In this module we will be focusing on the variation in energy levels and temperature across your state. I will introduce how we are going to analyze these using the state of Wisconsin and then you will do the same type of analysis for your state. Make sure to read thoroughly through the Wisconsin part paying particular attention to the equations, example graphs, and how I analyze the data. As you go through this section, please feel free to reach out to me if you have any questions about how things are completed. This way you can be successful in your analysis of your state.
Part 1: Solar Intensity
In this section, we will examine and calculate the changes in solar angles and, thus, solar intensity across Wisconsin throughout the year. This is the most direct way to examine and see the occurrence of seasons.
In the building knowledge section, you learned the latitude of the sun’s direct solar energy varies throughout the year. Since this location changes every day of the year that causes the intensity of the radiation a location receives to change. These measurements are easy to determine by following a few simple steps and plugging some numbers into some equations. When analyzing a larger amount of data one tool we can use to help organize that is Excel. As the different concept are introduced, I will also introduce the techniques to do this analyze in Excel.
Determining Solar Declination
We already know the solar declination for 4 days out of the year, the two solstices and the two equinoxes because these four days are benchmarks in the solar declination. The March Equinox occurs on March 21 and the solar declination is 0°, the June Solstice occurs on June 21 and the solar declination is 23.5°N, the September Equinox occurs on September 21 and the solar declination is 0°, and the December Solstice occurs on December 21 and the solar declination is 23.5°S
To determine the solar declination on other days of the year an analemma (figure below) must be utilized. Each day is represented by a black or white box and once the appropriate day of the year is found then a latitude of the solar declination can be determined from the left-hand scale on the image.
Example: If asked to find the solar declination on October 7, find the box that corresponds to October 7. The answer you should get is 5°S.
Determining zenith angle
The next step leading us to find solar intensity is to find the zenith angle (Z) using the following equation:
𝑍
=
|
𝑋
−
𝑌
|
Where X is the latitude of the solar declination and Y is the latitude of the location you are trying to determine the zenith angle for. For X and Y, use a positive number for latitudes of the location and/or solar declination in the northern hemisphere and negative numbers for latitudes of the location and/or solar declination in the southern hemisphere.
Example: What is the Zenith Angle of Wisconsin Dells (43.6°N) on October 7. Above we found that the solar declination was 5°S (since this is in the southern hemisphere it needs to be entered as a negative number) on October 7. Thus, our equation would be:
𝑍
=
|
−
5
−
43.6
|
=
|
−
48.6
|
=
48.6
Determining the Sun Angle (S)
The next step is to determine the sun angle (S) using the following equation:
𝑆
=
90
−
𝑍
Example: What is the Sun Angle on October 7 in Wisconsin Dells.
𝑆
=
90
−
48.6
=
41.4
Determining the Solar Intensity
The final step is to calculate the solar intensity (SI) in a percentage using the following equation:
𝑆
𝐼
=
100
×
(
𝑆
𝐼
𝑁
(
𝑆
)
)
Example: What is the solar intensity on October 7 in Whitewater:
𝑆
𝐼
=
100
×
(
𝑆
𝐼
𝑁
(
41.4
)
)
=
100
×
0.6631
=
66.3
Wisconsin Example of These Steps
To see how solar intensity changes throughout the year and across space we are going to analyze the above items for the 21st of each month at three locations: 1) the southernmost latitude of the state, 2) the northernmost latitude of the state, and the center latitude of the state.
Again, this will be a lot of calculations so a good way to organize this is in Excel. Here is an Excel template that you can use when you end up doing this for your state.
The first step is we need to find the northernmost and southernmost latitudes of Wisconsin. We will accomplish this by doing a search online. Make sure to make a reference/citation for where you get this information because for most people this is not general knowledge. After doing this search for Wisconsin, I found:
Southernmost latitude: 42.5°N
Northernmost latitude: 47.3°N
Center latitude: Find the midpoint between the above 2; find the difference between the above 2 points and then divide by 2, finally add that result to the southernmost latitude. For Wisconsin, 47.3 – 42.5 = 4.8/2 = 2.4; 42.5+2.4 = 44.9°N
Equations to use in Excel to calculate zenith angles, sun angles, and solar intensities for these points: (NOTE: all US states will have their points in the northern hemisphere, however, some of the solar declinations will be in the southern hemisphere and should be entered as negative numbers for calculations to work properly)
Zenith Angle: “=ABS([cell of solar declination] – latitude of northernmost/center/southernmost point)”
An “=” indicates to Excel that it is the start of a formula or calculation
“ABS” tells Excel to take the absolute value of whatever is in the parentheses
For example, using the template file for January 21 for the northernmost latitude would be “=abs(B3-47.3)”
Sun Angle: “=(90-[cell with zenith angle])”
For example, using the template file for January 21 for the northernmost latitude would be “=(90-C3)”
Solar Intensity: “=(100*(SIN(RADIANS([cell with sun angle]))))”
“SIN” tells Excel to take the sin value of what is in the parentheses
Excel works in radians but our calculations are in degrees so we need to tell Excel to convert our degrees into radians by using the RADIANS function.
