyclone is the weather pattern around a high-pressure thermal that sinks, contracts adiabatically, and warms, then the winds blow outward while circulating clockwise in the northern hemisphere and counterclockwise in the southern hemisphere.

The low-pressure air at the center of a cyclone rises, expands adiabatically, and cools, but cold air is at a high pressure. We conclude that low-pressure air at lower elevations in the troposphere transitions to high-pressure air at higher elevations in the troposphere. In brief, low-pressure air near mean sea level becomes high-pressure air aloft. The word aloft simply means up toward the sky. The loft of a house is the highest room in the house (often the attic), the choir loft of a church is high above the pews, and lofty dreams are high goals. If winds blow inward toward low air pressure near mean sea level, these winds must eventually blow outward from the high air pressure aloft. This circulation of air is a necessary feature of convection, as we discussed earlier in the course. Cyclones may initially form from low air pressure at lower elevations in the troposphere (near mean sea level) or from high air pressure at higher elevations in the troposphere (aloft), but generally cyclones initially form from both occurring in conjunction with each other, from the appropriate vertical motion of air throughout the troposphere. Similarly, we conclude that high-pressure air at lower elevations in the troposphere transitions to low-pressure air at higher elevations in the troposphere. In brief, high-pressure air near mean sea level becomes low-pressure air aloft. If winds blow outward from high air pressure near mean sea level, these winds must blow inward toward the low air pressure aloft. Again, this circulation of air is a necessary feature of convection, as we discussed earlier in the course. Anticyclones may initially form from high air pressure at lower elevations in the troposphere (near mean sea level) or from low air pressure at higher elevations in the troposphere (aloft), but generally anticyclones initially form from both occurring in conjunction with each other, from the appropriate vertical motion of air throughout troposphere.

Relative humidity is a concept that everyone believes that they understand, but in actuality almost no one correctly understands this concept of relative humidity. Most people believe that the relative humidity of air is the amount of moisture in the air. This is such a gross simplification of the correct definition of relative humidity that it is actually an incorrect understanding. Firstly, air is only able to hold a maximum amount of moisture. We may demonstrate this with the following experiment. We place a lid upon a cup of water; a simple piece of paper will serve as a satisfactory lid. Liquid water continuously evaporates into water vapor, but the lid will confine the water vapor to the trapped air between the lid and the liquid water. When this confined air holds the maximum amount of water vapor that it is able to hold, some of the water vapor must condense back into liquid water so that additional liquid water may evaporate into water vapor. Some of this water will condense back into the liquid within the cup, but some of this water will condense into drops of liquid water on the sides of the cup and even underneath the lid. When the air holds the maximum amount of moisture that it is able to hold, the air is said to be saturated. To saturate anything means to fill it to capacity; the air is saturated when it holds the maximum moisture that it is able to hold. The saturation amount of air is itself a function of temperature. Warm air has a greater saturation amount since warm air is able to hold a greater quantity of moisture, while cold air has a lesser saturation amount since cold air is not able to hold as much moisture as warm air. The strict definition of the relative humidity of air is the amount of moisture in the air as a fraction of the saturation amount at the given temperature. Let us devote some time to carefully understand this definition. Firstly, the relative humidity of air is directly related to the amount of moisture in the air. Adding moisture to air increases the relative humidity, while subtracting moisture from air decreases the relative humidity. However, it is possible to change the relative humidity of air without adding or subtracting water. By simply changing the temperature of the air, we change the saturation amount of the air and thus we change the fraction of the moisture to the new saturation amount. If air becomes warmer, the saturation amount is greater, making the amount of moisture that is actually within the air a smaller fraction of that greater saturation amount. In other words, warming air decreases its relative humidity. If air becomes colder, the saturation amount is lesser, making the amount of moisture that is actually within the air a greater fraction of that lesser saturation amount. In other words, cooling air increases its relative humidity. An analogy would be helpful to understand these processes. Imagine a large bucket and a small cup. A large bucket is able to hold a large amount of water, while a small cup is only able to hold a small amount of water. The large bucket is analogous to hot air, since hot air has a large saturation amount, meaning it is able to hold more moisture. The small cup is analogous to cold air, since cold air has a small saturation amount, meaning it is not able to hold as much moisture as hot air. Now suppose the small cup is mostly full. If we pour this water into a large empty bucket, the large bucket will be mostly empty. If we take a large bucket that is mostly empty and pour this water into a small cup, the small cup will be mostly full. This is remarkable: it is the same amount of water in the small cup and the large bucket. Nevertheless, this same amount of water makes the small cup mostly full and makes the large bucket mostly empty. We always keep in mind that the small cup is analogous to cold air and the large bucket is analogous to hot air. If we take cold air and warm it, this decreases the relative humidity, since this is analogous to taking a small cup that is more full and pouring its water into a large bucket that will now be more empty. If we take warm air and cool it, this increases the relative humidity, since this is analogous to taking a large bucket that is more empty and pouring its water into a small cup that will now be more full. This is remarkable: we have not changed the amount of moisture in the thermal. We are changing its relative humidity without adding or extracting water; we are changing its relative humidity by changing its temperature. We now realize that regarding relative humidity as simply the amount of moisture in the air is a grossly incorrect understanding of relative humidity. As another remarkable example, consider two thermals both at fifty percent relative humidity. Does this mean they hold the same amount of moisture? Isn’t fifty percent equal to one-half? Therefore, are not both thermals holding moisture equal to half of their respective saturation amounts? This is certainly true, but two thermals will almost always have two different temperatures. The hotter thermal has a greater saturation amount, while the colder thermal has a lesser saturation amount. Half of a greater amount is a larger number, and half of a lesser amount is a smaller number. Thus, the warmer thermal actually holds more moisture and the cooler thermal actually holds less moisture, even though both thermals have the same relative humidity! This is analogous to a large bucket and a small cup that are both half full. The large bucket holds more water and the small cup holds less water, even though both are half full! We always keep in mind that the small cup is analogous to cold air and the large bucket is analogous to hot air. If a large bucket and a small cup are both half full and yet the large bucket holds more water and the small cup holds less water, we conclude that two thermals both at fifty percent relative humidity hold different quantities of moisture. The warmer thermal holds more moisture (analogous to the large bucket), while the cooler thermal holds less moisture (analogous to the small cup). As an extreme example, consider two thermals: one at ninety percent relative humidity and the other at ten percent relative humidity. Which thermal holds more moisture, and which thermal holds less moisture? We are tempted to conclude that surely it must be the ninety-percent humid thermal that holds more moisture, and we are tempted to conclude that surely it must be the ten-percent humid thermal that holds less moisture. In actuality, we cannot draw any conclusions about the moistures of the two thermals without knowing their temperatures. Again, we imagine a large bucket and a small cup. Suppose the large bucket is only ten-percent full, while the small cup is ninety-percent full. Nevertheless, suppose the large bucket is so large that it still holds more water at ten-percent capacity than the small cup at ninety-percent capacity. We always keep in mind that the small cup is analogous to cold air and the large bucket is analogous to hot air. Suppose we have two thermals: one at ninety percent relative humidity and the other at ten percent relative humidity. Now suppose that the ten-percent-humid thermal is so warm that its saturation amount is so large that ten percent of that large saturation is nevertheless more moisture than the ninety-percent-humid cold thermal. Therefore, it is possible for a ten-percent-humid thermal to hold more moisture than a ninety-percent-humid thermal if the ten-percent-humid thermal is sufficiently warm and if the ninety-percent-humid thermal is sufficiently cold.

Since warming air decreases the relative humidity, the least humid time of the day is typically in the late afternoon before sunset, since the Sun has spent the entire daytime warming the air. Since cooling air increases the relative humidity, the most humid time of the day is typically in the very early morning hours before sunrise, since the air has spent the entire nighttime cooling in the darkness. Just before sunrise, the air may have cooled sufficiently for the relative humidity to increase to one hundred percent. That is, the air has become saturated with water vapor. At one hundred percent relative humidity (saturation), water vapor must condense into liquid water so that additional liquid water may evaporate. The temperature to which we must cool air until it becomes saturated is called the dew point, since the water vapor that condenses into liquid water is called dew. In the early morning, we may see the leaves of trees and the surface of our car covered with water as if it had rained overnight. In actuality, it became sufficiently cold overnight that the dew point was achieved. The air became saturated, and water vapor began condensing into liquid water. Even in the summertime, the nighttime air may become sufficiently cold that the dew point is achieved, thus forming dew.

