Earth sun geometry and insolation

GEO 200 In-Class Activity

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In-class activity 4: Earth – Sun Relationships

Introduction
Solar radiation that enters the Earth-Atmosphere system is the primary source of energy for nearly every atmospheric process on Earth. The unique relationship between the Earth and Sun is what causes the seasons, controls the length of days, and organizes the basis for keeping track of time. An understanding of this relationship is essential when learning about atmospheric processes on Earth.

Basic Earth-Sun Geometric Relationships
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The earth’s orbit around the sun is elliptical, varying the distance between the earth and sun throughout the year. While the average distance between the earth and the sun is approximately 150 million kilometers (93 million miles), the actual distance at any given time fluctuates by as much as 5 million kilometers (3 million miles). The earth is nearest the sun (perihelion) during the Northern Hemisphere’s winter (January) and is farthest from the sun (aphelion) during the Northern Hemisphere’s summer (July).

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The sun’s rays are close to parallel to each other as they stream toward earth, so if the earth’s axis of rotation was perpendicular to the plane of the ecliptic, the sun’s most direct rays would always be received at the Equator. In this case, there would be no seasons.

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Seasons occur due to the tilt of Earth’s axis of rotation. The axis is an imaginary line that connects both poles, and it is tilted at an angle of 23.5 relative to the plane of the ecliptic, the plane on which the Earth revolves around the Sun. Since the axis of rotation is always oriented in the same direction (pointing toward the North Star), different latitudes receive direct solar radiation at different times throughout the year.

Due to its rotation, half of the Earth is always receiving some portion of Sunlight, known as the circle of illumination. However, the tilt of the Earth’s axis also controls daylength. During June, the Northern Hemisphere is tilted toward the Sun and experiences longer daylengths. During December, the Northern Hemisphere is tilted away from the Sun and experiences shorter daylengths.

The Arctic Circle (66.5N) and the Antarctic Circle (66.5S) outline the polar regions of our planet. The area within each circle experiences 24 hours of daylight on its June Solstice (Summer in the Northern Hemisphere; Winter in the Southern Hemisphere); likewise, the December Solstice (Winter in the Northern Hemisphere; Summer in the Southern Hemisphere) brings 24 hours of darkness. During both Equinoxes (Vernal in March and Autumnal in September), daylength is 12 hours at all latitudes across the globe.

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Solar Declination

The seasonal temperature changes are controlled by the amount of direct radiation received at the surface. As a result of the tilt of the axis and the curvature of the Earth, some latitudes receive direct radiation while other latitudes receive radiation at an oblique angle. When radiation strikes an object at an oblique angle, the energy is distributed over a larger area and is less intense.

The latitude at which the Sun is directly overhead at noon is the solar declination. The solar declination for the June Solstice is 23.5N (Tropic of Cancer), and 23.5S (Tropic of Capricorn) for the December Solstice. During both Equinoxes, the solar declination is at the Equator (0). The solar declination changes every day as the Earth revolves around the Sun, but is constrained between the Tropics.

1. List the date and the solar declination for each position.

Date

Solar Declination

Summer Solstice

Autumnal Equinox

Winter Solstice

Vernal Equinox

2. Label the diagram below with the appropriate date for each position.

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3. In the diagram below, what is the date?

4. Using the diagram above, describe the day or night length from the Arctic Circle to the North Pole.

5. What percentage of the Earth is illuminated at noon December 21 (or at any time)?

6. How many hours of daylight does the South Pole receive on March 21?

7. How many hours of daylight does the South Pole receive on June 21?

8. Which latitude(s) experience the GREATEST seasonal change in daylight hours? (In other words, do any areas on the globe change from completely dark to completely lit over the year? Where does this happen?)

9. What would happen if the earth’s axis of rotation was NOT tilted at a 23.5° angle?

10. Give the numerical latitude and cardinal direction for the 5 major lines of latitude.

Arctic Circle

Tropic of Cancer

Equator

Tropic of Capricorn

Antarctic Circle

Solar Angle

In addition to the solar declination, it is useful to understand some related geometric terms: zenith angle: the angle between a point directly overhead and the Sun at solar noon, and solar angle: the angle of the Sun above the horizon at solar noon. These angles are important because they determine the amount of insolation (incoming solar radiation) potentially received at the surface of the Earth.

To determine the zenith angle at a particular location, calculate the number of degrees of latitude separating the solar declination and the location in question. If the declination or latitude is in the southern hemisphere, it will be a negative value. The zenith angle should always be positive; therefore, you should report the absolute value of the zenith angle.

Example: zenith angle = (location latitude) – (solar declination)

At Alexandria, VA (39N) on January 20 (solar declination: 20S)

Zenith angle = 39 - (-20)

Zenith angle = 59

At Sao Paulo, Brazil (23S) on January 20 (solar declination: 20S)

Zenith angle = -23 - (-20)

Zenith angle = -3

Absolute value zenith angle = 3

The solar altitude angle is calculated by subtracting the absolute value of the zenith angle from 90. As the solar declination progresses, the zenith angle decreases and the solar altitude increases. At solar noon at the latitude of the solar declination, the zenith angle is 0 and the solar altitude angle is 90. The zenith angle and the solar altitude angle are significant because the Sun’s rays are much more intense where they strike the Earth directly (zenith angle of 0 and a solar altitude of 90) (Figure 3.3).

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Figure 3.3: Zenith angle (A) and solar altitude angle (B) for 30N on December 21.

11. First, calculate the zenith angle for Alexandria, VA (39N), St. Petersburg, Russia (60N), and Sydney, Australia (33S) on the following dates. Show your work, and then check your work before you proceed with the solar angle table.

Alexandria

St. Petersburg

Sydney

March 21

June 21

September 21

December 21

12. Now, using your answers from the table of zenith angles, calculate the solar angle for Alexandria, VA (39N), St. Petersburg, Russia (60N), and Sydney, Australia (33S) on the following dates. Show your work.

Alexandria

St. Petersburg

Sydney

March 21

June 21

September 21

December 21

13. Graph your solar altitude angle results for Alexandria, St. Petersburg, and Sydney on a line graph. Your x-axis should be time of year, and your y-axis should be solar altitude angle. A line graph requires that you connect the plotted data with a line, per each location, so you will have 3 different lines. Make sure that you follow the rules of making graphs and supply a name for the graph, and correct units and labels for each axis.

Answer the following questions using your graph.

14. Which location likely receives the most insolation during June?

15. Which location is probably the warmest during December?

16. In which month does Sydney likely receive the most insolation?

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