Name ____________________________________________ Lab 5 Angle of Insolation Purpose The purpose of this lab is to have you determine changes in the angle of insolation that occur throughout the year at different latitudes on the Earth. You will then use this information to identify the relationship between temperature and angle of insolation, and how this affects the seasons. Activities and diagrams in this lab show how Earth-Sun geometry influences seasons and changes in the amount of daylight we receive. We study the angle of insolation because most atmospheric processes are ultimately driven by spatial variations in solar energy. Materials Calculator (with trigonometric functions) protractor Microsoft Excel Earth-Sun Relationships The distance between the Earth and the sun averages about 150 million kilometers (93 million miles). Because of this distance and the Earth’s relatively small size compared with that of the sun, it is reasonable to assume that the sun’s rays strike the nearly spherical Earth in straight paths. The Earth’s axis of rotation is tilted 23 ½°. This tilt is oriented in the same direction throughout the year, with the North Pole presently pointing toward the North Star, Polaris. The figure below shows that the Northern Hemisphere is tilted toward the sun during its summer months and away from the sun during its winter months. Our seasons occur because of this tilt. As the Earth revolves around the sun, the sun’s direct rays strike different latitudes. When the Northern Hemisphere is tilted toward the sun, it receives the more direct and, therefore, more intense rays of the sun. Locations in the Southern Hemisphere receive less direct solar radiation. Six months later, when the Southern Hemisphere is tilted toward the sun, it receives the more direct solar radiation. I hereby declare upon my word of honor that I have neither given nor received any unauthorized aid on this work. ______________________________________________________ Name ____________________________________________ Lab 5 Procedure A 1. Using a protractor, determine the angle at which incoming solar radiation (insolation) is striking the Earth’s surface at noon at the three latitude locations shown in diagram A. Record the angle to the nearest whole degree for each location on Table 5-1. 2. Use the above procedure to determine the angles of insolation for all of the latitude locations for diagrams B and C. Record the angles for each location on Table 5-1. 3. Using the data on the average monthly temperature for 42°N latitude provided in Table 5-2, create a line graph in Microsoft Excel that shows the relationship between average temperature and month during the year. The X-axis should be labeled “Month” and the Y-axis should be labeled “Temperature (°F).” These headings should be represented as column headings in your spreadsheet. TABLE 5-1 INSOLATION DIAGRAM DIAGRAM A LATITUDE ANGLE OF INSOLATION 42°N EQUATOR 42°S DIAGRAM B LATITUDE ANGLE OF INSOLATION 42°N EQUATOR 42°S DIAGRAM C LATITUDE 42°N EQUATOR 42°S 2 ANGLE OF INSOLATION Name ____________________________________________ Lab 5 TABLE 5-2 AVERAGE TEMPERATURE TABLE MONTH AVERAGE TEMPERATURE AT 42°N (°F) JANUARY 20.7 FEBRUARY 27.6 MARCH 40.1 APRIL 45.3 MAY 59.3 JUNE 65.8 JULY 67.6 AUGUST 68.5 SEPTEMBER 59.3 OCTOBER 50.0 NOVEMBER 38.0 DECEMBER 22.1 1. Using your data on the angle of insolation for Diagram A, what season of the year do you believe this diagram represents? 2. Using your data on the angle of insolation for Diagram B, what season of the year do you believe this diagram represents? 3. Using your data on the angle of insolation for Diagram C, what season of the year do you believe this diagram represents? 4. What is the lowest angle of insolation that you determined the equator receives throughout the year, and during what season does it occur? 5. What is the lowest angle of insolation received at 42°N latitude that you determined throughout the year, and during what season does it occur? 6. What is the highest angle of insolation received at 42°N latitude that you determined throughout the year, and during what season does it occur? 