Condensation is the changing of state from water vapor to liquid water. The condensing water must liberate heat to its surroundings to condense; this liberated heat warms the surroundings. Therefore, condensation is a warming process. Evaporation is the changing of state from liquid water to water vapor. The evaporating water must extract heat from its surroundings to evaporate; this extracted heat cools the surroundings. Therefore, evaporation is a cooling process. This is why we feel chilly immediately after taking a shower. Our bodies are covered with water that evaporates; the evaporating water extracts the heat needed for that evaporation from our bodies, thus cooling our bodies. Drying our bodies with a towel removes water that would have evaporated; this is why we feel less chilly whenever we dry ourselves with a towel. This is also why humans and some animals perspire (sweat). The act of perspiring (sweating) covers our bodies with water that evaporates; the evaporating water extracts the heat needed for that evaporation from our bodies, thus cooling our bodies. Suppose the surrounding air is very humid, perhaps close to saturation. Some of the water vapor in the air must condense to liquid water so that additional liquid water may evaporate. Whereas perspiration (sweat) on our skin may evaporate which cools our bodies since evaporation is a cooling process, some water vapor in the surrounding air condenses to liquid water onto our skin, adding heat back to our bodies since condensation is a warming process. In this case, our bodies cannot cool effectively, and we feel uncomfortable. As a result, humid air feels warmer than its actual temperature. We can convert this discomfort into an effective air temperature that is warmer than the actual air temperature. This effective air temperature is called the heat stress index (or the heat index for short). For example, a meteorologist may report in the summertime that the actual temperature today will be ninety degrees fahrenheit, but it will feel like ninety-five degrees fahrenheit. The ninety degrees fahrenheit is the true air temperature, while the ninety-five degrees fahrenheit is the heat stress index (or simply the heat index). In the wintertime, wind makes the air feel colder than its actual temperature. We can convert this discomfort into another effective air temperature that is colder than the actual air temperature. This effective air temperature is called the windchill. For example, a meteorologist may report in the wintertime that the actual temperature today will be thirty-five degrees fahrenheit, but it will feel like twenty-five degrees fahrenheit. The thirty-five degrees fahrenheit is the true air temperature, while the twenty-five degrees fahrenheit is the windchill. We may use all of these principles to construct a hygrometer, a device that measures the relative humidity of the air. A hygrometer is simply two thermometers. One thermometer is wrapped in a wet cloth; this is called the wet-bulb of the hygrometer. The other thermometer that is not wrapped in a wet cloth is called the dry-bulb of the hygrometer. Water will evaporate from the wet-bulb thermometer. Since evaporation requires heat, the evaporating water will extract heat from the wet-bulb thermometer, giving it a colder temperature than the dry-bulb thermometer. Again, evaporation is a cooling process. From the difference in temperature between the wet-bulb of the hygrometer and the dry-bulb of the hygrometer, we can calculate the relative humidity of the air.

We now apply everything we have discussed about relative humidity to cyclones and anticyclones. As we discussed, the low-pressure, low-density thermal at the center of a cyclone rises, expands adiabatically, and cools. Since it cools, its relative humidity increases. As we also discussed, the high-pressure, high-density thermal at the center of an anticyclone sinks, contracts adiabatically, and warms. Since it warms, its relative humidity decreases. In summary, the thermal at the center of a cyclone becomes more humid as it rises, while the thermal at the center of an anticyclone becomes less humid (or more dry) as it sinks. If the thermal at the center of a cyclone becomes more humid as it rises, the dew point could be achieved, causing water vapor to condense into liquid water. However, even if the dew point is achieved, water vapor cannot condense into liquid water in midair. The liquid water requires a surface upon which to condense, such as the surface of the leaves of trees or the surface of our car. Fortunately, the atmosphere is not just air; there are tiny pieces of dust and silt and salt in the atmosphere. When the dew point is achieved, the water vapor can condense into liquid water around these tiny pieces of dust and silt and salt, forming a microscopic drop of water around each tiny piece of dust or silt or salt. For this reason, this tiny piece of dust or silt or salt is called a condensation nucleus, since it is at the center of the microscopic drop of water. The center of anything is called its nucleus. For example, the center of a biological cell is called the cellular nucleus, the center of an atom is called the atomic nucleus, and the center of an entire galaxy is called the galactic nucleus. If the dew point is achieved causing water vapor to condense into microscopic drops of water around these condensation nuclei, the thermal becomes opaque. Ordinarily, air is transparent, as we know from our daily experience. Almost every second of every day of our lives, we effortlessly see through the air around us, since air is ordinarily transparent. However, liquid water is opaque. Actually, a small quantity of liquid water is transparent; we can see through a glass of water for example. However, larger and larger quantities of liquid water become less and less transparent and more and more opaque. It is rather difficult seeing through a fish tank for example, and it is hopeless trying to see through the ocean to the seafloor. Therefore, when the dew point is achieved causing water vapor to condense into liquid water, the thermal does indeed become opaque. We can no longer see through the air; the thermal has turned from invisible to visible. This is so remarkable that the thermal deserves a special name. A thermal that has achieved the dew point causing its water vapor to condense into liquid water and thus the thermal has turned from transparent to opaque (from invisible to visible) is called a cloud. We conclude that clouds form when thermals rise, expand adiabatically, cool, and become more humid until the dew point is achieved. This dew point is a specific temperature. Therefore, thermals must be lifted to a specific elevation to cool to the dew point. This elevation is called the lifting condensation level (or the condensation level for short). We can almost always see the lifting condensation level (or simply the condensation level) with our own eyes, since clouds often have flat bottoms. This flat bottom is the lifting condensation level (or simply the condensation level). Below this elevation, the dew point has not been achieved, and the thermals are still transparent (invisible). Above this elevation, the dew point has been achieved, and the thermals are opaque (visible) clouds.

We can categorize clouds into three broad types: cumulus clouds, cirrus clouds, and stratus clouds. Cumulus clouds have the appearance of cauliflower or puffs of cotton. Cirrus clouds have the appearance of individual wisps or feathers. Finally, if there are so many clouds in the sky that they all blend together to form one giant layer of cloud covering the entire sky, this is a stratus cloud. The word stratus is derived from a Latin word meaning layer. As we discussed, the word stratify (meaning layered) is derived from the same Latin word. The word stratum (a layer of sedimentary rock) also derives from the same Latin word, as we discussed earlier in the course. Note that there are other cloud types in addition to these three. For example, many cirrus clouds that seem to almost blend together into one giant layer of cloud covering the entire sky is called a cirrostratus cloud, meaning intermediate between cirrus clouds and stratus clouds. As another example, many cumulus clouds that seem to almost blend together into one giant layer of cloud covering the entire sky is called a stratocumulus cloud, meaning intermediate between cumulus clouds and stratus clouds. If it is precipitating (raining or snowing) out of a cumulus cloud, then it is called a cumulonimbus cloud. If it is precipitating (raining or snowing) out of a stratus cloud, then it is called a nimbostratus cloud. If the air becomes sufficiently cold that it achieves the dew point without having to be pushed up to higher elevations, a cloud will form at or near the ground. This type of cloud is called fog.

We have already discussed enough meteorology to somewhat reliably predict weather over a timescale of a few hours using only a barometer. The rising or the falling of the air pressure as indicated by the barometer is called the barometric tendency. If the barometric tendency is falling, then low-pressure, low-density thermals must be rising, expanding adiabatically, cooling, and becoming more humid. The relative humidity may increase sufficiently for the dew point to be achieved, forming clouds and perhaps even precipitation (rain or snow). Conversely, if the barometric tendency is rising, then high-pressure, high-density thermals must be sinking, contracting adiabatically, warming, and becoming less humid. The relative humidity may decrease sufficiently for liquid water to evaporate back into water vapor. In other words, thermals will turn from opaque (visible) clouds to transparent (invisible) air; we will have a clear day. In summary, a falling barometric tendency is an indication of what is commonly considered to be bad weather, while a rising barometric tendency is an indication of what is commonly considered to be good weather.

The rate at which a rising thermal cools before it becomes a cloud is called the dry adiabatic rate of cooling (or the dry adiabatic rate for short). The rate at which a rising thermal cools after it becomes a cloud is called the wet adiabatic rate of cooling (or the wet adiabatic rate for short). A thermal becomes a cloud when water vapor condenses into liquid water. This liberates heat, thus making the thermal warmer. Again, condensation is a warming process. Therefore, the wet adiabatic rate of cooling is always more shallow than the dry adiabatic rate of cooling. That is, the dry adiabatic rate of cooling is always more steep than the wet adiabatic rate of cooling. The rate at which the surrounding atmosphere cools with rising elevation is called the environmental lapse rate of cooling (or the environmental lapse rate for short). Suppose the environmental lapse rate is more shallow than the wet adiabatic rate which itself must be more shallow than the dry adiabatic rate. In other words, both adiabatic rates are more steep than the environmental lapse rate. In this case, either before or after a thermal becomes a cloud, its rate of cooling is very steep. The rate of cooling of the thermal may be sufficiently steep that the thermal becomes so cold and so dense that it is forced to sink to lower elevations. This is called absolute stability, and what is commonly considered to be bad weather such as clouds or precipitation (rain or snow) will be less likely. Conversely, suppose the environmental lapse rate is steeper than the dry adiabatic rate which itself must be steeper than the wet adiabatic rate. In other words, both adiabatic rates are more shallow than the environmental lapse rate. In this case, either before or after a thermal becomes a cloud, its rate of cooling is shallow. Thermals will probably not cool sufficiently to become dense enough to sink to lower elevations. In other words, thermals are more likely to rise to higher elevations. This is called absolute instability, and what is commonly considered to be bad weather such as clouds and perhaps even precipitation (rain or snow) will be more likely. It is also possible for the environmental lapse rate to be steeper than the wet adiabatic rate but more shallow than the dry adiabatic rate. In this case, a thermal before it becomes a cloud may cool to attain sufficiently high density to sink, resulting in what is commonly considered to be good weather. However, if the thermal reaches the lifting condensation level and becomes a cloud, its rate of cooling slows. Hence, the thermal will continue to rise, resulting in what is commonly considered to be bad weather. This is called conditional instability, and either good weather or bad weather may result under these circumstances.

