(For classes starting Monday, Jan. 28)
Introduction. In this
exercise (not to be turned in—it
substitutes for lecture), you'll explore some relations between sun angle,
solar radiative intensity, latitude, time of day, time of year, and temperature
the earth's surface.
Objectives. Together with a supplemental mini-lecture, you
- Definition of a flux, and of radiative intensity as an example
of a flux.
- Relation between solar radiative intensity at the earth's surface and angle
of the sun above the horizon.
- Relations between local time of day and position on the earth relative to the
- Relation between sun angle (and solar radiative intensity) and position
on the earth relative to the sun.
- How and why sun angle (and hence solar radiative intensity) varies with
latitude, time of day, and time of year.
- Relation between aspects of radiative intensity and
global temperature patterns in space and time, as
revealed by My World GIS plots and
Questions. For the Questions below, refer to:
- several globes set up around the room (with light sources to simulate the
- handouts with Figures 2-1 (PDF file), 2-2 (PDF file), and 2-5 (PDF file);
- animation of the earth orbiting the sun (Geoscience Animations, Prentice Hall, Inc., 2003); and
- My World GIS software.
(1) Refer to handout Figure 2-1.
In all three panels, assume that the rate at which solar radiation strikes a unit of area directly facing the sun is the same, and the rate is one unit of energy per unit of time. In panel (a), suppose that one unit of solar radiative energy strikes
each unit of the earth's (horizontal) surface area in one unit of time.
- What is the angle of the sun above the horizon in each of the panels (a), (b), and (c)?
- In panels (b) and (c), how many units of solar energy strike
each unit of area on the (horizontal) earth's surface in one unit of time?
- What general connection can you deduce between the sun angle and the intensity
of solar radiation striking a horizontal surface?
(2) Effects of the atmosphere:
- Why does less solar radiative energy reach the earth's surface the farther that solar radiation travels travels through
- In handout Figure 2-2, what connection can you see between the angle
of the sun above the (northern or southern) horizon at each of the locations
shown, and the distance the radiation must travel through the atmosphere before
reaching the surface at each location?
- What general connection can you deduce between the sun angle and the intensity
of solar radiation reaching the surface as a consequence? How does this connection
compare to the one you made in (1) above?
(3) Refer to handout Figure 2-2 and Figure 2-5.
- In which direction does the earth rotate around its axis of rotation?
- From the perspective of an observer orbiting the sun along with the earth, consider any particular spot on the earth. What path does that spot describe through space over the course of a full 24-hour day? How does that path compare to the latitude circle on which the spot lies? (What can you conclude about the [local] time of day at each point on a given latitude circle, compared to the [local] time of day at every other point on the latitude circle?)
- At what locations on the earth is it (solar) noon in the
figure? (Don't restrict yourself only to the specific locations shown—you
should be able to give a more complete response by considering the whole
it's solar noon at one place on every latitude circle, including latitudes where the sun doesn't rise at all during the day at that time of year.)
- Where (on each latitude circle) is it midnight?
- Where (on each latitude circle) is it 6:00 p.m.? (How can you tell?)
- Where (at which locations on the earth in the diagram) is it sunset? (Note that not all latitudes might experience sunset at the time of year shown.)
- At the time of year shown in Figure 2-2, where is sunset later than 6:00 p.m.? Where is sunset earlier than 6:00
p.m.? Is there any place in the figure where sunset is at 6:00 p.m.?
- Pick any latitude on the diagram that experiences a sunset, then locate the spot on that latitude circle where sunset occurs. From that spot, identify the direction corresponding to due west. (At any location on the earth, due west is parallel to the latitude circle through that location.) Now identify the direction where the sun is located as seen from that spot. Of course, because it's sunset at that spot, the sun would appear to be on the horizon. In what direction on the horizon would you see the sun (in particular, due west, north of due west, or south of due west), and how
can you tell? Does your answer differ at other latitudes, in both hemispheres and at the equator? What about the same questions for sunrise?
- Figure 2-5 shows the earth at three particular times of year (two solstices and an equinox). Which of those three times corresponds to the time of year shown by Figure 2-2, and how can you tell? What accounts for the difference in how each diagram shows the earth at that time of year?
(4) Refer to handout Figure 2-5
and to the globes set up in the room. How can you deduce that the number of hours of daylight at the
of the June solstice at any particular latitude is less than 12 hours, exactly 12 hours, more than 12
hours, fully 24 hours, or none at all? Answer for each of the following latitudes:
North Pole, Arctic Circle, San Francisco's latitude (about 37.5°N), Tropic
of Cancer, Equator, Tropic of Capricorn, Antarctic Circle, and South Pole.
(5) Refer to handout Figure 2-5.
- Figure 2-5 shows the earth at three times of year (the two solstices and one of the equinoxes; in most respects the other equinox is identical to the one shown). At each of the solstices and equinoxes considered separately, at which latitude does the sun appear directly overhead
at solar noon?
