ASSIGNMENT # 1. SUN'S ALTITUDE CALCULATION - Tagged

GEOG. 1 Chapter 2. Solar Zenith Angle and Sun’s Altitude Fall 2020 Subsolar Point and Sun’s declination during the Solstices and Equinoxes Introduction: The solar zenith angle is defined to be the angle between the sun and a line that goes straight up (to the zenith) In reality the sun is very far from Earth and relative to this distance the Earth is very small. In the drawing (below) The Earth is drawn much larger than it should be if the vertical scale matched the horizontal scale. The main point is that all rays that leave the sun and hit the Earth travel essentially parallel to each other as they reach Earth. In the figure at left Z is the zenith angle and A is the altitude (A=90-z); the angle from the horizon to the sun. 1 | P a g e SSP SSP SSP SUN DECLINATION

GEOG. 1 Chapter 2. Solar Zenith Angle and Sun’s Altitude Fall 2020 2 | P a g e

GEOG. 1 Chapter 2. Solar Zenith Angle and Sun’s Altitude Fall 2020 Using the Analemma (on next page). 1. Using the analemma provided, determine is the approx. declination (latitude of the vertical ray) on: (you may round to the nearest degree) a. Sept 10 _____________ b. July 4 _____________ c. Dec 21 _____________ 2. Using the analemma provided, determine the approx date (or dates) when the declination is at: a. 10° N ____________ b. Equator __________ c. 19° S _____________ 3. Refer again to the Analemma (next page) accompanying this exercise: a. On what date does the sun have its highest declination in the Northern Hemisphere? _______________ b. On what date does the sun have its highest declination in the Southern Hemisphere? _______________ c. On what two dates does the sun cross the equator? ____________ d. Why is it better to refer to the June and December solstices rather than summer and winter solstices? In Summary, to calculate the solar Zenith Angle at noon for your latitude: 1. determine your latitude 2. determine the latitude for which the sun is directly overhead at noon (the declination). 3. subtract the declination from your latitude. For example: Calculating Noon Sun Angle (video) The noon zenith angle at the tropic of cancer on June 21 is zero since the sun is directly overhead 23.5 N on June 21 ***The noon zenith angle at the North Pole (90 N) on June 21 is 66.5 since the sun is directly overhead 23.5 N on June 21 I.e. 90-23.5 = 66.5 The noon zenith angle at in Anchorage (60 N) on Dec 21 is 83.5 since the sun is directly overhead -23.5 (23.5 S) on Dec 2 i.e. 60- (-23.5) = 83.5. The altitude of the sun above the horizon is 90 - zenith angle . For Anchorage on Dec. 21 the sun is 6.5 degrees above th horizon at noon. 4 | P a g e

GEOG. 1 Chapter 2. Solar Zenith Angle and Sun’s Altitude Fall 2020 5 | P a g e

GEOG. 1 Chapter 2. Solar Zenith Angle and Sun’s Altitude Fall 2020 On what day would you expect the sun to be overhead at Miami Florida (latitude 26 o N):? a.September 15 b.December 22 c.February 4 d.March 10 e.April 27 f. never Calculating a Maximum Sun Angle for Any Date. One of the critical factors which determines the amount of insolation (incoming solar radiation) received at a given location and date is the maximum sun angle (high angles=high energy, low sun angles=low energy). Max sun angle changes seasonally and is depended entirely on date and latitude. The basic formula is as follows: Altitude A = 90 – (Latitude L +/- Declination D) 1. What is the max sun angle for Seattle, WA on May 16? (Hint: Follow the formula above. You will need to get the declination from the analemma.) Does the sun pass through the northern or southern sky? (Hint: If declination is south of the location on that date, the answer is southern sky. Vice versa for Northen sky…) show your work 2. What is the max sun angle for Darwin, Australia on June 22? (Hint: Same as above, but beware that Darwin is in the Southern Hemisphere and the declination is in the Northern Hemisphere. This makes it a bit tricky.) Does the sun pass through the northern or southern sky? (Hint: Same as above.) show your work. Questions to test your understanding. When the sun is directly over your head the solar zenith angle is 0.0 degrees and the solar Altitude is 90 degrees __________ At sunrise or sunset the solar zenith angle is _____ 90 degrees ______ and the solar Altitude is _____ 0.0 degrees _______ What is the noon zenith angle in Orlando Florida (latitude 28.5 o ) on Sept 21? ____ 28.5 o ______ What is the noon zenith angle in Anchorage (60 N) on June 21? (show your calculations) 60-23.4=36.5 o More answer below What time of day is it? a. early morning b. late morning c. noon d. early afternoon e. late afternoon. f. not enough information 7 | P a g e