Our discussion leads us to conclude that weather is strongly determined by lifting, the rising of thermals. There are three mechanisms that could cause lifting: orographic lifting, convergence lifting, and frontal wedging. Orographic lifting is caused by mountains pushing air aloft. This term is derived from the Greek root oro- for mountain, as we discussed earlier in the course. When winds encounter a mountain, much of the air blows up over the mountain. As the air rises, it expands adiabatically, cools, and becomes more humid. If the dew point is achieved, clouds form, and precipitation may occur. Therefore, we expect a humid climate on the windward side of a mountain range. The windward side of anything is the side that faces the wind. The opposite of the windward side of anything is its leeward side, which faces away from the wind. The adjective leeward is derived from the noun lee, which means shelter. For example, the lee of a building or the lee of a rock faces away from the wind and hence provides shelter from the wind. On the leeward side of a mountain range, air sinks, contracts adiabatically, warms, and becomes less humid. Therefore, we expect an arid (dry) climate on the leeward side of a mountain range. Actually, we expect an arid (dry) climate for an additional reason: any moisture that was in the air probably precipitated out of the air on the windward side of the mountain range. With moisture subtracted and in addition warming temperatures from sinking air, we expect an extremely arid (dry) climate on the leeward side of mountain ranges. These are called rainshadow deserts. For example, the contiguous United States is at the midlatitudes, and the prevailing winds at the midlatitudes blow from the west, as we will discuss shortly. Therefore, the west side of the Rocky Mountains is its windward side, while the east side of the Rocky Mountains is its leeward side. The leeward side (the east side) of the Rocky Mountains is the Great Plains of the United States, which is a rainshadow desert. Although there is agriculture in the Great Plains, the soil is not as productive as the farmland of the midwestern United States, which is further east of the Great Plains. Convergence lifting is caused by crowded winds pushing air aloft. Consider an island or a peninsula surrounded on many sides by water. Every day, sea breezes will blow from the surrounding waters toward the island or peninsula, as we discussed. These breezes become crowded and thus push each other upward. As the air rises, it expands adiabatically, cools, and becomes more humid. If the dew point is achieved, clouds form, and precipitation may occur. Therefore, we expect islands and peninsulas to have humid climates. Actually, we expect the climate to be extremely humid, since the winds originally came from the surrounding waters, where evaporation added significant moisture to the sea breezes. With moisture added and in addition cooling temperatures from rising air, we expect extremely humid climates on islands and peninsulas. For example, Florida is a peninsula in the southeastern United States. Every day, a sea breeze blows from the Gulf of America (the Gulf of Mexico) from the west towards Florida. Every day, a sea breeze blows from the Atlantic Ocean from the east towards Florida. Every day, a sea breeze blows from the Caribbean Sea from the south towards Florida. These sea breezes were already humid, since they came from bodies of water where evaporation added moisture to the winds. In addition, these sea breezes become crowded over Florida and thus push each other upward. The air rises, expands adiabatically, cools, and becomes even more humid. The dew point is achieved, clouds form, and rain occurs. This explains why Florida has an extremely humid climate. In fact, the entire peninsula is infested with amphibians and reptiles as a result of this extreme humidity. Frontal wedging is caused by one air mass pushing another air mass aloft. This is the most important type of lifting that determines weather patterns, as we will discuss shortly.

The lightest type of liquid precipitation is called mist. Heavier than mist is drizzle, and the heaviest liquid precipitation is called rain. The lightest freezing precipitation is called snow. Heavier than snow is freezing drizzle. Heavier than freezing drizzle is called sleet. Even heavier than sleet is called graupel, and hail is the heaviest freezing precipitation. Hail is quite dangerous; many people have been killed from falling hail. Snow is very light because it is composed of individual snowflakes, which are themselves composed of mostly air. Since clouds form aloft (at higher elevations) in the troposphere where the air temperature is colder, precipitation almost always begins in the frozen state, such as snow or sleet. On its way down to lower elevations, the precipitation warms and melts into liquid precipitation such as rain. This is usually the case even in the summertime; warm rain in the summertime most likely began as snow or sleet from clouds at higher elevations in the troposphere that melted into rain on its way down toward lower elevations in the troposphere. We can personally experience this extreme temperature difference between the lower troposphere and the upper troposphere with a sufficiently tall mountain. As we climb the mountain, the air temperature becomes colder and colder until we reach the summit of the mountain, where it may be so cold that it is snowing. This is usually the case even in the summertime. The air temperature at the bottom of the mountain may be quite hot in the summertime. Nevertheless, the air temperature becomes colder and colder as we climb the mountain until (if the mountain is sufficiently tall) the air temperature is so cold that it is snowing at the summit of the mountain, even in summertime when the base of the mountain is still quite hot!

Global (Large-Scale) Meteorological Dynamics

The Coriolis force caused by the Earth’s rotation causes the global circulation of air in the atmosphere to be complex. In order to emphasize the complications caused by the rotation of the Earth, let us first suppose that the Earth were not rotating. In this case, the global circulation of air in the atmosphere would be simple. Since the equator is hot throughout the entire year, the air at the equator is at low pressure. Since the poles are cold throughout the entire year, the air at the poles is at high pressure. The pressure gradient force would then push air from high pressure at the poles toward low pressure at the equator. The result is that winds would blow from the north in the northern hemisphere and from the south in the southern hemisphere. Since we always name wind based on the direction it is blowing from, the winds in the northern hemisphere would be a north wind, while winds in the southern hemisphere would be a south wind. These are known as the prevailing winds. Caution: wind does not always blow in the directions of these prevailing winds; variations in pressure may cause winds to blow in various different directions. The prevailing winds are the directions in which the wind generally or usually blows, not the directions in which the wind always blows. If the Earth were not rotating, winds in the northern hemisphere would generally or usually be a north wind from the north pole toward the equator, and winds in the southern hemisphere would generally or usually be a south wind from the south pole toward the equator. At the equator, the low-pressure, low-density air would rise, becoming high pressure aloft. The high pressure at the poles is low pressure aloft. Again, the pressure gradient force pushes air from high pressure toward low pressure. Hence, the pressure gradient force would push the risen air at the equator toward the poles, where the air would sink until the pressure gradient force pushes the air back toward the equator. This overall motion is called a circulation cell. Notice there would be only one circulation cell in each hemisphere if the Earth were not rotating. This discussion completely summarizes the global circulation of air in the atmosphere if the Earth were not rotating.