For example, using the template file for January 21 for the northernmost latitude would be “=(100*(SIN(RADIANS(D3))))”
Round this to the nearest tenth of a percentage in Excel using the decrease decimal icon on the top banner of the home tab in Excel
Here are the results of doing these calculations for Wisconsin:
Date
Solar Declination
Northernmost Latitude (47.3°N)
Center Latitude (44.9°N)
Southernmost Latitude (42.5°N)
Zenith Angle
Solar Angle
Solar Intensity
Zenith Angle
Solar Angle
Solar Intensity
Zenith Angle
Solar Angle
Solar Intensity
21-Jan
-22
69.3
20.7
35.3
66.9
23.1
39.2
64.5
25.5
43.1
21-Feb
-11
58.3
31.7
52.5
55.9
34.1
56.1
53.5
36.5
59.5
21-Mar
0
47.3
42.7
67.8
44.9
45.1
70.8
42.5
47.5
73.7
21-Apr
11
36.3
53.7
80.6
33.9
56.1
83.0
31.5
58.5
85.3
21-May
20
27.3
62.7
88.9
24.9
65.1
90.7
22.5
67.5
92.4
21-Jun
23.5
23.8
66.2
91.5
21.4
68.6
93.1
19
71
94.6
21-Jul
21
26.3
63.7
89.6
23.9
66.1
91.4
21.5
68.5
93.0
21-Aug
12
35.3
54.7
81.6
32.9
57.1
84.0
30.5
59.5
86.2
21-Sep
0
47.3
42.7
67.8
44.9
45.1
70.8
42.5
47.5
73.7
21-Oct
-10
57.3
32.7
54.0
54.9
35.1
57.5
52.5
37.5
60.9
21-Nov
-20
67.3
22.7
38.6
64.9
25.1
42.4
62.5
27.5
46.2
21-Dec
-23.5
70.8
19.2
32.9
68.4
21.6
36.8
66
24
40.7
Now you will complete this same table for your state. Remember to first look up your northernmost and southernmost latitudes (keep track of where you find this data).
Use the solar intensity data for your 3 locations and create a line graph to visualize the changes throughout the year and across space. Here is a YouTube video on how to make graphs: https://youtu.be/TfkNkrKMF5c?si=PALP3oj3J6pa3eJPLinks to an external site.
You will have some reflection to write up based on this data, but we will save those directions for the end of this assignment.
Part 2: Converting to Solar Intensity to Energy Amounts
In this section, we are going to convert those solar intensity values to actual energy amounts. When doing this we will focus on what is called top of the atmosphere energy; in other words, the amount of energy that reached the top of the atmosphere. We will then use some average depletion percentages to determine the amount of energy that reaches the surface to examine the atmospheric depletion that occurs under different circumstances. These eventual leads us to calculate the amount of solar energy being absorbed by the surface of the Earth which in turn is what heats the lowest part of the atmosphere.
Calculating the top of the atmosphere energy levels
The average top of the atmosphere energy at the solar declination is 1360 Watts per square meter. To calculate the energy levels at a given location at a given time we can simply take the solar intensity value in a percent and multiply it by 1360. This will give us the solar energy levels received at that given location and time.
