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You can receive a maximum of 20 points (100%) for this exercise, including the extra credit.

Question

You can receive a maximum of 20 points (100%) for this exercise, including the extra credit.The purpose of

this exercise is to illustrate the differences in the solar radiation budget at different latitudes during different times of year. The amount of insolation (INcoming SOLar radiATION) absorbed by a particular geographic location is controlled by several factors:

  • The angle of incidence (i.e. the angle at which the sun’s rays hit the ground)
  • The daily duration of sunlight
  • The absorption and reflection by both the atmosphere and surface

We will consider the first two factors in this exercise.

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The angle of incidence and daily duration of sunlight are directly related to latitude and solar declination. Solar declination is another name for the subsolar point and is defined as the location (latitude) on the earth where the sun is directly overhead; declinations range from 23.5˚ N to 23.5˚ S.A. Latitude and the Angle of Incidence

Table 1 shows the angle of incidence horizon at noon and the time of sunrise and sunset during the March equinox, June solstice, and December solstice for three locations on the earth. Use these data to answer the following questions.

Table 1. The Sun’s PathLocationDateSunriseAngle of incidence at noonSunset 70˚ N (Prudhoe Bay, AK) 3/21 6:00 a.m. 20˚ 6:00 p.m. 6/22 4˚ above horizon
at midnight 43˚ 4˚ above horizon
at midnight 12/22 None None None 40˚ N (Provo, UT) 3/21 6:00 a.m. 50˚ 6:00 p.m. 6/22 4:30 a.m. 74˚ 7:30 p.m. 12/22 7:30 a.m. 27˚ 4:30 p.m. 1˚ S (Amazon Delta, Brazil) 3/21 6:00 a.m. 89˚ 6:00 p.m. 6/22 6:00 a.m. 66˚ 6:00 p.m. 12/22 6:00 a.m. 66˚ 6:00 p.m.

  1. Graphs: For each location (latitude) in Table 1 plot the sun’s “path through the sky” by marking the angle of incidence at sunrise, noon, and sunset and then connecting the three dots with a line (angle of incidence for sunrise and sunset will be 0 degrees above the horizon for all except Prudhoe Bay on June 22). The y-axis will represent angle of incidence and range from 0 to 90 degrees, and the x-axis will represent 24 hours, midnight to midnight. For each graph (3 total) be certain to include a descriptive title, a legend to indicate which line represents which day, and label both axes, including units of measure. You can use a program such as Excel or draw the graphs by hand. If you draw them by hand please use graph paper, and either scan them or take photos so you can upload the entire exercise as one file on Brain Honey (pdf is fine). (2 pts. per graph)
  2. Analysis: What is the effect of latitude on the sun’s path across the sky? Write a short paragraph summarizing what the graphs in step 1 show. Include a comparison of the similarities and differences among the latitudes in terms of sunlight duration and angle of incidence. (2 pts.)

B. Insolation Curves

Table 2 shows yearly insolation data measured in Langleys/day. All values are for the fifteenth day (24-hour period) of each month at three latitudes at sea level.

Table 2. Insolation dataLat. Jan.Feb.Mar.Apr.MayJun.Jul.Aug.Sep.Oct.Nov.Dec. 0° 480 512 530 518 500 485 490 520 550 547 507 475 45˚N 152 245 367 465 582 625 605 537 415 285 180 130 90˚N 0 0 0 155 482 667 610 303 27 0 0 0

  1. Plot the data with the months on the x-axis and insolation (Langleys/day) on the y-axis. Draw a curve connecting the data points for each latitude. Be sure to label the axes and include a legend, title, and units of measure. Again, you can either use a program such as Excel or draw the graph by hand and scan it or take a photo to include it with your document. (2 pts.)

Answer the following questions using your graphs, textbook, and course lecture material.

  1. From Table 2, identify the highest and lowest values of insolation for each latitude, and the month when they occur. Create a table like this one to fill in your data. (3 pts.)
    
45˚    
90˚    
  1. Which latitude exhibits the greatest yearly range of insolation (biggest difference between highest and lowest value)? (1/2 pt.)
  2. Explain why the range is greatest at this latitude. (Your explanation should include consideration of duration and intensity of insolation.) (2 pts.)
  3. Which latitude exhibits the smallest yearly range of insolation? (1/2 pt.)
  4. Explain why the range is smallest at this latitude. (Your explanation should include consideration of duration and intensity of insolation.) (2 pts.)
  5. Why are there two peaks on the 0˚ latitude curve? (2 pts.)

Extra Credit

Suppose the insolation data in table 2 were taken on the 25th day of the month, instead of the 15th. Explain how and why the values for September and March at 90˚ N would be different. (1 pt.)

 
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