Solutions to Lab Exercise #2: Solar Radiation & Temperature Part II: Exploring & Interpreting Data

METR 104: Our Dynamic Weather (w/lab) Solutions to Lab Exercise #2: Solar Radiation & Temperature Part II: Exploring & Interpreting Data (10 points) Dr. Dave Dempsey Dept. of Geosciences SFSU, Spring 2013 Prior Knowledge Required. Before starting this lab, you should know the meaning of: angle (a measure of the degree of "spread" between two intersecting lines) down (the direction in which gravity pulls, toward the center of the earth) horizon (the points far away where sky meets earth in the absence of obstructions) horizontal (oriented in a direction perpendicular to down) insolation (intensity of solar radiation striking a surface) midlatitudes (latitudes between 30 and 60, in both hemispheres) perpendicular (at an angle of 90 to, at right angles to) radiative intensity (rate at which radiative energy strikes a unit of surface area) sun angle (angle between the sun and a horizontal surface) In addition, you should know these facts: 1. The times of the year when the earth is closest to, and farthest from, the sun. 2. The average distance of the earth from the sun; how much that distance varies in a year. 3. The annual average insolation on a surface directly facing the sun at the top of the atmosphere. 4. The approximate diameter of the earth. 5. The depth of the atmosphere (at least, the part containing 99.9% of all air). And finally, you should be able to: 1. Identify three reasons why the intensity of solar radiation (insolation) striking a horizontal surface at the top of the atmosphere might vary over time. 2. Describe how insolation (at a given sun angle) depends on distance from the sun (due to a different "spreading out" effect). 3. Identify three things that can happen to solar radiation when it enters the atmosphere. 4. Describe how the distance that solar radiation travels through the atmosphere before reaching the earth's surface depends on sun angle. 5. Describe how insolation on a horizontal surface depends on sun angle due to a "spreading out" effect. 6. Describe how insolation on a horizontal surface at the earth's surface depends on sun angle (due to effects #4 and #5 above, combined). 1

Learning Objectives. After completing this activity, you should be able to: Identify ways in which insolation on a horizontal surface at the earth's surface does, or does not, seem to "explain" observed features of daily temperature cycles. Describe differences in observed solar radiation intensity: o over the course of a day o at the top of the atmosphere on a surface facing the sun vs. on a horizontal surface o at the top of the atmosphere vs. at the earth's surface (both on a horizontal surface) o at the earth's surface on a horizontal surface at different times of the year Propose possible explanation(s) for the differences listed above, and test those explanations using relevant evidence and reasoning Identify aspects of this investigation of solar radiation and temperature observations that illustrate aspects of the process of science. Materials Needed. To complete this activity, you will need: Meteograms for Hanford, CA (weather station KHJO) ending at these times: o 09Z May 24, 1999 o 07Z December 17, 1998 Plots of one-hour average solar radiation fluxes recorded at Hanford, CA on the days covered by the two meteograms above: 1. Insolation on a horizontal surface at the earth's surface (Dec. 16, 1998) 2. Insolation at the top of the atmosphere, on a surface directly facing the sun and on a horizontal surface (Dec. 16, 1998) 3. Insolation on a horizontal surface, at the top of the atmosphere and at the earth's surface (Dec. 16, 1998) 4. Insolation on a horizontal surface at the earth's surface (Dec. 16, 1998 and May 22, 1999) 5. Insolation on a horizontal surface at the earth's surface (May 22, 1999) 6. Insolation at the top of the atmosphere, on a surface directly facing the sun and on a horizontal surface (May 22, 1999) 7. Insolation on a horizontal surface, at the top of the atmosphere and at the earth's surface (May 22, 1999) (The solar radiation data used to create these plots come from the National Solar Radiation Database 1998-2005 Update. A Microsoft Excel file containing the edited data used to create the plots, along with the plots themselves, can be downloaded at SolarRadiation_HanfordCA_1998-99_Lab2-II_wColumnCharts.xlsx.) 2

