Lab 02: Earth-Sun Relationships and Earth’s Energy Budget

Andrew Perkins

Most of Earth’s energy comes from the Sun. This energy is what drives the function of many Earth systems. Understanding how this energy makes its way to the Earth and interacts with the atmosphere and surface is a big part of understanding how the Earth works.

Learning Objectives

After completion of this lab, you will be able to:

  • Measure how Earth relates to the Sun at different times of the year at different latitudes;
  • Convert between several common temperature scales;
  • Predict how temperature will generally change with latitude;
  • Assess how local variables like cloud cover, aspect and surface albedo affect local radiation balance.


Earth is dependent on the Sun’s energy to support almost all of the systems at work. The actual amount of energy received at the Earth’s surface at any specific location is dependent on three components:

  • The solar constant (~1367 watts/m2) – the amount of solar energy received at the top of the atmosphere (this changes slightly with solar output)
  • The angle of the suns rays – compared to the surface of the Earth (this changes with the seasons)
  • Atmospheric composition – the state of the atmosphere is variable (for example, how much water vapour is present above that location)

In order to complete this lab, some background information on Earth-Sun relationships, Earth’s energy budget, common temperature scales, albedo, and aspect is required.

 Earth-Sun Relationships and Earth’s Energy Budget

We are all aware that the quantity of sunlight varies over time and space. Over a 24-hour period, we know that sunlight is generally strongest around noon hour and nonexistent during the time of day we call night. Insolation (incoming solar radiation) can be defined as the solar radiation or sunlight that is received by the Earth’s ground surface or atmosphere. Many locations on our planet experience yearly variations in the quantity of insolation. If these variations are large enough, they contribute to the annual march of the seasons.

Read this short article about incoming solar radiation to the Earth.

The Sun is directly overhead of the Equator at noon on the equinoxes. It is directly overhead of the Tropic of Cancer at noon on the June solstice, and directly overhead of the Tropic of Capricorn at noon on the December solstice. In between these dates, you can determine the latitude at which the Sun is directly overhead at noon (also called the latitude of the subsolar point) using a diagram called the analemma.

To read the analemma follow the steps below:

  1. On the figure-8 shape, find the date for which you want to know the latitude of the subsolar point.
  2. Read across to the vertical axis to the left side of the analemma and read the latitude. Note: latitudes only go up to a maximum 23.5°, the latitude of the Tropic of Cancer and Capricorn.
  3. The analemma is split into the northern hemisphere (upper half) and southern hemisphere (lower half). Determine whether the latitude of the subsolar point is in the northern hemisphere or the southern hemisphere.
Figure 2.1. Latitude of Subsolar Point (modified from data from the US Coast and Geodetic Survey). CC-BY. View source.

The March of the Seasons and the Angle of the Noon Sun

Across the range of latitudes, locations near the Equator receive high quantities of insolation all year long. Locations near the poles only receive significant amounts of insolation during a relatively short summer period. For this reason,  localities near the poles have cold winter conditions during most of the year.

Read this short article about how Earth’s tilt and surface reflectivity impact how insolation behaves as it encounters the Earth:

The angle at which solar radiation encounters the Earth’s surface is important for how that energy is distributed.

The equation for calculating the angle of the noon sun (ANS) is

    \[ ANS = 90\degree - (Latitude \pm Latitude of the Subsolar Point) \]


  • ANS = the angle of the noon sun (expressed in degrees)
  • Latitude = the desired location on the surface of the Earth
  • Latitude of the subsolar point (LSP) = the latitude where the sun is directly overhead for that date of the year.

Note: We are interested in the total difference in latitude between our location and the LSP.

Figure 2.2. Scenarios for calculating Angle of the Noon Sun, based on varying positions of latitude and LSP. Source: Andrew Perkins, CC BY-NC-SA.

Note: You cannot have a sun angle greater than 90°.


When sunlight impacts the Earth’s surface at an oblique angle, the insolation is stretched over a greater area, reducing its intensity (Figure 2.3).

Figure 2.3. Reduction in solar intensity as sunlight encounters the Earth’s surface at an oblique angle. Source: Andrew Perkins, CC BY-NC-SA.


We can extend the ANS calculation to also look at the effect angle of incidence has on insolation intensity using the following equation:

    \[ Intensity = Sin(ANS) \]

Where ANS is the angle of the noon sun (expressed in degrees). This is a unitless value for intensity between 0 and 1, but it can be multiplied by 100 to yield a percentage of the 100% intensity currently experienced at the latitude of the subsolar point.

For the above example at 49° N on July 14, the solar intensity calculation would be:

    \[ Intensity = Sin(62.5) \]

    \[ Intensity = 0.89 \]


The final picture of incoming solar radiation might look something like Figure 2.4 below, where a protractor has been used to draw a line demonstrating the incoming angle of solar radiation for July 14 at 49° N latitude.