Of course, the Earth is rotating, causing a Coriolis force and hence tremendous complications to the simplistic model we have just presented. The low-pressure, low-density air still rises at the equator, and the pressure gradient force still pushes this risen air toward the poles. However, by the time the air reaches roughly thirty degrees latitude in each hemisphere, the air has cooled sufficiently to sink. The pressure gradient force then pushes this air back toward the equator, completing the tropical circulation cells. However, the Coriolis force causes rightward deflections in the northern hemisphere and leftward deflections in the southern hemisphere. The net result of the pressure gradient force together with the Coriolis force is that the prevailing winds (near mean sea level) from roughly 30°N latitude to 0° latitude (the equator) blow from the northeast; these are called the northeast trade winds, since we always name wind based on the direction it is blowing from. The prevailing winds (near mean sea level) from roughly 30°S latitude to 0° latitude (the equator) blow from the southeast; these are called the southeast trade winds, since we always name wind based on the direction it is blowing from. The term trade wind is used since these winds facilitated trade between the Old World and the New World by pushing sailing ships across the Atlantic Ocean from Europe and Africa toward North America and South America. The high-pressure, high-density air still sinks at the poles, and the pressure gradient force still pushes this air toward the equator. However, by the time the air reaches roughly sixty degrees latitude in each hemisphere, the air has warmed sufficiently to rise. The pressure gradient force still pushes this risen air toward the poles where it sinks, completing the polar circulation cells. However, the Coriolis force causes rightward deflections in the northern hemisphere and leftward deflections in the southern hemisphere. The net result of the pressure gradient force together with the Coriolis force is that the prevailing winds (near mean sea level) from 90°N latitude (the north pole) to roughly 60°N latitude blow from the northeast; these are called the polar northeasterlies, since we always name wind based on the direction it is blowing from. The prevailing winds (near mean sea level) from 90°S latitude (the south pole) to roughly 60°S latitude blow from the southeast; these are called the polar southeasterlies, since we always name wind based on the direction it is blowing from. Notice that air sinks at roughly thirty degrees latitude in each hemisphere, while air rises at roughly sixty degrees latitude in each hemisphere. Sinking air is high-density, high-pressure air, while rising air is low-density, low-pressure air. Therefore, we have high pressure at roughly thirty degrees latitude in each hemisphere, and we have low pressure at roughly sixty degrees latitude in each hemisphere. The pressure gradient force pushes air from high pressure toward low pressure. Hence, wind will blow from roughly thirty degrees latitude to roughly sixty degrees latitude in each hemisphere, where the air rises and is pushed back to thirty degrees latitude where it sinks, completing the midlatitude circulation cells. However, the Coriolis force causes rightward deflections in the northern hemisphere and leftward deflections in the southern hemisphere. The net result of the pressure gradient force together with the Coriolis force is that the prevailing winds (near mean sea level) from roughly 30°N latitude to roughly 60°N latitude blow from the southwest; these are called the southwesterlies, since we always name wind based on the direction it is blowing from. The prevailing winds (near mean sea level) from roughly 30°S latitude to roughly 60°S latitude blow from the northwest; these are called the northwesterlies, since we always name wind based on the direction it is blowing from. To summarize, there are three prevailing winds in each hemisphere, and there are three circulation cells in each hemisphere. In the northern hemisphere, the prevailing winds (near mean sea level) are the northeast trade winds near the equator, the southwesterlies at the midlatitudes, and the polar northeasterlies near the north pole. In the southern hemisphere, the prevailing winds (near mean sea level) are the southeast trade winds near the equator, the northwesterlies at the midlatitudes, and the polar southeasterlies near the south pole. The circulation cells are called the two Hadley cells (one in each hemisphere) near equator, named for the British meteorologist George Hadley, the two Ferrel cells (one in each hemisphere) at the midlatitudes, named for the American meteorologist William Ferrel, and the two polar cells (one in each hemisphere) near the poles. If the Earth rotated faster, the Coriolis force would be stronger, thus causing more prevailing winds and more circulation cells in each hemisphere. If the Earth rotated slower, the Coriolis force would be weaker, thus causing fewer prevailing winds and fewer circulation cells in each hemisphere. If the Earth stopped rotating, the Coriolis force would vanish, and there would be only one prevailing wind and only one circulation cell in each hemisphere, as we discussed with our simplistic non-rotating model. A spectacular example of the effects of a strong Coriolis force on the global circulation of air is the planet Jupiter, which rotates more than twice as fast as the Earth. In fact, Jupiter is the fastest rotating planet in the Solar System. Therefore, Jupiter has the strongest Coriolis force out of all the planets in the Solar System. This very strong Coriolis force has divided Jupiter’s atmosphere into many prevailing winds and many circulation cells. We can actually see these winds in photographs of Jupiter. We can even see these winds if we look at Jupiter with our own eyes through a sufficiently powerful telescope.

At the equator, there is little to no wind, since the air is rising; this is called the equatorial low, since low-pressure, low-density air rises. This rising air expands adiabatically, cools, and becomes more humid. The dew point may be achieved, forming clouds and rain. Indeed, there is a perpetual band of clouds at the equator, and the perpetual rain from these clouds causes tropical rainforests at and near the equator, such as the Amazon rainforest in northern South America, the Congo rainforest in central Africa, and the Indonesian rainforests. Sailing ships that found themselves at the equatorial low would become stuck, since there are no winds to push ships. For this reason, the equatorial low is also called the doldrums. Sailors would pray that their ship happens to drift slightly to the north or slightly to the south to catch one of the trade winds that would push them again. At least the sailors could drink the perpetual rainwater while stuck at the equatorial low (the doldrums). As we discussed earlier in the course, the lack of wind at the equatorial low permits the oceanic equatorial countercurrents to flow virtually unhindered against the direction of other oceanic surface currents near the equator. At roughly thirty degrees latitude in both hemispheres, there is also little to no wind, but for the opposite reason. The air is sinking; these are called the subtropical highs, since high-pressure, high-density air sinks. This sinking air contracts adiabatically, warms, and becomes less humid (more dry). Hence, we do not have clouds or rain. Indeed, there is a perpetual band of clear skies free of clouds at roughly thirty degrees latitude in both hemispheres. The perpetual lack of rain causes hot deserts at and near roughly thirty degrees latitude in both hemispheres. At roughly thirty degrees north latitude, we have the Basin and Range in southwestern United States and northwestern Mexico (including the Mojave Desert, the Sonoran Desert, and the Chihuahuan Desert), the Sahara in northern Africa, the Great Middle Eastern Desert (including the Arabian Desert, the Syrian Desert, and the Persian Desert), and the Gobi in China and Mongolia. At roughly thirty degrees south latitude, we have the Patagonian Desert in Argentina, the Kalahari in southern Africa, and the Great Australian Desert (including the Great Victoria Desert, the Great Sandy Desert, the Tanami Desert, the Simpson Desert, and the Gibson Desert). Sailing ships that found themselves at the subtropical high in either hemisphere would become stuck, since there are no winds to push ships. There would also be no rain for the sailors to drink. Therefore, not only would sailors pray that their ship happens to drift slightly to the north or slightly to the south to catch prevailing winds that would push them again, but the sailors would also kill their horses to stretch out their limited supply of drinking water. For this reason, the subtropical highs are also called the horse latitudes. At roughly sixty degrees latitude in both hemispheres, there is little to no wind, since the air is rising; these are called the subpolar lows, since low-pressure, low-density air rises. This rising air expands adiabatically, cools, and becomes more humid. The dew point may be achieved, forming clouds and rain. Indeed, there is a perpetual band of clouds at roughly sixty degrees latitude in both hemispheres, and the perpetual rain from these clouds causes boreal forests (cold forests or taigas) at and near roughly sixty degrees north latitude, including the Canadian boreal forests, the Scandinavian boreal forests, and the Russian boreal forests. Theoretically, there would be boreal forests (cold forests or taigas) at and near roughly sixty degrees south latitude if there were land at these latitudes. At the poles, there is also little to no wind since the air is sinking; these are called the polar highs, since high-pressure, high-density air sinks. This sinking air contracts adiabatically, warms, and becomes less humid (more dry). Hence, we do not have clouds or rain. Indeed, there is a perpetual area free of clouds at and near the poles in both hemispheres. To summarize, we have the equatorial low (the doldrums) at the equator, we have the subtropical highs (the horse latitudes) at roughly thirty degrees latitude in both hemispheres, we have the subpolar lows at roughly sixty degrees latitude in both hemispheres, and we have the polar highs at ninety degrees latitude in both hemispheres. At the lows, we have rising air, causing humid climates from perpetual clouds and rain. At the highs, we have sinking air, causing arid (dry) climates from the perpetual absence of clouds and rain. Actually, we expect arid climates at the highs for an additional reason: any moisture that was in the air precipitated out of the rising air at the equatorial low and at both subpolar lows before being pushed toward the highs where the air sinks. With moisture subtracted and in addition warming temperatures from sinking air, we expect extremely arid (dry) climates at both subtropical highs and at both polar highs.