I. Introduction II. Instructions 2) a) General Tasks: Task #1: Compare observations of insolation on a horizontal surface at the earth's surface in late May and mid December, at the same (midlatitude) location. Also compare each of them to the corresponding temperature observations at the same location over a full 24 hours. Task #2: Compare observations of solar radiation intensity at the top of the atmosphere (i) on a surface perpendicular to the sun's rays (that is, directly facing the sun) and (ii) on a horizontal surface. Task #3: Compare observations of insolation on a horizontal surface (i) at the top of the atmosphere and (ii) at the earth's surface, on the same day and at the same (midlatitude) location. b) Identify the meteograms and/or insolation graphs that seem most relevant to each task. (Group members should all agree.) Task #1: Figure #1, Figure #4, Figure #5 Task #2: Figures #2 and #6 Task #3: Figures #3 and #7 Task #1 details: In Step (d) below, for your explanations and evidence cited, try to use facts and/or ideas from Page 1 of this lab, the concept map, or data from Lab #2, Part I. a) You have been given two meteograms for Hanford, CA, each covering part of one day and all of the next. One starts on December 15 and runs through December 16, 1998 (local time). The other starts on May 22 and runs through May 23, 1999. The time is labeled in UTC (standard time in Greenwich, England). On each meteogram, identify and label some key local standard times, such as midnight, noon, sunrise and sunset. [On December 16, 1998, the sun rose at Hanford at 7:03 am and set at 4:45 pm. On May 22, 1999, the sun rose at 4:44 am and set at 7:04 pm. ] See annotated meteograms. 3

For each meteogram, as best you can, describe the pattern of temperature over the course of a 24- hour day on December 16, 1998 and on May 22, 1999 (local time). (For example, when (local standard time) is the temperature at a minimum, when does it reach a maximum, how does it behave between maximum and minimum points, what are the maximum and minimum temperatures, etc.?) On December 16, the temperature reaches a low of 31 F near sunrise (5-8 am), rises to a high of 59 F in midafternoon (3 pm), and falls again thereafter. On May 22, the temperatures reached a low of 57 F at a time that precedes the meteogram (but could be near sunrise), rises to a maximum of 88 F (based on the plot) or 90 F (based on the reported high) in late midafternoon (3-5 pm), and falls again thereafter to a low near sunrise (5 am) the next day. b) You also have two plots of insolation on a horizontal surface at the earth's surface recorded at Hanford, CA, for December 16, 1998 and for May 22, 1999. For each plot, describe (but don t compare) the pattern of insolation over the full day. On December 16, the insolation was zero from midnight through 7 am. From 7-8 am to 11am- 12 pm, the insolation increased to a peak of around 500 W/m 2. From the peak it decreases to zero again between 5-6 pm and stayed there to midnight. On May 22, the insolation was zero from midnight through 5 am. From 5-6 am it rose to a peak of almost 1000 W/m2 at 11 am- 12 pm and was almost as high at 12-1 pm. Then it decreased to zero again at 7-8 pm and stayed there to midnight. c) Identify ways (if any) in which the pattern of insolation observations appears to "explain" the pattern of temperature observations, and ways (if any) that it doesn't, at least not very satisfactorily. (Comment on what you mean by "explain.) By explain I mean that greater insolation should cause higher temperatures, so when the insolation increases or decreases, so should the temperature. On December 16, the insolation and temperature either are both decreasing or both increasing or both not changing from 5-7 am, from 8-9 am to 11 am- 12 pm; and from 3 pm to 5-6 pm. During these periods, insolation explains temperature well. At all other times the temperature is falling while the insolation doesn t change (at night), or temperature is increasing while insolation is decreasing (noon to 3 pm), and so insolation doesn t explain temperature well. On May 22, we don t know what the temperature was doing before 7 am. However, the insolation and temperature were otherwise varying in the same sense from 7 am through 11 am- 12 pm and from 5 pm to 7-8 pm, so insolation explains temperature well then. Otherwise not: the temperature was falling while insolation didn t change (after sunset at 7 pm), or temperature was rising while insolation was hardly changing or falling (12-1 pm to 3 pm). 4