Figure 2.4. Incoming solar radiation on July 14 at 49° latitude (Eiffel Tower). Relative intensity of solar radiation is also shown. Source: Andrew Perkins, CC BY-NC-SA.

Global Temperature Distribution and Common Temperature Scales

Based on what you now know about how the Sun’s energy is distributed around the globe, it should make sense that incoming solar radiation is unequally received at the Earth’s surface. One of the easiest ways to see this is by examining average temperatures by latitude.

The three maps at the links below show global surface temperatures (displayed as colour: reds = hotter, blues = colder) at the two solstice positions and at the equinox. What do you notice about latitudinal changes in temperature as you move from the equator to the poles? You can click anywhere on the map to get a temperature reading for that location.

June Solstice

December Solstice


Temperature is a measure of the average kinetic energy of a substance. It is a way of measuring heat energy, as heat always flows from material at a high temperature to material at a lower temperature, raising the temperature of the cooler material. There are three temperature scales that are commonly used: Celsius (°C), Fahrenheit (°F), and Kelvin (K). Most of the world (including most of the scientific world) uses the Celsius scale for measurement and reporting.

The following formulas allow you to convert between these scales:

Celsius and Farenheit:

    \[ T_{(\degree C)} = \frac{5}{9} \times (T_{(\degree F)} - 32) \]

    \[ T_{(\degree F)} = \frac{9}{5} \times (T_{(\degree C)} + 32) \]

Celsius and Kelvin:

    \[ T_{(\degree C)} = T_{(\degree K)} - 273 \]

    \[ T_{(\degree K)} = T_{(\degree C)} + 273 \]

T_{(\degree C)} =  Temperature in degrees Celsius

T_{(\degree F)} =  Temperature in degrees Fahrenheit

T_{(\degree K)} =  Temperature in Kelvins

Temperature Gradients

Gradient (also known as slope) gives us the rate of change for a value over a given distance. It can be useful for many environmental variables like imaging how topography changes over space (slope of the land surface) or how temperature varies vertically or horizontally through the atmosphere (temperature gradient).

Temperature changes along a gradient through the atmosphere are called lapse rates.

Lapse rates can be calculated using the following formula:

    \[ lapse rate = \frac{\Delta T}{\Delta z} \]

In this formula:

  • \Delta = (delta symbol), represents the change in the variable it precedes (for example, the change in temperature)
  • T = air temperature (normally in °C)
  • z = altitude (normally in metres). This term can be replaced with distance if calculating a horizontal temperature gradient

For example, let’s say you wanted to know the temperature gradient between the two temperature readings in the atmosphere shown in Figure 2.5.


Figure 2.5. Lapse rate locations. Source: Andrew Perkins, CC BY-NC-SA.


In this example, the temperature gradient (or lapse rate) is calculated as follows:

    \[ \Delta T = 10\degree C - (-30\degree C) = 40\degree C \]

    \[ \Delta z = 2km - 8km = -6km \]

    \[ lapse rate = \frac{40\degree C}{-6km} = -6.6\degree C/km \]

Notice that the lapse rate above is a negative value. This means that based on the series in which the measurements were taken, the temperature is decreasing as the altitude increases. If you went in the opposite direction on the graphic, the temperature would increase as the altitude decreased.

Albedo and Aspect

Local variations in surface reflectivity—called albedo—and the direction a surface faces—its aspect—can have a major influence on that surface’s absorption and retention of solar radiation.

Albedo is measured as the percentage of radiation reflected from a surface. High albedo surfaces have a high reflectivity. Surfaces like ice are highly reflective and absorb very little incoming solar radiation. Surfaces like asphalt and concrete have a very low reflectivity and absorb significant amounts of incoming solar radiation. This difference in albedo leads to significant differences in heating. Clouds have a very high albedo.


Figure 2.6 Common albedo measurements. Source: Left: H. Grobe (2000) CC BY-SA 2.5. View source. Right: Prevedello et al (2019). CC BY. View source.

Aspect refers to the direction a topographic slope is facing (Figure 2.7). We refer to direction based on the cardinal points of a compass. A southerly aspect means that the topographic slope is facing to the south. In the mid latitudes of the northern hemisphere, a southerly aspect means that a slope is tilted towards incoming solar radiation (based on angle of the noon sun). A northerly aspect in the same location would mean that the slope is tilted away from incoming solar radiation.

Figure 2.7. Left: Cardinal directions on the compass. Source: Andrew Perkins, CC BY-NC-SA. Right: An illustration of the concept of aspect in the northern hemisphere. The slope labelled with a yellow star has a north-facing aspect in the image, whereas the slope labelled with the pink star has a south-facing aspect. Modified after Olsen & Rupper (2019) CC BY. View source.