An air mass is an enormous mass of air that has roughly the same temperature and pressure throughout its volume at a given elevation. We can classify air masses based on their temperature. An air mass that forms near the equator will be warm; these are called tropical air masses, which we label with the uppercase (capital) letter T for tropical. An air mass that forms near the poles will be cold; these are called polar air masses, which we label with the uppercase (capital) letter P for polar. We can also classify air masses based on their moisture. An air mass that forms over the ocean or any body of water will be humid, since evaporating water will add moisture to the air mass; these are called maritime air masses, which we label with the lowercase letter m for maritime. An air mass that forms over a continent will be dry, since there is little water on the continent to evaporate to add moisture to the air mass; these are called continental air masses, which we label with the lowercase letter c for continental. To summarize, there are four different types of air masses. An air mass that forms over a body of water near the equator will be humid and warm; these are called maritime tropical air masses, which we label with the symbol mT. An air mass that forms over a body of water near the poles will be humid and cold; these are called maritime polar air masses, which we label with the symbol mP. An air mass that forms over a continent near the equator will be dry and warm; these are called continental tropical air masses, which we label with the symbol cT. Finally, an air mass that forms over a continent near the poles will be dry and cold; these are called continental polar air masses, which we label with the symbol cP. We must emphasize that once an air mass is born of a certain type, it does not remain that type permanently. In other words, the particular type of an air mass can change. For example, an air mass that forms near the equator will be warm. This would be a tropical air mass, but if this air mass happens to move toward one of the poles, it may become colder and colder until we must reclassify it as a polar air mass. The reverse can occur. An air mass that forms near one of the poles will be cold. This would be a polar air mass, but if this air mass happens to move toward the equator, it may become warmer and warmer until we must reclassify it as a tropical air mass. As another example, an air mass that forms over a continent will be dry. This would be a continental air mass, but if this air mass happens to move over the ocean or any body of water, it may become more and more humid as evaporating water adds more and more moisture to the air mass. Eventually, we must reclassify it as a maritime air mass. The reverse can occur. An air mass that forms over the ocean or any body of water will be humid. This would be a maritime air mass, but if this air mass happens to move over a continent, it may lose more and more moisture through precipitation that will not be replenished, since there is little water on the continent to evaporate. The air mass becomes less and less humid until we must reclassify it as a continental air mass. A spectacular example of the changing of an air mass is lake-effect snow. The five Great Lakes are between the United States and Canada, two countries in the North American continent. Cities on the windward side of the Great Lakes may experience very little snow, since air masses that form over either Canada or the United States would be continental (dry) air masses. However, a city on the leeward side (the opposite side of the windward side) of the Great Lakes may experience enormous amounts of snow. This is because a continental air mass that moves over the Great Lakes will become more and more humid as water evaporates from the Great Lakes. By the time the air mass has crossed the Great Lakes, the air mass has become so humid that it is now a maritime air mass. The humid maritime air mass then precipitates snow onto these cities on the opposite side of the Great Lakes from cities that experienced no snow from the same air mass when it was formerly a continental (dry) air mass before crossing the Great Lakes. As a result, two cities that are not particularly distant from each other may nevertheless experience vastly different amounts of precipitation, since these two cities are on two opposite sides of a large body of water.

The Bjørgvin Theory of Meteorology

The fundamental theory of meteorology was formulated by the Norwegian meteorological physicist Vilhelm Bjerknes and other meteorologists in Bjørgvin, Norway. Consequently, we will refer to the fundamental theory of meteorology as the Bjørgvin Theory of Meteorology. According to the Bjørgvin Theory of Meteorology, the Earth’s troposphere (the lowest layer of the atmosphere) is divided into many pieces called air masses. These air masses are pushed by the prevailing winds, and much meteorological activity (commonly known as weather) occurs at the boundary between two air masses, which is called a front. This Bjørgvin Theory of Meteorology, the fundamental theory of meteorology, is remarkably similar to the Theory of Plate Tectonics, the fundamental theory of geology. As we discussed earlier in the course, the Theory of Plate Tectonics states that the Earth’s lithosphere (the uppermost layer of the geosphere) is divided into many pieces called tectonic plates. These tectonic plates are pushed by convection cells in the asthenosphere (underneath the lithosphere), and much geological activity occurs at the boundary between two tectonic plates. These two fundamental theories have further similarities. Just as there are different types of tectonic plate boundaries that cause different types of geological activities as we discussed earlier in the course, there are different types of fronts (air mass boundaries) that cause different types of meteorological activities (commonly known as weather). A cold air mass pushing on a warm air mass is called a cold front. The symbol for a cold front on a weather map is triangles along the front pointing in the direction in which the cold front is moving. A warm air mass pushing a cold air mass is called a warm front. The symbol for a warm front on a weather map is semicircles along the front again pointing in the direction in which the warm front is moving. Cold fronts move faster than warm fronts, as we will discuss shortly. Therefore, a faster-moving cold front can catch up to and merge with a slower-moving warm front. This is called an occluded front. We will discuss the meaning of the term occluded shortly. The symbol for an occluded front on a weather map is both triangles and semicircles along the front again pointing in the direction in which the occluded front is moving. A front that does not move for several days or perhaps even a couple weeks is called a stationary front. The symbol for a stationary front on a weather map is both triangles and semicircles along the front, but the triangles and the semicircles point in two opposite directions.

The meteorological term front is borrowed from military terminology. Vilhelm Bjerknes and other meteorologists formulated the Bjørgvin Theory of Meteorology during and shortly after the Great War (commonly known as the First World War or World War I) roughly one hundred years ago. The Great War (the First World War or World War I) was the most global and most horrific war in human history up to that time, compelling many people throughout the world to often draw military analogies. A military front is the boundary between two opposing armies. If one army advances over (or pushes) the other army, the military front will move with the advancing army. If two armies are equally matched, the military front will not move. This is called a stationary military front, the textbook example being the western front of the Great War (the First World War or World War I). The western front remained stationary for most of the years of the Great War since the combined British and French armies on the western side of the western front equally matched the German army on the eastern side of the western front. The western front did not move until the United States joined the British and the French toward the end of the Great War. The combined British, French, and American armies now had sufficient momentum to advance upon the German army, finally pushing the western front eastward. As Vilhelm Bjerknes and other meteorologists formulated the Bjørgvin Theory of Meteorology during and shortly after the Great War, they imagined air masses pushing each other as if they were opposing armies. It is for this reason that meteorologists to the present day refer to the boundary between two air masses as a front. The term for a meteorological front that does not move, a stationary meteorological front, was literally copied from the term for a military front that does not move, which is again a stationary military front.

Since warm air rises and cold air sinks, the actual front between two air masses is not a perfectly vertical wall. The actual front between the two air masses is an inclined wall, since the rising warm air will be above the sinking cold air. In other words, the sinking cold air will be below the rising warm air. Therefore, a cold front is inclined backward as the cold air mass pushes the warm air mass, while a warm front is inclined forward as the warm air mass pushes the cold air mass. Moreover, since cold air is more dense than warm air, the cold air mass can strongly push the warm air mass, making the cold front more vertical than a warm front. That is, a warm front is more shallow than a cold front. Since warm fronts are more shallow, it takes a longer duration of time for a warm front to move over any particular location. Since cold fronts are more vertical, it takes a shorter duration of time for a cold front to move over any particular location. Along both cold fronts and warm fronts, rising hot air will expand adiabatically and cool thus becoming more humid; the dew point could be achieved, causing clouds and possibly precipitation along the front. Since a warm front is more shallow, all of the precipitation will be spread over a larger area; consequently, the precipitation along a warm front is often mild. The usual weather associated with a warm front is gentle precipitation over a long duration of time (often many hours) followed by warmer temperatures as compared with the temperatures before the warm front arrived. Since a cold front is more vertical, all of the precipitation will be concentrated over a smaller area; consequently, the precipitation along a cold front is often severe. The usual weather associated with a cold front is intense precipitation over a brief duration of time (often only a few minutes), followed by colder temperatures as compared with the temperatures before the cold front arrived.

As a concrete application of the Bjørgvin Theory of Meteorology, consider weather patterns in the contiguous United States, which is at the midlatitudes of the northern hemisphere. The prevailing winds of the midlatitudes of the northern hemisphere are the southwesterlies. Therefore, weather patterns (both good weather and bad weather) are pushed from the west toward the east by these southwesterlies. This explains why weather patterns move across the United States from the west toward the east. Philadelphia is west of New York City, and Chicago is further west from Philadelphia. A weather pattern in Chicago will move from Chicago toward Philadelphia, and the weather pattern will continue to move from Philadelphia toward New York City. Now consider a low-pressure system being pushed from the west toward east by the southwesterlies. Winds will blow inward toward this moving low-pressure system. Winds from the south will carry warmer air, since they are from equatorial latitudes. Winds from the north will carry cooler air, since they are from polar latitudes. Since the United States is in the northern hemisphere, the Coriolis force deflects all of these winds to the right ultimately circulating them counterclockwise around this moving low-pressure system. Hence, the warmer winds from the south will be deflected to the east and will collide with cooler air. Warm air pushing cold air is a warm front; hence, there will be a warm front to the east of the moving low-pressure system. Also, the cooler winds from the north will be deflected to the west and will collide with warmer air. Cool air pushing warm air is a cold front; hence, there will be a cold front to the west of the moving low-pressure system. As this low-pressure system is pushed by the southwesterlies, any given geographical region of the United States will first be attacked by the warm front, often bringing many hours of gentle precipitation followed by warmer temperatures. Then, the same geographical region will be attacked by the cold front, often bringing only a few minutes of intense precipitation followed by colder temperatures. Since cold fronts move faster than warm fronts, the cold front to the west of the low-pressure system may catch up to and merge with the warm front to the east of the low-pressure system, forming an occluded front. The cold air to the west of the former cold front merges with the cold air to the east of the former warm front, thus squeezing the warm air between them and wedging it upward, since warm air rises. Hence, the formation of the occluded front begins the dispersion of the entire low-pressure system. This is the reason these fronts are called occluded fronts. In colloquial English, the verb to occlude means to stop or to obstruct or to close.

