CH. 1 THE CLIMATE SYSTEM
Section 1: Earth's Temperature
Consider the following problem: Estimate the temperature of the Earth. In this section, we'll
attempt to solve this by creating a model, and then compare our answer to the Earth's
measured temperature.
The problem as stated above is too general and raises many questions. For example, what
temperature are we finding? From our experiences, we know that an asphalt parking lot is
usually warmer than a nearby patch of grass, and that a spot in the shade is usually cooler than
one in the sun. We also know that nighttime temperatures tend to be lower than daytime
temperatures. At this point, our problem is too difficult to make any progress. Instead, let's make
a few assumptions to necessary to solve this problem
First, let's find the average temperature; we'll average over the surface of the Earth -accounting for factors such as different surfaces, season, and day-night cycles are averaged
out. In other terms, we’ll consider the Earth a single system, and not worry about the inside
details of the system.
Second, on the basis of our daily experiences, we know the sun to the primary source of warmth
for the earth. So, for a reasonable approximation, let's assume that there are no other major
sources of energy contributing to Earth's temperature. More specifically, we'll assume that any
energy that enters the Earth system from other sources -- say, the light of the stars at night -- is
negligibly small. This assumption is corroborated by our daily experiences.
Let's begin to build our model. We know that energy from the sun arrives at the earth in the form
of electromagnetic radiation. We also know that the sun is approximately spherical, and radiates
light in a mostly uniform pattern (is this not also an assumption? What of flares/sunspots). The
Earth is approximately a sphere of radius
at a distance of from the Sun. As radiation
leaves the sun, it spreads out into a spherical pattern; when the radiation eventually reaches the
Earth, the area of this sphere is
The Earth intercepts a region of this sphere given
by
Based on this, we can say that the fraction of the Sun’s radiation that reaches the
earth is Figure \textbf{INSERT FIGURE HERE} depicts this scenario.
The total amount of radiation emitted from the Sun is called the Sun’s luminosity, . So, based
on our work so far, we can say that the amount of radiation the earth receives on average
is
. As electromagnetic radiation from the Sun falls on the Earth, it is either reflected into
space, or absorbed by the Earth. The fraction of this radiation that is reflected back is referred to
as Earth's albedo, usually written as a unitless decimal value. The albedo of a perfectly
absorbing surface would be 0, while the albedo of a perfectly reflective surface would be 1.
Fresh snow typically has an albedo of approximately 0.85, while the average albedo of the
ocean is around 0.06. Satellite measurements estimate Earth's average albedo to be around 0.3.
Combining our work up to here, we find that, on average, the Earth as a whole takes in this
much energy from the Sun:
Of course, if the temperature of the Earth is about constant on average, the amount of energy
leaving the Earth must match the amount enter the Earth -- otherwise, the earth would cool or
warm. Much like how a light bulb’s filament emits light when heated by electricity, the Earth
emits EM radiation because it has been heated by the Sun. Of course, since the Earth is much
cooler on average than the light bulb’s filament, the wavelength at which the Earth emits is
much longer -- so long, in fact, that it isn’t visible to the human eye. From thermodynamics,
there is an equation that relates the temperature of an object with the amount of radiation it
emits:
(Here, is a constant known as the Stefan-Boltzmann Constant, not to be confused with the
Boltzmann Constant.)
Equating the energy out with the energy in:
Solving for temperature, we find:
And now, we have our planetary temperature model!
Analyzing the Model
When a new scientific model is presented, scientists usually attempt to check that their model is
a reasonable approximation of reality in two main ways:
1. Does the model make logical sense? (This is just common sense.)
2. When the input values for situations where the actual results are known are fed into the
model, do we get the results we expect? This is called validation.
For this model, we should go through these steps:
1. Common Sense: It’s certainly tempting to just say yes and move on, but we should be
careful here. Unfortunately, there’s no clear way to be sure we’ve caught everything and
are ready to move on, but we should at least note some reassuring factors this model
possesses.