For example, if we go back to the previous section for Wisconsin, we see that the solar intensity for January 21 at the northernmost latitude was 35.3% or .353. Thus, to calculate the solar energy amount at the top of the atmosphere is: 1360 X 0.353 = 480 W m-2
Calculating the amount of energy received at the surface
Now we will determine the amount of that solar energy that reaches the surface of the Earth. As solar energy passes through the atmosphere, that energy is depleted due to gases and other materials that make up the atmosphere. For these calculations, you will use a set of averages to determine the amount of solar energy loss by the time it reaches the surface. Here are those averages:
19% of the top of the atmosphere (TOA) solar energy is absorbed by atmospheric gases
4% of TOA solar energy is absorbed by clouds
23% of TOA solar energy is reflected by clouds
For example, Using the January 21st time and the northmost latitude we saw above that the TOA energy is 480 W m-2. On a clear day (i.e. no clouds), that energy would be depleted by 19% due to the gases in the atmosphere. Another way to look at this is that 81% (100-19) will reach the surface. So, 81% of 480 is 389 W m-2 (480 X 0.81). On a cloudy day, the energy would be decreased by 46% (19% + 4% + 23%) or 54% will reach the surface. So, 54% of 480 is 259 W m-2 (480 X 0.54).
Calculating the amount of solar energy absorbed by the surface
Of that solar energy that reaches the surface of the earth some of it will be reflected and the rest will be absorbed. This absorbed amount is critical because this is the energy that will end up heating the atmosphere. Let’s just examine two types of surfaces on opposite ends of the spectrum; one that reflects very little and thus absorbs a lot versus one that reflects a lot so absorbs very little.
Fresh white snow reflects 90%
Asphalt reflects 5%
All other surfaces (e.g., grass, trees, buildings, crops, water, etc.) will all vary and be somewhere between those two extreme examples.
For example, on a clear day on January 21 at the northernmost latitude in Wisconsin we have 389 W m-2 of solar energy reach the surface. If the surface is covered by fresh white snow, then 90% will be reflected and only 10% will be absorbed. Thus, 38.9 W m-2 would be absorbed under this circumstance. If there was exposed asphalt in that situation then 5% would be reflected and 95% absorbed; so, 369.6 W m-2 is absorbed on the exposed asphalt surface.
Wisconsin Example of these calculations
Here is an Excel template to use to do these calculations.
TOA Energy calculations, use this Excel formula:
Copy the values of the solar intensity from your first template file to this one in the appropriate column. Make sure to use copy and then Paste Special (Values) to do this.
“=(1360*[cell with solar intensity])/100”
We need to divide by 100 since our percentages are in whole numbers
Clear day calculations, use this Excel formula:
“=([cell with TOA energy levels]*0.81)
Remember 19% is absorbed by the atmospheric gases, so only 81% reaches the surface
Cloudy Day calculations, use this Excel formula:
“=([cell with TOA energy levels]*0.54)
Remember 46% is absorbed/reflected by the atmospheric gases and clouds, so only 54% reaches the surface
Snow cover calculations, use this Excel formula:
“=([cell with cloudy/clear solar energy reaching the surface]*0.1)”
Remember that snow reflects 90% of the energy so only 10% is absorbed
Asphalt cover calculations, use this Excel formula:
“=([cell with cloudy/clear solar energy reaching the surface]*0.95)”
Remember that asphalt reflects 5% so 95% is absorbed
Here are the results of the Wisconsin calculations
Date
Northernmost Latitude (47.3°N)
Center Latitude (44.9°N)
Southernmost Latitude (42.5°N)
Solar Intensity
TOA Energy
Clear Day
Cloudy Day
Clear Day
Cloudy Day
Solar Intensity
TOA Energy
Clear Day
Cloudy Day
Clear Day
Cloudy Day
Solar Intensity
TOA Energy
Clear Day
Cloudy Day
Clear Day
Cloudy Day
Snow Cover
Asphalt Cover
Snow Cover
Asphalt Cover
Snow Cover
Asphalt Cover
Snow Cover
Asphalt Cover
Snow Cover
Asphalt Cover
Snow Cover
Asphalt Cover
21-Jan
35.3
480.7
389.4
259.6
38.9
369.9
26.0
246.6
39.2
533.6
432.2
288.1
43.2
410.6
28.8
273.7
43.1
585.5
474.3
316.2
47.4
450.5
31.6
300.4
21-Feb
52.5
714.6
578.9
385.9
57.9
549.9
38.6
366.6
56.1
762.5
617.6
411.7
61.8
586.7
41.2
391.1
59.5
809.0
655.3
436.8
65.5