As rising air and sinking air rub against each other, electrons are transferred from one thermal to another. This may create an electric field between the clouds and the ground. Usually, air is a poor conductor of electricity; air is usually an electrical insulator. However, all electrical insulators will conduct electricity if subjected to electric fields of sufficiently enormous strength. The threshold electric field at which an electrical insulator becomes an electrical conductor is called the dielectric breakdown of the material. The dielectric breakdown of air is roughly three million volts per meter. If the electric field in air exceeds roughly three million volts per meter, the air actually becomes an electric conductor. In this case, electrons can flow between the clouds and the ground. This flow of electrons is called lightning. There is an enormous quantity of energy associated with lightning. Some of this energy is transferred to the air itself, causing a loud, explosive sound called thunder. In brief, lightning causes thunder. The light from the lightning propagates at the speed of light, which is almost one million times faster than the speed of sound. In other words, sound propagates almost one million times slower than the speed of light. The speed of light is so fast that we never notice its propagation in our daily experiences; light seems to propagate instantaneously fast. However, sound propagates sufficiently slow that we notice its propagation in some of our daily experiences. For example, some of us notice while sitting near the outfield of a baseball stadium that there is a delay between seeing and hearing a baseball bat crack a baseball. Some of us notice while sitting near the infield of a baseball stadium that there is a delay between seeing and hearing a baseball land in the baseball mitt of an outfielder. Some of us notice that there is a delay between seeing and hearing a hockey stick strike a hockey puck. In all such examples, we see the event first, then we hear the event second. Again, light seems to propagate instantaneously fast, while sound propagates slow enough that the sound arrives noticeably after the light. The speed of sound through air is roughly one mile per five seconds, which we may restate as roughly five seconds per mile. We can use this relatively slow propagation of sound to estimate how far away a storm is occurring from our location. We simply count the number of seconds starting from when we see lightning until we hear thunder. For every five seconds we count, the storm is roughly one mile distant. For example, if we see lightning and count fifteen seconds until we hear thunder, the storm is roughly three miles distant, since every five seconds we counted corresponds to roughly one mile of distance. If we count many seconds after seeing lightning but never hear thunder, this means that the storm is very far away. Thunder propagates outwards in all directions, spreading its total energy thinner and thinner. By the time the thunder arrives at our location, the sound energy was too diluted for our ears to hear. At the opposite extreme, suppose we see lightning and immediately thereafter we hear thunder; in other words, suppose we did not have the opportunity to count to even one second before hearing thunder. This means that the storm is very close; we are probably located within the storm itself.

A tornado is a continental storm with fast, circulating winds around an extremely low-pressure thermal. Most tornadoes are a few dozen meters across. A large tornado could be a couple hundred meters across. Enormous tornados that are one kilometer across are very rare. Most of the tornadoes in the world occur in the midwestern United States. This is because cP air masses (continental polar air masses) form over Canada, since Canada is in the North American continent and is near the north pole, while cT air masses (continental tropical air masses) form over Mexico, since Mexico is also in the North American continent but near the equator. Moreover, there are two mountain ranges along both coasts of North America: the Rocky Mountains along the Pacific coast (the west coast) and the Appalachian Mountains along the Atlantic coast (the east coast). These two mountain ranges tend to confine air masses between them. Hence, cP air masses that form over Canada and cT air masses that form over Mexico tend to collide over the country that is between Canada and Mexico; that country is the United States. For all these reasons, most of the tornadoes in the entire world occur in the midwestern United States.

The Fujita scale (or F-scale) is a tornado wind-speed scale, named for the Japanese-American meteorologist Tetsuya Theodore Fujita who formulated this scale. The weakest tornadoes are designated F0. More powerful than F0 would be called F1 followed by F2, F3, and F4. The most powerful tornados are designated F5. Even an F0 tornado is powerful enough to destroy entire towns; many people have been killed by F0 tornados, the weakest scale of tornado. We must always seek shelter during a tornado warning, regardless of the Fujita-scale designation of the tornado.

The largest storms in the entire world form from low-pressure mT air masses (maritime tropical air masses). These storms are called hurricanes if they form in the Atlantic Ocean, and they are called typhoons if they form in the Pacific Ocean. Other than their oceanic location, there is no difference between a hurricane and a typhoon. The development of a hurricane/typhoon is as follows. A slightly low-pressure mT air mass is called a tropical disturbance. If a tropical disturbance happens to form at or near the equator, the Coriolis force will be too weak to cause any circulation of winds, and the tropical disturbance will quietly disperse. However, if a tropical disturbance happens to form significantly north or south of the equator, the Coriolis force may be strong enough to circulate the winds. When the winds are sufficiently strong, the tropical disturbance becomes a tropical depression. On rare occasions, the winds are so strong that the tropical depression may become a tropical storm. At this point, the tropical storm is given a human name, as we will discuss. On very rare occasions, the winds become so extraordinarily strong that the tropical storm becomes a hurricane/typhoon. In this case, the hurricane/typhoon retains its tropical-storm human name, as we will discuss. To summarize, first we have a tropical disturbance, then we have a tropical depression, then we have a tropical storm, then we have a hurricane/typhoon.

Since a hurricane/typhoon is a low-pressure system, the winds in a hurricane/typhoon circulate counterclockwise in the northern hemisphere but circulate clockwise in the southern hemisphere. The winds circulate around the eye of the hurricane/typhoon, where there is calm weather and clear skies. When a northern-hemisphere hurricane/typhoon attacks a continent, the winds to the right of the eye push the ocean waters onto the continent. This is called the storm surge. The winds to the left of the eye push the ocean waters away from the continent; thus, there is no storm surge to the left of the eye. Therefore, most of the destruction to the left of the eye is from the winds themselves. To summarize, most of the devastation from a northern-hemisphere hurricane/typhoon is from the storm surge to the right of the eye, but most of the devastation from a northern-hemisphere hurricane/typhoon is from the winds to the left of the eye. These directions are reversed in the southern hemisphere, but note that hurricanes/typhoons are rare in the southern hemisphere. This is because winds would circulate clockwise around hurricanes/typhoons in the southern hemisphere, causing the winds on the southern edge of the storm to blow from the east. However, the prevailing winds at the midlatitudes of the southern hemisphere blow from the west, thus weakening the storm winds and preventing tropical storms from strengthening to hurricanes/typhoons. Of course, we could present the same argument for the northern hemisphere. Winds circulate counterclockwise around hurricanes/typhoons in the northern hemisphere, causing the winds on the northern edge of the storm to again blow from the east. Again, the prevailing winds at the midlatitudes of the northern hemisphere blow from the west, which should again weaken the storm winds and prevent tropical storms from strengthening to hurricanes/typhoons. Indeed, this is an important reason why the strengthening of tropical storms to hurricanes/typhoons is rare even in the northern hemisphere. However, the Antarctic Circumpolar Current at the midlatitudes of the southern hemisphere is the strongest oceanic surface current in the entire world, as we discussed earlier in the course. Although the Antarctic Circumpolar Current is caused by the prevailing winds at the midlatitudes of the southern hemisphere, this oceanic surface current is so strong that it actually pushes back on the atmosphere, making the midlatitude prevailing winds in the southern hemisphere stronger than the midlatitude prevailing winds in the northern hemisphere. The stronger prevailing winds at the midlatitudes of the southern hemisphere make the formation of hurricanes/typhoons in the southern hemisphere much less likely than the formation of hurricanes/typhoons in the northern hemisphere. In either hemisphere, most of the devastation inland from a hurricane/typhoon is from flooding from rain. As we will discuss later in the course, flooding is the most common and the most destructive of all natural disasters.

The human name of a tropical storm in the Atlantic Ocean is chosen from six lists each containing twenty-one alphabetized human names. For example, the first tropical storm in the Atlantic Ocean in the year 2023 was named tropical storm Arlene, the second was named tropical storm Bret, the third was named tropical storm Cindy, and so on and so forth. Notice that the names are in alphabetical order. Although the English alphabet has twenty-six letters, these six lists each have only twenty-one names because names beginning with the five letters Q, U, X, Y, and Z are not used, since human names beginning with any of these five letters are rare. If a tropical storm is promoted to a hurricane, then it retains its human name. For example, tropical storm Franklin was promoted to hurricane Franklin in the year 2023. These six lists of human names are recycled every six years. However, if a hurricane is particularly destructive, then its name is permanently retired and is forever associated with the hurricane for that particular year. A new human name beginning with the same letter of the English alphabet must then replace that name for future years. For example, the fourth tropical storm in the year 2013 should have been named Dean, but hurricane Dean was so destructive in the year 2007 that the name Dean was permanently retired and replaced with the name Dorian. If there happens to be more than twenty-one tropical storms in the Atlantic Ocean in any given year, then the letters of the Greek alphabet are used after reaching the end of the list of twenty-one names. For example, the twenty-second tropical storm in the Atlantic Ocean in the year 2005 was named tropical storm Alpha, the twenty-third was named tropical storm Beta (later promoted to hurricane Beta), the twenty-fourth was named tropical storm Gamma, the twenty-fifth was named tropical storm Delta, the twenty-sixth was named tropical storm Epsilon (later promoted to hurricane Epsilon), and so on and so forth. There are other lists of names for tropical storms in the Pacific Ocean. Again, there are twenty-one human names in each list of names for the Atlantic Ocean, and there are twenty-four letters in the Greek alphabet. Twenty-one plus twenty-four equals forty-five. What do we do if there are more than forty-five tropical storms in the Atlantic Ocean in a single year? In this case, we run to the nearest church, since it is probably the end of the world!