d) Referring to the two graphs: o What differences do you see between the two graphs? 1. Insolation is greater on May 22 than December 16 at every hour. 2. Insolation doesn t become greater than zero until 3 hours later on Dec. 16 than May 22, and it goes back to zero two hours earlier (that is, there were fewer hours of daylight). 3. (Other differences are trivial I hope they don t crop up.) o For one of the differences not already used as an example by the instructor, pose two possible explanations. The second difference above was used as an example, so it s no eligible. Other differences are too trivial to address, or I m missing something significant. 1. a. The sun angle is greater at every hour on May 22 than on Dec. 16. b. The earth is closer to the sun on May 22 than on Dec. 16. c. The output of the sun was greater on May 22 than on Dec. 16. d. It was cloudier on Dec. 16 than on May 22. 2. (Not eligible used as an example.) o For each possible explanation, cite a piece of evidence that either supports or contradicts the explanation. 1. a. Check sun angle observations on original data table. (Supports the explanation.) b. Check facts: earth is closest to the sun in early January, farthest in early July, so not likely closer in May than in December. (Does not support the explanation.) c. Consult plot of solar output from 1975 to 2012 or so (presumably at earth s average distance from the sun). Shows no more than perhaps 10 W/m 2 variation over 38 years, but difference between May and December insolation is close to 500 W/m2 during many hours of the day. (Does not support the explanation.) d. Meteograms show clear or mostly clear skies on both days. (Does not support the explanation.) 5

Task #2 details: In Steps (a) through (c) below, for your explanations and evidence cited, try to and/or ideas from Page 1 of this lab, the concept map, or data from Lab #2, Part I. 1. You have been given two graphs: Figures #2 and #6. o On the graph for December 16, 1998, what similarities and differences do you see between the two plots shown? 1. On the surface directly facing the sun, the insolation doesn t vary over the course of the day (except for the first and last hours), while on a horizontal surface the insolation increases to a peak from 11 am- 12 pm and then decreases again. 2. On the surface directly facing the sun, the insolation is greater than on the horizontal surface at every hour. o For one of the differences not already used as an example by the instructor, pose two possible explanations. 1. a. The sun angle varies on the horizontal surface but not on the surface directly facing the sun. b. The distance from the sun didn t change for the surface directly facing the sun, while it varied for the horizontal surface. c. The clouds or something else in the atmosphere varied for the horizontal surface but not for the surface directly facing the sun. d. The output of the sun varied for the horizontal surface but not for the surface directly facing the sun. 2. a. The sun angle was greater on the surface directly facing the sun than it was on the horizontal surface. b. The surface directly facing the sun was closer to the sun than the horizontal surface was. c. There were more clouds or something else in the atmosphere over the horizontal surface than over the surface facing the sun. d. The output of the sun was greater for the surface facing the sun than for the horizontal surface. 6

o For each possible explanation, cite a piece of evidence that either supports or contradicts the explanation. 1. and 2. a. Consult the sun angle observations on the original data table. Invoke the fact that on a surface directly facing the sun, the sun angle is 90. (Supported.) 1. and 2.b. Both surfaces are located at the same spot at the top of the atmosphere, so they must be at the same distance from the sun. (Not supported.) 1. and 2.c. Both surfaces are at the top of the atmosphere, so clouds can t explain any differences. (Not supported.) 1. and 2.d. The insolation on each surface was observed at the same time and same place, so the output of the sun had to have been the same for both. (Not supported.) b) Refer to the plots of observed insolation on a surface perpendicular to the sun's rays on May 22, 1999 and on December 16, 1998. o What differences do you see between the two plots? 1. The insolation on December 16 was about 80 W/m 2 greater than it was on May 22. 2. The length of daylight was greater on May 22 than on December 16 (by several hours) o For one of the differences not already used as an example by the instructor, pose two possible explanations. 1. a. The earth was closer to the sun on December 16 than on May 22. b. The output of the sun was greater on Dec. 16 than on May 22. c. The sun angle was greater on Dec. 16 than on May 22. d. Cloud cover was greater on May 22 than on Dec. 16. o For each possible explanation, cite a piece of evidence that either supports or contradicts the explanation. 1. a. The earth is in fact closest to the sun in early January and farthest in early July. Hence, we d expect the earth to be closer to the sun on Dec. 16 than on May 22. (Supported.) 7