1. First off, we can look at the units of the equation; if the units don’t work, it’s
clearly bogus. Write out the units, and you will see that they work out. State the
units here
2. For another check, we can look how each variable affects the temperature. The
luminosity appears in the numerator. Higher luminosity means higher
temperature, which makes sense. The distance from the star is in the
denominator, which also makes sense.
1. Curiously enough, the temperature doesn’t seem to depend upon the
radius of the planet! Does this make sense? Looking back through the
initial steps, we see that the radius canceled out with another term, which
seems to make sense: since the rate at which a planet emits radiation
and the rate at which a planet absorbs radiation are both proportional to
the square of the radius, and no other term depends on the planet radius;
thus, the planetary radius won’t matter in our final answer.
2. Validation: Ideally, a good model should be validated on many different known scenarios.
Since we want our model to accurately predict the average temperature of a planet -- the
Earth -- we should feed our model values for distance from the sun, planet radius etc.
that correspond to planets whose temperatures we've measured. Table 1 lists these
values, as well as our output from the model.
\subsection{Understanding the Discrepancy}
\indent Why is the previous model so inaccurate? (i.e. ghgs, etc.)
Section 2: Climate and its Natural Variations
From our experience, we know that temperature, rainfall, humidity, and factors of the like vary
greatly over time in a given geographic location, cycling both over the course of a day and a
year. Abnormalities in these factors punctuate the cycles with severe weather events. Because
of this, observations of the state of a local environment at single points in time are insufficient for
characterizing a location’s environment. To better achieve this, we instead define climate, the
average weather patterns over an extended period of time (i.e. several years). Climate, along
with terrain, oceans and other geographic features, is an important abiotic factor that determines
the region’s habitability to different species of life.
Geographic Climate Variations
Although climate is an average of weather over time, it can vary drastically in different
geographic locations. For example, in the month of August, the Western Ghats of the Indian
subcontinent may be hot and wet, with flourishing biodiversity, whereas the Atacama Desert of
western South America may be cool and dry, relatively barren of much biodiversity. Such
geographic differences in climate may seem obvious to us, but their underlying reasons are
often less so. Most significant variations are a result of five geographic factors, which are
discussed below:
Latitude is generally the most important factor affecting a region’s climate. The angle of latitude
determines the angle at which sunlight strikes the surface, and thus significantly affects the
intensity of the intercepted sunlight. (More exactly, the light-intensity relationship with angle
is
, where
is the incoming intensity of sunlight,
is the
intensity actually intercepted by the Earth’s surface, and is the angle at which sunlight strikes
the Earth. This relationship is due to the concept of flux, a topic in physics not covered in this
textbook.) Because of this, regions closer to the equator receive a greater fraction of sunlight
than regions closer to the poles. This unequal distribution of sunlight, in turn, creates significant
temperature imbalances across the surface of the planet.
Earth’s tilt relative to the ecliptic (the plane of the orbit of Earth around the Sun) causes annual
variations in the angle of sunlight for given geographic locations, causing corresponding
variations in the atmosphere, hydrosphere, and biosphere. These variations should be familiar;
they are seasons. Due to the dependency of intercepted sunlight on the cosine of the solar
angle, the seasonal variations in solar angle have a greater effect on polar regions (the
derivative of the cosine function has greatest magnitude at ±90°). As a result, polar regions
generally experience the greatest seasonal temperature changes, whereas tropical regions are
more consistent in their temperature.
Our explanation so far has utilized an ideal model of Earth as a smooth sphere. While this
model can often be effective for describing the climactic effects of latitude, the ellipsoidal nature
of Earth and the unevenness of the geosphere render this model incomplete. This unevenness
determines the altitude of a local region and is critical in determining the climate of a region.
Altitude is the second of the five major geographic factors affecting climate. As the insulating
effect of atmospheric gases (especially greenhouse gases) increases with more insulating
layers overhead, high altitudes experience weaker insulation. Thus, higher altitudes (within the
troposphere) tend to be cooler than lower altitudes. This effect of altitude can even
counterbalance that of latitude, and is capable of producing climates in equatorial mountains
that one would expect in polar plains.