3 Name ____________________________________________ Lab 5 7. Using your data on angle of insolation during spring and fall at different latitudes, what is the general relationship between angle of insolation and latitude location on the Earth? 8. Using your data, describe the relationship between the season of the year in the Northern Hemisphere and the angle of insolation. 9. Using your line graph showing the average monthly temperature, describe the relationship between the angle of insolation and average temperature on the Earth. Earth-Sun Relationships (continued) ๏ท ๏ท ๏ท As you have seen in the diagrams, sun angle varies with season and location. Since such variability greatly influences weather patterns, it is useful to be able to calculate the noon sun angle for a given latitude. We must first define a few terms: Solar declination—the latitude at which the sun is directly overhead (90°) at solar noon. Zenith angle—the angle between a point directly overhead and the sun at solar noon. Noon sun angle—the angle of the sun above the horizon at solar noon. o Noon sun angle for a given date and location can be found by using the following: o ๐๐๐๐ ๐ ๐ข๐ ๐๐๐๐๐ = 90° − ๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐๐๐ก๐๐ก๐ข๐๐ ๐๐๐๐ ๐กโ๐ ๐ ๐๐๐๐ ๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐ ๐ฆ๐๐ข๐ ๐๐๐๐๐ก๐๐๐ You can approximate the value of the solar declination using the following formula: ๐๐๐๐๐ ๐๐๐๐๐๐๐๐ก๐๐๐ ≈ 23.5 × sin ๐ Where N = the number of days to the closest equinox, expressed in degrees. (By convention, N is positive between the March and September equinoxes and negative from the September to March equinoxes.) For example, on April 20, N=30 (number of days from the closest equinox, March 21) and ๐๐๐๐๐ ๐๐๐๐๐๐๐๐ก๐๐๐ ≈ 23.5 × sin 30 = 23.5 X (0.5) = 11.75° or 11°45’N So, on April 20, the sun’s direct rays are at 90° overhead at 11°45’N latitude. For our location, approximately 39°N, the noon sun angle for April 20 would be: 90°-(27.25°) = 62.75° above the horizon 4 Name ____________________________________________ Lab 5 On December 9, N= (-78). The number of days from September 22 is 78, and it is negative since it is between the September and March equinoxes. ๐๐๐๐๐ ๐๐๐๐๐๐๐๐ก๐๐๐ ≈ 23.5 × sin(−78) =23.5 X (-0.978) = -22.90° or 22°53’S So, on December 9, the sun’s direct rays are at 90° overhead at 22°53’S latitude. For our location, approximately 39°N, the noon sun angle for December 9 would be: 90°-(61.90°) = 28.10° above the horizon 1. Calculate the solar declination on the following dates: Date Solar Declination March 21 June 21 September 22 December 22 Today’s Date 2. Calculate the noon sun angle for New Orleans, USA (30°N), and for Helsinki, Finland (60°N) on each of the following dates: Date New Orleans Helsinki March 21 June 21 September 22 December 22 Today’s Date 3. What is the noon sun angle for our location (39°N) today? Show your work. 5 Name ____________________________________________ Lab 5 Daylight Hours Daylight hours also have an effect on the amount of solar radiation received at a given location. At any given time only half of the Earth is illuminated (lit up) by the sun. The division between the light and dark halves of the Earth is called the circle of illumination. This division runs through the poles during the spring and fall equinoxes. On these dates, every latitude is bisected (cut in half) and there are 12 hours of daylight and 12 hours of darkness everywhere on Earth. During most of the year, however, individual lines of latitude will not be bisected but will be disproportionately divided between light and dark. The figure below illustrates this phenomenon. You can use the figure to calculate the proportion of each latitude that is illuminated during the 24-hour day. 6 Name ____________________________________________ Lab 5 4. Use the figure on the previous page and a ruler to estimate what fraction of each latitude is illuminated during the 24-hour day. From this estimation, record the approximate number of hours of daylight on each of the following dates: Date 0° 30°N 60°N 30°S 60°S June solstice Equinoxes December solstice 5. Which latitudes experience the greatest seasonal change in daylight hours? Where is the change the smallest? 7