The Saffir-Simpson scale is a hurricane/typhoon scale, named for American engineer Herbert Saffir and American meteorologist Robert Simpson who together formulated this scale. The weakest hurricane/typhoon is called Category 1, stronger is called Category 2, even stronger is called Category 3, stronger is called Category 4, and the strongest hurricane/typhoon is called Category 5. We must keep in mind that even a Category 1 hurricane/typhoon is stronger and more destructive than a tropical storm. For example, hurricane Sandy was a Category 1 hurricane when it attacked and devastated New Jersey in the year 2012. Even tropical storms, which are themselves weaker than Category 1 hurricanes/typhoons, can destroy entire towns; many people have been killed by tropical storms, themselves weaker than the weakest hurricanes/typhoons. We must always seek shelter during a tropical storm warning, and we must certainly always seek shelter during a hurricane/typhoon warning, regardless of the Saffir-Simpson-scale designation of the hurricane/typhoon.

Climatology

The study of short-term trends and variations in the atmosphere is called meteorology, and someone who studies short-term trends and variations in the atmosphere is called a meteorologist. By short-term, we may mean a few minutes, a few hours, a few days, or a few weeks. The study of long-term trends and variations in the atmosphere is called climatology, and someone who studies long-term trends and variations in the atmosphere is called a climatologist. By long-term, we may mean months, years, decades, centuries (hundreds of years), millennia (thousands of years), or even millions of years. The study of the atmosphere (short-term and/or long-term) is called atmospheric sciences, and someone who studies the atmosphere (short-term and/or long-term) is called an atmospheric scientist.

Statistics is used to study trends and variations of any kind. Any collection of numbers is called data, and the purpose of statistics is to calculate two quantities about data: the central tendency of the data and the dispersion of the data. The central tendency of the data is a number that is a typical representative of most of the data. The most common way of measuring central tendency is the average, which we will call the mean. The mean of the data is the sum of the numbers divided by the number of numbers. The most common way of measuring dispersion is the standard deviation, but in this course we will measure dispersion with the range. The range of the data is the difference between the largest number and the smallest number. In atmospheric sciences, the daily temperature mean is the average of the hottest temperature and the coldest temperature in any given day. For example, if the hottest temperature today is eighty degrees fahrenheit and if the coldest temperature today is seventy degrees fahrenheit, then the daily temperature mean for today is seventy-five degrees fahrenheit, since eighty plus seventy is one hundred and fifty, and dividing this by two yields seventy-five. The daily temperature range is the difference between the hottest temperature and the coldest temperature in any given day. In the previous example, the daily temperature range for today would be ten fahrenheit degrees, since eighty minus seventy equals ten. The monthly temperature mean is the average of all the daily means for that month. For example, if a particular month happens to have thirty days, the monthly temperature mean for that month would be the sum of all the daily means for that month divided by thirty. The monthly temperature range is the difference between the hottest daily mean and the coldest daily mean during that month. The annual temperature mean is the average of all the monthly means for that year. In other words, the annual temperature mean is the sum of all the monthly means for that year divided by twelve, since there are twelve months in one year. The annual temperature range is the difference between the hottest monthly mean (almost always July or August in the northern hemisphere) and the coldest monthly mean (almost always January or February in the northern hemisphere) of that year.

Generally, temperature means are hotter at the equatorial latitudes, while temperature means are colder at the polar latitudes. At the midlatitudes, temperature means are hotter during summertime and colder during wintertime. However, we must not only specify trends and variations in the temperature, but trends and variations in the precipitation must also be specified in any climatological analysis. Generally, precipitation means are high at and near the equator due to the equatorial low (the doldrums). Precipitation means are low at and near roughly thirty degrees latitude in both hemispheres due to the subtropical highs (the horse latitudes). Precipitation means are high at and near roughly sixty degrees latitude in both hemispheres due to the subpolar lows. Finally, precipitation means are low at and near the poles due to the polar highs.

Temperature ranges are smaller at coasts and shores due to the marine effect: the oceans stabilize temperatures due to the relatively large heat capacity of water. Temperature ranges are larger inland due to the continental effect: continents do not stabilize temperatures due to the relatively small heat capacity of land. In other words, inland winters tend to be colder and inland summers tend to be hotter as compared with coasts and shores where both winters and summers tend to be relatively mild. Extending this logic across the entire planet, temperature ranges are generally smaller in the water hemisphere (the southern hemisphere), since the abundance of southern-hemisphere oceans stabilize temperatures in that hemisphere. Conversely, temperature ranges are generally larger in the land hemisphere (the northern hemisphere), since the abundance of northern-hemisphere continents do not stabilize temperatures in that hemisphere. In other words, winters in the northern hemisphere tend to be colder and summers in the northern hemisphere tend to be hotter as compared with the southern hemisphere, where both winters and summers tend to be relatively mild.

For most of the history of planet Earth, the hot temperatures at the equatorial latitudes and the cold temperatures at the polar latitudes have been moderated by the oceans due to the relatively large heat capacity of water. However, the moving tectonic plates of the lithosphere slowly change the configuration of the continents and the oceans over enormous timescales (millions of years). If there happens to be relatively isolated continents and/or microcontinents at the poles, the relatively small heat capacity of these landmasses will permit the temperatures at the poles to become extremely cold. The result is an ice age, an extremely long period of time (millions of years) when the temperature at the poles is so cold that enormous icecaps cover these landmasses. There have been several ice ages throughout the entire history of the Earth, each lasting many millions of years. As we discussed earlier in the course, the Current Ice Age began roughly thirty million years ago when South America ripped off of Antarctica, completely isolating Antarctica at the South Pole and establishing the Antarctic Circumpolar Current surrounding Antarctica. Hence, Antarctica became extremely cold, and our entire planet Earth plunged into the Current Ice Age. The Current Ice Age began roughly thirty million years ago and continues to the present day. The Current Ice Age will last many more millions of years as long as Antarctica remains isolated at the South Pole surrounded by the Antarctic Circumpolar Current that further isolates Antarctica. There are only two scenarios that can end the Current Ice Age. In one scenario, Antarctica may move off of the South Pole, which would make it less cold. This would also interrupt the Antarctic Circumpolar Current, which would contribute to warming temperatures. In the other scenario, another continent may move to the South Pole and collide with Antarctica. This would end the isolation of Antarctica, making it less cold. This would also interrupt the Antarctic Circumpolar Current, again contributing to warmer temperatures. Whether Antarctica moves away from the South Pole or another continent moves toward the South Pole, it takes millions of years for tectonic plates to move significantly, as we discussed earlier in the course. Therefore, the Current Ice Age will continue for millions of more years to come. During the Current Ice Age, the southern icecap covers the continent Antarctica, and the northern icecap covers the microcontinent Greenland.

Within the Current Ice Age, there have been many periods of time when the Earth has become even colder. These are glacial periods of the Current Ice Age. Between two glacial periods is an interglacial period when the Earth is not as cold. The Earth becomes so cold during a glacial period that the icecaps expand beyond the poles and advance onto other continents. A major glacial period lasts roughly one hundred thousand years, while a minor glacial period lasts between roughly twenty-five thousand years and roughly fifty thousand years. We are currently within an interglacial period of the Current Ice Age. This interglacial period began roughly twelve thousand years ago at the end of a major glacial period that lasted roughly one hundred thousand years. Plate tectonics cannot be responsible for the alternation between glacial periods and interglacial periods within the Current Ice Age, since tectonic plates do not move appreciably over timescales of thousands of years. The alternation between glacial periods and interglacial periods within the Current Ice Age is caused by the Milanković cycles, named for the Serbian climatologist and astronomer Mulutin Milanković who formulated this theory. The Earth’s orbit around the Sun is presently almost a perfect circle. In other words, the eccentricity of the Earth’s orbit around the Sun is close to zero, but this has not always been the case nor will it always be the case. Gravitational perturbations (tugs) from the other planets, primarily Jupiter, change the eccentricity of the Earth’s orbit. When the Earth’s orbit is perturbed to become more elliptical, the Earth will be significantly further from the Sun, causing the Earth to become significantly colder thus causing a major glacial period of the Current Ice Age. Calculations show that the eccentricity of the Earth’s orbit changes once every one hundred thousand years (roughly), which is roughly the duration of time of a major glacial period within the Current Ice Age. Minor glacial periods are caused by the precession and the nutation of the Earth’s rotational axis. Precession is the turning of an axis around another axis. Nutation is the nodding of an axis resulting in a change in obliquity. The Earth’s rotational axis precesses and nutates, and this changes the amount of sunlight the Earth receives from the Sun, which in turn causes minor glacial periods within the Current Ice Age. Calculations show that the Earth’s rotational axis precesses once every twenty-six thousand years (roughly), and the Earth’s rotational axis nutates once every forty-one thousand years (roughly). These are roughly equal to the duration of time of minor glacial periods within the Current Ice Age.