Before discussing the third major factor, we need to step aside to discuss wind. As previously
mentioned, variations in sunlight intensity across Earth cause corresponding variations in
surface and air temperature. Because warm surface air is less dense than the usually cooler air
above, the warm air from the surface rises to create areas of low air-pressure. Elsewhere, cool
air sinks to produce high-pressure areas. The pressure differential, or difference in pressure
between such areas induces wind in an attempt to balance the air pressure. The linking of highpressure and low-pressure regions worldwide produces the troposphere’s winds, which circulate
globally through wind belts and jet streams.
Depending on their temperature and pressure, moving air masses can carry differing levels of
humidity. When allowed to move unimpeded, air masses usually exhibit no weather events;
however, when impeded, they often release their humidity in the form of precipitation. A
mountain range or similar topographic impedances force incoming air masses upward, causing
precipitation on the range’s windward side and drying out the air mass on its way over the range.
If winds tend to blow in one direction more than the other, the leeward side of the mountain
range will receive significantly less humid air than the windward side, forming a desert on the
leeward side. This phenomenon is known as the rain shadow effect, and it is a classic example
of how topography is one of the major determining factors of climate. The previously
mentioned Atacama Desert of western South America is an example of a rain-shadow desert,
having formed in the shadow of the Andes mountains.
Alone, the effects of daily and yearly oscillations in solar angle due to the day/night cycle and
the seasonal cycle are capable of causing great temporal variations in temperature for a given
location. However, regions that are adjacent to large bodies of water often experience more
stable climates than those that do not. This is a result of the large specific heat capacity of
water, which results in large bodies of water buffering the temperature variation of air masses
above the bodies of water. This buffering results in a temperature inequality between the land
and water air masses, which causes a pressure inequality and, consequently, sea
breezes and land breezes. These exchange heat between the air above land and the air above
water, extending the water’s temperature buffer effect to include land near the coast. This effect
allows maritime climates to have a milder temperature than inland climates. Thus, when land
further inland is hot (such as during the day or the summer), coastal climates will be cooled by
their body of water, and when inland land is cold (such as during the night or the winter), coastal
climates will be warmed by their body of water.
The fifth major factor in determining local climate is the effect of ocean currents. Comparable
to wind currents, these result from pressure differentials in ocean water. They often form cycles
in major ocean basins, and they act to exchange heat between polar and tropical
regions. Along with wind belts, the ocean currents act to cool the tropical regions, preventing
them from overheating; similarly, they warm polar regions, preventing them from overcooling. A
notable example of the effect of ocean currents is the temperature difference between
northwestern Europe and northeastern Canada; both are at approximately the same latitude,
and are both adjacent to large bodies of water; however, coastal Canada is much colder than
coastal Europe. The difference can be attributed the fact that Canada is flanked by the cold,
polar Labrador Current, whereas Europe is warmed by the incoming tropical Gulf Stream
current.
In conclusion, geographic climate variations stem from five major
factors: latitude,altitude, topography, large bodies of water, and ocean currents. However, the
effects of all these factors are ultimately the result of temperature inequalities caused by the
interaction of Earth with the Sun’s incoming radiation. Thus, it would reasonable to conclude
that changing either the amount of incoming radiation or the way the Earth’s systems interact
with it would significantly affect climates worldwide.
Climate Variations over Time: Milankovitch Cycles
Over long periods of time, Earth’s climate has exhibited regular oscillations in its climate.
Glossary Entries
Albedo: Latin for “whiteness”. The percentage of incoming light reflected by a given surface,
expressed as a decimal.
Climate: The average state of the troposphere in a geographically limited region
over an extended period. Climate functions to characterize the abiotic properties
of an environment which are influenced by the atmosphere and sun.
Seasons: Annual variations of conditions in Earth’s systems due to the
oscillation of solar angle caused by Earth’s tilt relative to the ecliptic. Seasonal
changes have greater effects far from the equator than near the equator.
Altitude: Vertical (i.e. radial) distance of a location from a reference gravitational
equipotential, commonly sea level. Higher regions tend to be colder due to a
decreased greenhouse effect.
Wind: movement of an air mass due to pressure imbalance