622.5
43.7
415.0
21-Mar
67.8
922.3
747.1
498.0
74.7
709.7
49.8
473.1
70.8
963.3
780.3
520.2
78.0
741.3
52.0
494.2
73.7
1002.7
812.2
541.5
81.2
771.6
54.1
514.4
21-Apr
80.6
1096.1
887.8
591.9
88.8
843.4
59.2
562.3
83.0
1128.8
914.3
609.6
91.4
868.6
61.0
579.1
85.3
1159.6
939.3
626.2
93.9
892.3
62.6
594.9
21-May
88.9
1208.5
978.9
652.6
97.9
930.0
65.3
620.0
90.7
1233.6
999.2
666.1
99.9
949.2
66.6
632.8
92.4
1256.5
1017.7
678.5
101.8
966.9
67.8
644.6
21-Jun
91.5
1244.3
1007.9
671.9
100.8
957.5
67.2
638.3
93.1
1266.2
1025.7
683.8
102.6
974.4
68.4
649.6
94.6
1285.9
1041.6
694.4
104.2
989.5
69.4
659.7
21-Jul
89.6
1219.2
987.6
658.4
98.8
938.2
65.8
625.5
91.4
1243.4
1007.1
671.4
100.7
956.8
67.1
637.9
93.0
1265.4
1024.9
683.3
102.5
973.7
68.3
649.1
21-Aug
81.6
1109.9
899.1
599.4
89.9
854.1
59.9
569.4
84.0
1141.9
924.9
616.6
92.5
878.7
61.7
585.8
86.2
1171.8
949.2
632.8
94.9
901.7
63.3
601.1
21-Sep
67.8
922.3
747.1
498.0
74.7
709.7
49.8
473.1
70.8
963.3
780.3
520.2
78.0
741.3
52.0
494.2
73.7
1002.7
812.2
541.5
81.2
771.6
54.1
514.4
21-Oct
54.0
734.7
595.1
396.8
59.5
565.4
39.7
376.9
57.5
782.0
633.4
422.3
63.3
601.8
42.2
401.2
60.9
827.9
670.6
447.1
67.1
637.1
44.7
424.7
21-Nov
38.6
524.8
425.1
283.4
42.5
403.9
28.3
269.2
42.4
576.9
467.3
311.5
46.7
443.9
31.2
296.0
46.2
628.0
508.7
339.1
50.9
483.2
33.9
322.2
21-Dec
32.9
447.3
362.3
241.5
36.2
344.2
24.2
229.4
36.8
500.6
405.5
270.4
40.6
385.2
27.0
256.8
40.7
553.2
448.1
298.7
44.8
425.7
29.9
283.8
Now you will complete this same table for your state.
You will have some reflection to write up based on this data, but we will save those directions for the end of this assignment.
Part 3: Temperature Patterns
Over the last two sections you have investigated the changes in energy levels that are received at the top of the atmosphere and at the surface of the Earth under various conditions. Your understanding of these concepts is the start to understanding the main cause of temperature patterns across your state and really at any locations around the world. Now, you are going to investigate the impact this and other temperature controls (recall the important ones from the building knowledge section) has on temperature patterns across your state throughout the year.
The first step in this process is to create some maps and graphs by accessing some data from the Midwest Regional Climate Center (MRCC). While this website is called the Midwest Regional Climate Center, they have a data portal that provides information for the entire continental United States. You will need to create an account with the MRCC website. We will be using this website multiple times throughout the semester for the state climate project. This is a free account if you use your UWW email address (i.e., don’t use any other email because it will lock you out and charge you a fee for some of the data). Here are the directions to set up the account:
Go to the Midwest Regional Climate Center’s website: https://mrcc.purdue.edu/Links to an external site.
Click on the Data tab and open the cli-Mate link OR click on the cli-Mate button on the homepage
When the new page loads, click the Register Here button in the upper-right-hand corner
Fill out the information using your uww.edu email address (using the .edu address allows free access to most of the site’s data)
When choosing a state, you can either choose Wisconsin or your state you are researching for your state climate report
Once you register go back to the cli-MATE Online Data Portal page and login
Once you have created your account and logged in you can begin making the items needed for this section.
State Temperature Maps
Create a minimum of five average temperature maps for your state. These are important so that you can see how temperatures change spatially and temporarily across your state and determine what temperature controls might play a role in these patterns for your state. At minimum we will create the following maps:
Annual average temperature map
January average temperature map (to represent the coldest month of the year)
April average temperature map
July average temperature map (to represent the warmest month of the year)
October average temperature map
To create these maps, you will use the cli-MATE data portal, since you are gaining data from this website you should create a citation and reference listing to include in your final report.