b. The plot of solar output over the last 38 years shows output varying by no more than maybe 10 W/m 2, which is nowhere near enough to account for the observed difference of 80 W/m 2. (Not supported.) c. and d. (Trivially addressed.) c) Refer to the plots of observed insolation on a horizontal surface at the top of the atmosphere, on May 22, 1999 and on December 16, 1998. o What differences do you see between the two graphs? 1. Insolation is greater at every hour on May 22 than on December 16 (except at night). 2. Insolation becomes non- zero several hours earlier and returns to zero several hours later in May than in December. o For one of the differences not already used as an example by the instructor, pose two possible explanations. 1. a. Sun angle is greater on May 22 at every hour than on December 16. b. The earth is closer to the sun on May 22 than on December 16. c. There was more cloud cover on December 16 than on May 22. d. The output of the sun was greater on May 22 than on December 16. 2. (Not eligible: used as an example by the instructor.) o For each possible explanation, cite a piece of evidence that either supports or contradicts the explanation. 1. a. Check observed sun angles on the original data table. (Supported.) b. Earth is closer to the sun in December than in May. (Not supported.) c. According to the meteograms, both days were essentially cloud free. (Not supported.) d. According to the plot of solar output provided, solar output varies by no more than perhaps 10 W/m 2 over the last 38 years, whereas the observed insolation differences between December 16 and May 22 are perhaps around 800 W/m 2. (Not supported.) 8

Task #3 details: In Step (a) below, for your explanations and evidence cited, try to use facts and/or ideas from Page 1 of this lab, the concept map, or data from Lab #2, Part I. a) You have two graphs that each show plots of observed insolation from Hanford, CA on a horizontal surface, at (a) the top of the atmosphere and (b) the earth's surface. One graph shows observations for the period from midnight to midnight on May 22, 1999 (standard time), while the other shows observations from midnight to midnight on December 16, 1998. o On the graph for December 16, 1998, what similarities and differences do you see between the two plots? 1. Difference: Insolation is greater at every hour at the top of the atmosphere than at the surface. 2. Similarity: Insolation is greater than zero during the same period of time for both. o For one of the differences not already used as an example by the instructor, pose three possible explanations. 1. a. The atmosphere absorbed some solar radiation and scattered and reflected some back to space, thereby preventing part of it from reaching the surface. b. Clouds in particular prevented some solar radiation from reaching the surface. c. The top of the atmosphere is closer to the sun than the surface is. d. The sun angle at the top of the atmosphere was greater than it was at the surface. o For each explanation, cite a piece of evidence that either supports or contradicts the explanation. 1. a. If true, then the ratio of insolation at the surface to insolation at the top of the atmosphere should decrease with decreasing sun angle. Calculating these ratios from the original data table or eyeballing the ratios from the graph, and cross- comparing them with the observed sun angles from the data table, shows that the ratio in fact does decrease with increasing sun angle. (Supported.) b. The meteogram shows essentially no cloud cover on December 16. (Not supported.) 9

c. If true, then this explanation must account for differences in insolation of up to 200 W/m 2 or a bit more. The top of the atmosphere (or 99.9% of it, anyway) is about 30 miles above the surface. The difference in distance to the sun between the top of the atmosphere and the earth s surface is maximum at noon, and although it isn t the full 30 miles (because the sun isn t directly overhead at noon at Hanford), we ll give it the benefit of the doubt. Now, we note that for the observations of insolation on a surface directly facing the sun at the top of the atmosphere on December 16, the sun angle doesn t vary and the atmosphere has no effect, but the distance to the sun varies as the earth rotates, from noon (closest to the sun) to sunrise and sunset (farthest), by something close to the radius of the earth (4,000 miles) or, because the diameter of Hanford s latitude circle is smaller than the earth s diameter, something less than that (let s estimate very conservatively, 1000 miles). Hence, if the possible explanation would predict that we d see a much larger variation in insolation than the ~200 W/m2 variation to which we attribute a difference in distance to the sun of only about 30 miles. However, the observations show no discernible difference in insolation over the course of the day at the top of the atmosphere facing the sun. Hence, the distance from the sun explanation is not supported. Similarly, we could look at the insolation at the top of the atmosphere facing the sun on May 22 and December 16. Those insolation observations differ by about 80 W/m 2, but the difference in distance to the sun between those times is close to 3,000,000 miles. Hence, a difference in distance of 30 miles couldn t produce a difference in insolation of ~200 W/m 2. (Not supported.) d. Both surfaces are horizontal (according to the plot title). Horizontal means perpendicular to up (and down ), but up is in the same direction at the earth s surface and at the top of the atmosphere, so horizontal surfaces at each place are parallel. Since the sun s rays at each location are also parallel, the sun angle must be the same at both places. (Not supported.) 10