- Again at each time of year separately, at which latitude does the sun appear
directly on the horizon at noon?
(6) Refer to handout Figures
and (c). By determining (1) the direction from which the sun's rays strike
the earth and (2) the direction toward the southern horizon locally, show by drawing appropriate angles carefully
that the sun appears higher in the sky at noon in San Francisco at the June
solstice than it does at the time of the December solstice. (That is, show that
the sun angle in San Francisco at noon is greater at the time of the June solstice
than it is at the December solstice.) If you plotted this angle as a function
of time of year, what would it look like?
(7) Using My World GIS and monthly-average intensity of incoming
solar radiation (that is, insolation at the top of the atmosphere) data available for each month of 1987, we can plot cross
sections (profiles) along the prime meridian (0° longitude) of the monthly average intensity of incoming
solar radiation for any month of the year 1987. (Other years would look virtually the same.) In particular, we can do this for the months containing the solstices (December and June) and an equinox (for example, March). Note that for this particular data (in particular, because of the multi-day averaging), profiles along all lines of longitude are identical. (This is certainly not true for most other quantities, though!)
Here are three plots of monthly-average incoming solar radiative energy flux (insolation at the top of the atmosphere on horizontal surfaces) vs. latitude on the same graph for:
- Examine each of these three plots, and note what you consider to be their most significant features.
- How can you account for the features on the three plots (e.g., the latitude of the
maximum intensity; the strong asymmetry of the December and June plots; the almost (but not quite) symmetry of the March plot; the almost (but not quite) antisymmetry (that is, the same shape except reversed) of the June and December plots; and the latitudes where the monthly-average insolation is zero)?
(8) We can also use My World GIS and the same monthly-average insolation data to determine the global average of the monthly average incoming solar radiative intensity for any month of 1987. We'll in particular consider December and June, which contain the two solstices. To do this, do the following:
- Start My World GIS and fill the screen with it.
- Pull down the "File" menu, select "Open Project..."
- In the resulting "Open Project" dialog window, click on the "Home" icon and navigate to Courses > E535 > Class.
- Select the file "MonthlyAvgIncomingSolarRad_1987.m3vz", then click on the "Open" button.
- In the left-hand sub-window ("Layer List"), highlight (click on) the "MonAvg_IncomingSolar.wwf" panel.
- In the row of icons across the top of the "Layer List" sub-window, click on the "Show Statistics for Active Layer" icon (which looks like the capital Greek letter sigma, which is commonly used in mathematics to represent summation).
- In the resulting table of statistics about monthly average incoming solar radiation, locate the row that represents the global mean value ("Mean") and the columns for area-weighted incoming solar radiation for June and December, respectively (near the far right-hand end of the table).
Why the "area-weighted" mean and not the ordinary, unweighted mean? The global average should not be a simple (unweighted) average of monthly-average insolation values over all 10,368 grid cells in the data set. The reason is because the cells, although they are all 2.5° longitude x 2.5° latitude in size, do not all have the same area. That's because longitude lines converge at the poles, making grid cells skinnier and skinner—and hence smaller and smaller in area—the closer they are to the poles. Grid cells at lower latitudes (closer to the equator) should therefore carry more "weight" than cells at higher latitudes when computing the global average insolation. Hence, the global averages should use area-weighted values: the incoming solar radiation intensity value on each grid cell should be multiplied by the area of the grid cell; these products should be summed over the globe; and the sum should be divided by the sum of the areas of the grid cells, which is just the surface area of the earth.
- How do the area-weighted and unweighted global average values for June differ? Which one is greater, and why?
Answer the same questions about December.
- Compare the area-weighted, global-average values for June and December. Are they different? If so, by how much, and why?
(9) Using My World GIS and the same data set as above, we can determine the items listed below for
both the U.S. and for Argentina. In particular, My World GIS allows us to calculate averages (and area-weighted averages, if we need to) over subsets of the earth, including individual oceans or countries or continents. In this case, we're interested in average temperature and incoming solar radiation intensity for each month of 1987 over the contiguous 48 states of the U.S. and over Argentina, a country that spans a range of latitudes similar to the U.S., except that it is in the Southern Hemisphere.
- month with the warmest monthly-average surface temperature of 1987
- month with the coldest monthly-average surface temperature of 1987
- month with the greatest monthly-average incoming solar radiation
intensity in 1987
- month with the least monthly-average incoming solar radiation
intensity in 1987
Here are the results:
- For each country (the contiguous U.S. states and Argentina) and for each quantity (temperature and incoming solar radiation intensity), identify the highest and lowest values for the year.
- Do the highest and lowest surface temperatures and incoming solar
radiation intensities occur simultaneously—that is, in each country, is the month
with the warmest (or coolest) average surface temperature the same as the month
with the greatest (or least)
incoming solar radiation intensity?
Assignments, Handouts, etc.