In the left-hand menu select Maps of Data, MRCC Gridded Data, Long Term averages
For Years to average over
First Year to 1991 (this is the default)
Last Year to 2020 (this is the default)
For Calendar period
For Annual Average Temperature, set dates to January 1 and December 31
For January Average Temperature, set dates to January 1 and January 31
For April Average Temperature, set the dates to April 1 and April 30
For July Average Temperature, set dates to July 1 and July 31
For October Average Temperature, set the dates to October 1 and October 31
For Variable
Select Average Temperature
For Location
Select State and then choose your state from the drop-down menu
Click on Create Map
Once the map loads right click and save the maps
Here are the maps for Wisconsin, remember that you can use the information for comparison to your state in your state climate project final report. So, feel free to save these maps for future reference.
City Temperature Graphs
Create graphs showing the annual temperature patterns for a minimum of 4 cities in your state (if your state has a more complex temperature pattern you will need to do more than 4). You should choose these cities wisely to help illustrate the main temperature controls across the state. You should keep in mind the temperature controls that were discussed in the building your knowledge section of this module. You can draw on anything you learned in your background research you completed back in Module 1.
From the cli-MATE data portal, follow this path:
Daily Observed Data
Monthly
Monthly NCEI Normals
Once this page loads you can unclick the Precipitation, Heating Degree Days, Cooling Degree Days. Keep Max. Temperature, Min. Temperature, Mean Temperature checked because these are the values we want to graph.
To select locations/cities to get data, follow these steps:
Click on the Select Daily Station button across the top banner
It will probably be best to use the Map Selector; so, click on that link
On the page, I would advise to click on the Only Show Active button and under Networks the Select/Unselect All button. You can also uncheck precipitation and snow fall/depth since in this module we are focusing on temperature.
Once you click on a blue dot on the map it will bring up some basic station information. Throughout the lab you will want to use the More Info button to see more details in choosing your locations. To get the data for the NCEI Normals the station must have data going back to 1991; so, make sure you choose stations that have data going back to that time or before.
Once you find a suitable station, click on the Select button, Then, click the Go button on the new page that loads. This will take you back to the Monthly NCEI Normals page. The station you choose should be listed at the top of the page under Current Daily Station.
To access the data, click Plot Climate Data button. Make sure to save these graphs; I have found that the PNG file format works best. With any other format the headers and numbers get jumbled and can’t be read very well.
Once this page loads you will have a graph showing the monthly averages throughout the year. You will also want to note the warmest and coldest months throughout the year and what the temperature is in that month. You can scroll over the line to each month’s node to get that information.
Here are the graphs for the 4 cities I choose for Wisconsin. I choose these stations to try to investigate and show the changes in temperature across latitude (a southern city versus a northern city), from my AI output I need to investigate if Lake Michigan has impact on temperature patterns (choosing a location near the lake and one away from the lake), and I can also want to think about if Lake Michigan can impact temperature patterns then Lake Superior should too (so if my northern city is close to Lake Superior then I can investigate that).
Part 4: Discussion of Energy and Temperature Patterns and Controls
Your submission for this module should include the following:
Your tables and graphs completed in the first two sections of solar intensity and solar energy amounts across your state throughout the year. You can just submit your Excel files for this.
Your state temperature maps
Your city temperature graphs
Your discussion on all of this. At this point you can just do this as bullet points (i.e., an outline) but remember in the end if you do a written report this will need to be written as prose (i.e. sentence/paragraph format). With an oral presentation you can use these bullet points as your talking points as giving your presentation. The top things I am going to be looking for:
How does your solar intensity change throughout the year and at the three locations. What impact do you think this will have on temperature patterns.
How does solar energy levels absorbed at the surface under the different circumstances change throughout the year and across the state. What impact would this have on temperature on a large scale and the small scale (e.g., could you potential experience a temperature difference if we had some fresh snow but it melted from an asphalt area quickly and thus is exposed)?
How do you see the solar intensity and absorbed solar energy at the surface playing a role in temperature patterns across your state?
What are the temperature patterns across your state? Be specific, talk specific number from the maps and graphs your created to illustrate this?
With city graphs, do you see a difference between the max. temperature patterns and the min. temperature patterns? Why might this be?
What are the temperature controls at play in your state? Give examples where you can see this from the state maps or city graphs.
Again, you can use the maps and graphs from Wisconsin to also do some comparisons if you would like.
Make sure to create a citation and reference list entry for any source you received data or information from
