The graph that shows variation in average temperature with latitude results largely from the increase in angle of incidence for the sun's rays as one moves from the equator toward the poles. Because the most direct rays deliver the most energy to the Earth's surface, it follows that the equator, because rays always strike at an angle near 90° will receive more energy than Philadelphia, at 40° N latitude where the angle of incidence ranges from a low of 107° at the summer solstice to a noon-time high of 153° on the first day of winter. The most important effect of the differential heating is that the tropics, that part of the earth between 23.5° S and 23.5° N latitude are on average warmer than the temperate and arctic zones. However, because heat is not distributed evenly, the second law requires that heat move from the tropics towards the poles. It is this transfer of energy that creates winds, storms (including hurricanes and tornadoes) and many other aspects of weather and climate. Ocean currents are also an important transfer mechanism. The Gulf Stream, for example, has a huge impact on the climate of Europe. It almost never snows in European cities that lie at a latitude similar to the town of Churchill on Hudson Bay in Canada. Churchill is famous for the polar bears that scavenge at the town dump in the winter. Because areas at the same latitude must receive approximately the same amount of solar energy over a year, these climatic differences must result from the ways in which energy transfer from the tropics affects regional climates. Europe benefits greatly from the transfer; central and eastern Canada, not nearly as much

Although I am sure it is no surprise to you that Brazil is on average warmer than Pennsylvania, you might not know that on the first day of summer, Philadelphia receives more energy from the sun than a city like Recife, Brazil which is located near the equator. This is because of seasonal changes in aver age temperature that result from the revolution of the earth about the sun. The graph showing change in temperature with latitude is an oversimplification -- averages usually are. It might be more useful to show a graph with the average value and the range of temperatures experienced at different latitudes by giving daily averages on the first day of summer and winter with the yearly average. As you can see in this graph it is true to say that the Alaska at 60° N latitude is cold, but to leave it at that misses the point that it can get quite hot in the summer. Temperatures of 90° in the Yukon R. valley of central Alaska are not uncommon. As this graph shows, seasons have quite an impact on climate, especially at the mid and high-latitudes.

Season are a result of changes in the geometric relations of the earth and sun as the earth moves around the sun during a year. If we begin an imaginary year on Dec. 21, the winter solstice for the northern hemisphere, days are short in Philadelphia and the sun during the day is low in the southern sky. It never gets more than 27° above the horizon. (If you happen to be driving south at this time of the year, you will find the sun is almost always in your eyes.) Perhaps, this drawing will help explain the reasons.

The first thing to remember is that because the earth is so far away from the sun, all the light that strikes the earth is traveling nearly parallel paths. As a result we can represent the path of the light with a few parallel lines. The second fact that is important, is that the earth is tilted on its axis so that the an imaginary line drawn through the north and south poles, the spin axis of the earth, forms an angle of 23.5° with the plane that contains the sun, the earth and its orbit. The north end of the axis always points in the same direction -- towards the North Star, the last star in the handle of the Little Dipper. On Dec. 21, the tilt of the earth is aligned with the sun so that the south pole is angled towards the sun and the north pole is angled away. This means that the most direct rays of the sun are striking not at the equator, but on a point at latitude 23.5° S also known as the Tropic of Capricorn. It also means that at noon in Philadelphia on that day, the angle of incidence is equal to 90° plus the angle between a line drawn from Philadelphia to the center of the earth and out to 23.5° S. Because the earth's surface describes an arc within that angle, the angle is equal to 63.5°, the latitude of Philadelphia, 40°, plus 23.5° -- the angle between the Tropic of Capricorn and the equator.

Try to determine the angle of incidence at noon in a city located at 55° N. And at 80° N. Also try 40° S latitude. (The answers are 168.5, 203.5 and not in sunlight and 106.5 degrees.)

The angle of incidence, however, is not the only thing that changes. The hours of sunlight also changes. Half the area of the earth in sunlight at any time. That half is centered on the latitude with the most direct rays as shown by the lightened area of the earth in the drawing. Because the spin of the earth is not aligned with the dividing line between light and dark, different parts of the earth remain in the lighted area for different lengths of time. The time in and out of sun is proportional to the portions of a line of latitude within the lighted and unlighted parts of the earth. The equator is half in and half out so it receives 12 hours of sunlight. (Determine the hours of sunlight in Philadelphia.) As you realize if the sun is shining on a portion of the earth for a longer time, it gives more energy to that area. So two factors control the energy received at a point on the earth's surface -- directness of the sun's rays, and the time of exposure to the sun's rays. Because a location at 80° N is always outside the illuminated area, it receives no direct energy input from the sun. It of course is still warmer than outer space and so continues to radiate energy to space. As a result, what happens to its temperature?

Now as the earth moves around the sun, the tilt of the earth stops being aligned with sun and by the time March 21 arrives, 1/4 of a year later, the tilt is at right angles to a line drawn between the earth and sun. As a result neither pole is pointed toward or away from the sun and the most direct rays fall on the equator. This is the spring equinox. Because the sun's rays are most direct at the equator, the angle of incidence at Philadelphia is 40°+90° = 130°. The more direct rays cause increased heating of the surface and by the various processes described above the atmosphere is also warmed. Also acting to warm the region is the fact that we are in sunlight for 12 hours instead of the 8 hours of the first day of winter.

Of course, the earth does not stop on its travel around the sun. By the first day of summer, the winter relationships have been reversed. The north pole is now angled toward the sun and in sunlight for 24 hours a day. The south pole is in darkness for 24 hours. Because the arctic is exposed to sunlight for twenty four hours, areas that are ice free are able to soak up considerable energy -- more than is being radiated back into space and so can become quite warm. So temperatures away from the coast can easily rise into the 80's and 90's during the hottest days of late July and early August.

The pattern that emerges is one of nearly constant temperature in the equatorial regions, but rising and falling temperatures with the seasons at higher latitude. The seasonal changes become more extreme as one moves north or south from the equator. However, one more aspect of the heating/cooling pattern needs to be considered, the effect of the oceans. Water does not heat (or cool) as rapidly as the land. This is caused mostly by the fact that light is absorbed by the surface of the solid earth and so only the upper few inches of the surface are effected by solar heating. In contrast, the light striking the ocean may penetrate to a depth of several hundred meters (more than 500 feet). And, although the majority of the solar energy is transferred to the upper few meters, mixing of the upper waters by wind and waves cause the energy to be distributed to considerable depth. As a result a day's worth of sunlight has less effect on the temperature of the ocean than it does on the temperature of the land. Because the land heats more quickly, it has a bigger effect on the air above it -- warming it more than ocean would. At night, however, and in winter when there is more energy output than input, the relationship is reversed. Because the ocean gives up its energy more slowly, it will remain warmer than the land and so warm the air above. As a result coastal climates are usually more moderate -- cooler summers and warmer winters -- than climates of the interior of continents.

In the end though, it does grow colder on average with increasing latitude. This inequity in energy results in forcing the earth to move energy from the tropics to the poles in response to the Second Law of Thermodynamics. However, because the pattern of heating and cooling shifts with the seasons and with position relative to continents and oceans, we might expect the processes that move the heat are also affected by seasonal change. They are. We will examine at least one aspect of this change when we consider the reasons for the fact that the highest temperatures and warmest averages are reached not at the equator, but at 15-20° N and S latitudes.

Reading question: Determine the angle of incidence for the three latitudes listed above (55° N, 80° N, and 40° S) on the first day of northern summer.  Show your method.

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