Lab Exercises

In this lab you will explore how Earth-Sun relationships generate latitudinal and seasonal differences in temperature, and the foundations for Earth’s radiation budget. You will use several online maps and interactive websites to complete this exercise.

EX1: Earth-Sun Relationships and Earth’s Energy Budget

  1. According to the NASA article you read, day and night, averaged around the globe, how much energy reaches the Earth from the Sun?
  2. The above number describes an average value across the Earth. Describe the three factors that determine the actual amount of radiation received at the Earth’s surface at a specific location.

The solar constant measures the approximate solar radiation received at the top of the atmosphere. But at various times throughout the year, certain latitudes may be tilted towards or away from the Sun, based on Earth’s orbit. For example, in December, the northern hemisphere is tilted away from the Sun, whereas in July, the southern hemisphere is tilted away from the Sun.

Use this interactive diagram to answer questions 3 and 4. Note this interactive is simplified to only communicate changes in radiation based on Sun angle and does not include the influence of the atmosphere on incoming solar radiation.

  1. Set the month in the box at the bottom of the interactive to “March.” Explain how the amount of solar radiation received at the Earth’s surface changes as you move from the equator to the north pole.
  2. Cycle through the four months in the box at the bottom of the interactive. Record the actual amount of radiation received at the Earth’s surface for three latitudes: Equator, Tropic of Cancer and the North Pole. Graph the points for each month on the graph below, connecting each with lines (use different symbology for each line and include a legend to reference the symbology).

Use the analemma (Figure 2.1) to answer the following questions:

  1. At what latitude is the Sun directly overhead on your birthday? Record the date and the latitude of the subsolar point.
  2. Earth Day is celebrated on April 22nd every year. At what latitude is the sun directly overhead on this date?

EX2: The March of the Seasons and the Angle of the Noon Sun

The latitude at which the Sun is directly overhead may be helpful in understanding overall Sun patterns, but let’s say you want to set up a solar panel at your house. You need to know the sun angle for your location on a specific date so that you can setup your solar panel for optimal effectiveness.

Complete the following calculations for angle of the noon sun and relative solar intensity.

  1. On Oct. 3rd, if you are located at 0° latitude.

Angle of Noon Sun Relative Intensity of the Sun Angle
  1. On April 2nd, if you are located at 61° North latitude.

Angle of Noon Sun Relative Intensity of the Sun Angle
  1. On Dec. 9th, if you are located at 85° North latitude.

Angle of Noon Sun Relative Intensity of the Sun Angle
  1. It’s August 1st and you are climbing up the south facing slope of Mount Denali in Alaska (the highest peak in North America). At noon you come across another climber in distress and need to contact emergency services for a helicopter rescue, but your satellite phone battery is dead. Quickly you remember that you have a portable solar panel charger in your backpack. You unpack it and plug it in to the phone. It begins to charge, but very slowly. You decide to speed up the charge by setting up the solar panel at an angle. At what angle should you set the solar panel to take the best advantage of the incoming solar radiation? Show all relevant calculations.

EX3: Global Temperature Distribution and Common Temperature Scales

Seasonality and Sun angle is just one way incoming solar radiation can vary for a specific location. Using satellite measurements it is possible to get a sense of how cloud cover affects incoming solar radiation.

This website displays temperature data collected by a satellite looking through the atmosphere from above. It calculates the temperature from the reflective surface in the image.

  1. Choose a location on the map where you can see a cloudless area near the coast. Compare the land and ocean temperatures at this latitude. Is there a difference between the temperatures? Explain why this is the case.
  2. Now compare the temperatures in the previous question with the temperature measurement at the top of a nearby cloud.

a. Is the temperature at the top of the cloud higher or lower than the land and water surfaces?

b. What does this tell you about how energy radiated from the Earth’s surface is affected as it interacts with clouds in the atmosphere on its way out to space?

c. Assume the top of the cloud is at the top of the troposphere, 18 km above the land surface for your location. What is the vertical temperature gradient between the Earth’s surface and the top of the cloud?


On April 10, 1912 the steamship Titanic left Southampton England on its maiden voyage across the Atlantic Ocean to New York. By the evening of April 15, the Titanic was sinking in the middle of the Atlantic Ocean, after striking an iceberg. The Titanic sank in the cold waters of the northern Atlantic.


Figure 2.10. Titanic on its maiden voyage, off the coast of Ireland (Photo taken on April 11, 1912). Source: Cobh Heritage Centre, Public Domain. View source.


  1. The surface temperature when the Titanic left Southampton, England was 53.1° F. Convert this temperature to degrees Celsius.
  2. The average daily maximum temperature for Southampton, England in April 1912 was 288.5 K. Was the temperature when the Titanic left higher or lower than this average?
  3. The city of Calgary, Alberta is located at a similar latitude to the city of Southampton, England. In April 1912, the average daily maximum temperature in Calgary was 5.5 °C. Explain the physical geography surrounding why this temperature is so much different than the average daily maximum temperature in Southampton (Hint: you may need to look at a map of where Calgary is located relative to where Southampton is).

