Clocks set for solar time for a particular site will read exactly 12:00 noon when the sun is true south (or true north). This is solar noon. The sun is "as high" in the sky as it will get that day for the site. The solar incidence angle (qz) between the perpendicular to the horizontal and the sun beam is minimum for the day. For this period of the year (ie, about January 15th), in terms of Pacific Standard Time, when is it solar noon in Seattle? Clearly show how you arrived at your answer.
Where are you?
Imagine it is January 1, 2003. The weather is clear, so you can see your shadow. You are standing on flat, horizontal ground. The elevation of the land is fairly high, about 1 mile. There is a very famous mountain about 200 km south southeast from your location. The length of your shadow is 40% of your height – your shadow is as short as possible for the day. It is 1:23 AM (ie, 23 minutes after 1AM) solar time in Seattle. Where are you? Clearly show how you arrived at your answer. Note the longitude of Seattle is West 122.30 degrees. You may need to use an atlas. There are some on the web, eg, http://atlas.dhs.org/RealWorld/Applicatio/WorldAtlas
Solar energy for Honolulu for May 25th.
Hourly solar energy flux data for May 25, 1990 for Honolulu are given in the first part of the MS EXCEL file I’m sending you (342.02.HW2.data.xls).
Define
the solar radiation data listed in each of the columns F, G, H, I, and J. For example, one of the columns is GLOBAL (for the ground).
To the right of the columns a plot is shown. This is a plot of the extraterrestrial solar energy flux component perpendicular to the ground (ie, received by a 1 meter square surface parallel to the ground at the edge of the earth’s atmosphere). Note the peak value of this solar energy flux (w/m2). What does this value tell you about the position of the sun in the sky at solar noon on May 25th in Honolulu? Would one see their shadow (assuming cloud is not blocking the sun)? Provide answer and explanation.
Suppose you made a new plot, dividing the solar energy flux data in my plot by 1331 w/m2, the "solar constant" for the day. Your new plot would be the cosine of a very important angle. What is this angle called? Write the angle’s equation in terms of sines and cosines of other angles.
Farther to the right, seethe plot of the global, beam, and diffuse solar energy flux at ground level versus the solar time. Using bullet format, succinctly point out four major and interesting features of the data plotted.
The transmissivity of the atmosphere above Honolulu on this day may be determined by dividing the ground-level beam radiation by the extraterrestrial beam radiation. Did at least 70% of the solar constant radiation reach the ground as beam radiation? Show your calculation.
Make a plot of the diffuse solar energy flux divided by the global solar energy flux. Restrict your ratio to the red/yellow sector on the spread sheet. Comment on your plot: generally, how does the diffuse/global ratio vary over the day (when the sky is clear or mostly clear-as the case for 5/25/90 in Honolulu).
If you are unfamiliar with making plots on MS EXCEL spread sheets, please follow these steps:
Copy and paste the existing plot, thus, making a new template,
Click your new plot, thus highlighting it with black squares at the corners.
A right-click of the plot should cause a menu to appear.
Click "source data" on the menu.
On the new image that appears, click "series".
Note the three boxes:
Name: type in the new name of the data you want to show (= "name").
X-Values: this is OK, do not change.
Y-Values: click the icon at the right. A new box will appear. Go into the data columns, highlight the data you want to plot, and then click the icon in the box. The new data should now replace the old data on your plot. To add a new set of data to your plot, click "add". Insert the name (as above), and the X-Values and Y-Values (as done above). The new data should appear on your plot.
If you are unsure of this procedure, please visit one of our Office Hours for tutorial.
Comparing daily average solar energy.
Now look at the second part of 342.02.HW2.data. That is, look at the average daily data for Honolulu, Seattle, and Phoenix. These data are shown for each month and for the year. (The data are 30-year averages.) To the right of the Honolulu data, I’ve made a plot of the global data (watt-hours/m2/day) for the three cities and for eastern Montana (which has about the same latitude as Seattle, but is pretty sunny).
Look at the yearly value for AETRN. It is the same for the three cities (16405 watt-hours/m2/day). Explain why it is independent of location. (Note that a very famous value appears if you divide by 12.)
Now look at the yearly values for AVETR. These vary with location. Divide by 24. Explain the variation with respect to location and relative to the familiar value of 342 w/m2.
Now look at the monthly AVGLO data. Divide by 24. Do any of the locations have a 6-months hourly average exceeding 300 w/m2 This was mentioned in class as indicative of a very sunny location?
Look at my plot of the three cities plus eastern Montana. In bullet format, briefly state four distinct differences or similarities between the three cities.
Seattle cannot do much about its location (47.5 degrees latitude). What if there were fewer clouds and rain – about much how increase in the yearly solar energy might be possible? Express your answer as a percentage increase, and show how you obtain it.