Long-term variations in global temperature (over millions of years) are caused by slowly moving tectonic plates, resulting in ice ages when continents and/or microcontinents happen to be relatively isolated at or near the poles, as with the Current Ice Age. Intermediate-term variations in global temperature (over thousands of years) cause glacial periods and interglacial periods within the Current Ice Age. These intermediate-term variations in global temperature (over thousands of years) are caused by the Milanković cycles (the variations of the eccentricity of the Earth’s orbit around the Sun, the precession of the Earth’s rotational axis, and the nutation of the Earth’s rotational axis). However, there are also short-term variations in global temperature, from centuries to decades, and even as short as a few years. Extremely short-term variations in global temperature (over a few years) are caused by violent igneous eruptions. As we discussed earlier in the course, a single igneous eruption can cause global cooling for a few years, since igneous eruptions eject ash into the atmosphere, reducing the amount of incoming sunlight to the Earth. Short-term variations in global temperature (from decades to centuries) are caused by a combination of the Pacific Decadal Oscillation (PDO), the Atlantic Multidecadal Oscillation (AMO), and variations in solar activity. As we discussed earlier in the course, the Pacific Decadal Oscillation (PDO) is the alternation between decades of El Niño domination in the Pacific Ocean and decades of La Niña domination in the Pacific Ocean. The Atlantic Multidecadal Oscillation (AMO) is a similar oscillation in the Atlantic Ocean, as we also discussed earlier in the course. Although direct observations of the PDO and the AMO only stretch back several decades, measurements of the radioactive isotope carbon-fourteen within trees have revealed that the PDO and the AMO each undergo roughly sixty-year cycles, where one complete PDO for example consists of roughly three decades of El Niño domination followed by roughly three decades of La Niña domination. Quantitative observations of solar activity stretch back a few centuries, giving us a stronger understanding of how variations in solar activity affect global temperatures. At times, the Sun is more active, radiating more energy that warms planet Earth; at other times, the Sun is more quiet, radiating less energy that cools planet Earth. These variations in solar activity manifest themselves through sunspots, regions on the surface of the Sun where magnetic field strengths are particularly strong. These sunspots have been directly observed for roughly four hundred years, since the invention of the telescope. Astronomers have observed that the number of sunspots goes through an eleven-year cycle. This is the Schwabe solar cycle, named for the German astronomer Samuel Heinrich Schwabe who discovered this cyclic variation in the number of sunspots. In one Schwabe solar cycle, the number of sunspots increases then decreases over a time period of eleven years. For example, the Sun experienced a period of increasing activity during the last few years of the twentieth century and the first few years of the twenty-first century (the current century). This period of increasing solar activity was followed by a period of decreasing solar activity. During that particular period of decreasing solar activity, some of the coldest monthly temperature means over the last one hundred years occurred. At the end of each Schwabe cycle, the Sun’s magnetic field reverses itself, and then the Schwabe cycle occurs again while the Sun has a reversed magnetic polarity. Consequently, a complete solar cycle is actually twenty-two years. This is the Hale solar cycle, named for the American astronomer George Ellery Hale who correctly explained that these solar variations were magnetic in origin. We will refer to this twice-eleven year (twenty-two year) cycle as the Schwabe-Hale solar cycle. Moreover, this twice-eleven year (twenty-two year) Schwabe-Hale solar cycle goes through an eighty-eight year cycle. This is the Gleissberg solar cycle, named for the German astronomer Wolfgang Gleissberg who discovered this longer solar cycle. Furthermore, measurements of the radioactive isotope carbon-fourteen within trees and continental ice sheets have revealed that the Schwabe-Hale solar cycle and the Gleissberg solar cycle together go through a roughly two-hundred-year cycle. This is the Suess solar cycle, named for the Austrian American physicist Hans Suess. This two-hundred-year cycle is also called the de Vries solar cycle, named for the Dutch physicist Hessel de Vries, one of the pioneers of radiocarbon dating. According to the Suess-de Vries solar cycle, the Sun gradually increases in activity to what is called a solar maximum then gradually decreases in activity to what is called a solar minimum. Caution: the twice-eleven year (twenty-two year) Schwabe-Hale cycles and the eighty-eight year Gleissberg cycles continue to occur throughout each two-century Suess-de Vries cycle. Since one complete Suess-de Vries cycle lasts for roughly two centuries, each solar maximum and each solar minimum lasts for roughly one hundred years. Over the past twelve thousand years (since the beginning of the current interglacial period of the Current Ice Age), there have been roughly sixty complete Suess-de Vries cycles, with each Suess-de Vries cycle having one solar maximum and one solar minimum. The Modern Maximum occurred throughout most of the twentieth century, and the Modern Minimum began toward the beginning of the twenty-first century (the current century). These Suess-de Vries cycles have caused variations in global temperatures over the past several thousand years. For example, a solar maximum contributed to the Roman Warm Period, lasting from the ancient Late Roman Republic to the ancient Early Roman Empire. As another example, a solar minimum contributed to cold temperatures during the Early Middle Ages followed by a solar maximum contributing to warm temperatures during the High Middle Ages. As yet another example, a solar minimum contributed to the cold temperatures during the Little Ice Age, lasting from the Late Middle Ages to the Early Modern Ages. Most recently, the Modern Maximum that occurred throughout most of the twentieth century contributed to warming temperatures during that century, and the Modern Minimum that began toward the beginning of the twenty-first century (the current century) has already caused cooling temperatures that will continue for the rest of the current century. By combining the roughly sixty-year PDO, the roughly sixty-year AMO, the twice-eleven year (twenty-two year) Schwabe-Hale solar cycle, the eighty-eight year Gleissberg solar cycle, and the roughly two-century Suess-de Vries cycle, we obtain a nearly perfect model of global temperature variations over the past couple thousand years. As we just discussed, this model predicts that there will be gradual global cooling during the current century. Caution: an unexpected violent igneous eruption may cause additional global cooling in addition to these cyclic variations.

To summarize the climate of planet Earth, the average temperature of the atmosphere is determined primarily by the Earth’s distance from the Sun together with the concentration of greenhouse gases in the atmosphere, primarily water vapor, which warms the Earth sufficiently so that it is habitable for life. Temperature means are hot at the equatorial latitudes, temperature means are cold at the polar latitudes, and temperature means vary at the midlatitudes based on the seasons (warmer in the summertime and cooler in the wintertime). The abundance of liquid water that covers the Earth (the oceans) stabilizes global temperatures due to the large heat capacity of water. Temperature ranges are smaller in the southern hemisphere (the water hemisphere), while temperature ranges are larger in the northern hemisphere (the land hemisphere). Temperature ranges are smaller at coasts and shores due to the marine effect, while temperature ranges are larger inland due to the continental effect. Precipitation means are high at and near the equator due to the equatorial low (the doldrums), precipitation means are low at and near roughly thirty degrees latitude in both hemispheres due to the subtropical highs (the horse latitudes), precipitation means are high at and near roughly sixty degrees latitude in both hemispheres due to the subpolar lows, and precipitation means are low at and near the poles due to the polar highs. Long-term variations in global temperature (over millions of years) are caused by slowly moving tectonic plates, resulting in ice ages when continents and/or microcontinents happen to be relatively isolated at or near the poles, as with the Current Ice Age that began roughly thirty million years ago and continues to the present day. Intermediate-term variations in global temperature (over thousands of years) cause glacial periods and interglacial periods within the Current Ice Age. These intermediate-term variations in global temperature (over thousands of years) are caused by the Milanković cycles (the variations of the eccentricity of the Earth’s orbit around the Sun, the precession of the Earth’s rotational axis, and the nutation of the Earth’s rotational axis). We are currently in an interglacial period of the Current Ice Age, and this interglacial period began roughly twelve thousand years ago. Short-term variations in global temperature (over a few decades or a few centuries) are caused by the twice-eleven year (twenty-two year) Schwabe-Hale solar cycle, the eighty-eight year Gleissberg solar cycle, the roughly two-century Suess-de Vries solar cycle, the roughly sixty-year PDO, and the roughly sixty-year AMO. We just began a century of gradual global cooling resulting from these solar cycles and oceanic cycles. Finally, extremely short-term variations in global temperature (over a few years) may result from powerful igneous eruptions.

copyeditor: Michael Brzostek (Spring2023)

Links

Libarid A. Maljian homepage at the Department of Physics at CSLA at NJIT

Libarid A. Maljian profile at the Department of Physics at CSLA at NJIT

Department of Physics at CSLA at NJIT

College of Science and Liberal Arts at NJIT

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