The Titanic sailed in April, between the extreme conditions of summer and winter. Consult the global isotherm maps below for an example of January and July temperatures:

The maps at the links below show temperature (displayed as colour: reds = hotter, blues = colder). You can click anywhere on the map to get a temperature reading for that location.

July Temperatures

January Temperatures

  1. Is the temperature contrast between the equator and the Arctic region greatest in winter or summer for the northern hemisphere?
  2. If latitude were the only control on temperature, isotherms should run straight across the map from east to west.

a. Identify one area on the map where this occurs (use your knowledge of place names or use an atlas/Google Earth to determine the name of the location you identified).

b. What physical geography conditions explain why the isotherms follow this pattern in the place you identified?

  1. Compare the January and July maps isotherm maps

a. Describe one area of the world that exhibits a large annual temperature range.

b. What physical geography conditions explain the large annual temperature range for the place you identified?

The atmospheric conditions on the night of April 15, 1912 were clear (no cloud cover).

  1. How do you think the lack of clouds affected the air temperature, according to what we know about local energy budget and how clouds interact with radiation?

The last emergency communication from the Titanic before it sank gave its position at the following coordinates: 41˚ 46’ N, 50˚ 14’ W. Go back to the satellite image.

  1. Find some open water in the Atlantic Ocean at a latitude of around 41°N. Record the surface water temperature in Celsius.
  2. Survival rates for humans in specific water temperatures are given below. Based on the water temperatures in the previous question, how long would an individual have been able to survive in open water after abandoning the Titanic?
Water Temperature (°F) Expected Time of Survival
32.5° 45 minutes
32.5–40° 30 – 90 minutes
40–50° 1 – 3 hours
50–60° 1 – 6 hours
60–70° 2 – 40 hours
70–80° 3 hours – indefinite
> 80° Indefinite

EX4: Temperature Gradients

Several distress rockets were fired into the air to alert nearby ships of the Titanic’s position and to aid in the rescue effort.

Atmospheric layer Altitude (km) Temperature (°C)
Surface (Northern hemisphere) Sea level (0) 15
Tropopause 18 -57
Stratopause 50 0
Mesopause 80 -90
Thermopause 480 1200
  1. Plot the following standard atmospheric temperature values on a graph (in Worksheets), connecting the points with a line and labelling the troposphere, stratosphere, mesophere and thermosphere.
  2. The distress rockets passed through the lowest part of the atmosphere. Calculate the average temperature gradient (lapse rate) in the lowest 10 km of the troposphere from the graph you created.

EX5: Albedo and Aspect

Take a look at the glaciers that cover Mount Rainier, a stratovolcano in Washington, USA.

Figure 2.11. Mount Rainier, WA glacier coverage. Source: Tom Sisson, USGS, Public Domain. View source.


Use this image to answer the questions below:

  1. Mount Rainier contains the greatest amount of glacier ice of any mountain in the lower 48 United States.

a. Do you think aspect has a role in controlling the distribution and size of glaciers around the central peak of Mount Rainier? Explain your answer.

b. Choose 3 different glaciers from different locations around the main peak. Compare their aspect and relative size.

  1. The zones in between the glaciers are covered mostly in bare rock and light forested vegetation.

a. How do you think the albedo differences between the middle of the glacier and the locations between the glaciers affects how the glacier melts?

b. As the glacier melts further back, more sediment and bare rock is revealed. Do you think this negatively or positively reinforces the melt rate of the glacier? Explain your answer.

Reflection Questions

  1. Imagine if the Earth was not tilted 23.5° on its axis, but instead had no tilt. How would this affect the Earth’s energy budget?
  2. If the Titanic had sunk on a cloudy night, how would that have affected air temperature conditions and potential survivability for those who had to abandon the ship as it sunk?
  3. The southern hemisphere is about 81% water at the surface, whereas the northern hemisphere is about 61% water how do you think this difference affects the local energy budget for these two different hemispheres?


Click here to download Lab 02 worksheets as a PDF file.





Grobe, H. 2000. Albedo. [computer graphic] retrieved from:

Prevedello, J.A., Winck, G.R., Weber, M.M., Nichols, E., & Sinervo, B. (2019) Impacts of forestation and deforestation on local temperature across the globe. PLoS ONE 14(3): e0213368.

Olson, M. & Rupper, S. (2019) Impacts of topographic shading on direct solar radiation for valley glaciers in complex topography, The Cryosphere, 13, 29–40,

Sisson, T. No Date. Glaciers of Mount Rainier overlaid on a base map LiDAR image. [computer graphic], Retrieved from:

Combined Media Attributions

Figure 2.6

Media Attributions