The Earth's Radiation Budget, Part II.

I. Purpose

Last week you explored the geographical variations of Earth's albedo, reflected solar radiation, and Earth's radiation received by satellites from cloud free areas of the Earth's surface. The patterns you observed were controlled by the curvature of the earth, variations in seasonal radiation received from the sun, and varying properties of the Earth's surface. This week we will explore the effect of clouds on these patterns. Accordingly, the data sets you will first look at this week will be that under the category: total (this link will open a new window with these data).

We will want to compare some of the cloud free data sets from last week's lab with the total datasets used this week. These comparisons, which we recommend you do when looking at the albedo data sets, will allow you to differentiate between reflectivity that is caused by clouds and that which is caused by Earth surface properties such as ice and snow. As you look at these data, note what areas of the Earth clouds persistently cover and what areas are generally cloud free. The reasons for these patterns will become clear as the course continues.

II. Examining the ERBE Data.

A. Total albedo

Go to the window you opened earlier that contains the total fields. Look at the January map of total albedo (adjust your graphical interface so continental outlines are shown, set your colorscale range from 0 to 100 and then choose the option of "colors | contours"). Access clear-sky albedo from last week's lab in your other opened window (make the same display choices as above).

Task I: Comparing between clear-sky and total.

B. Total short wavelength reflected radiation

Go back to the windows that contain the total and clear-sky data and navigate to the shortwave fields. We will now calculate the globally averaged amount of reflected solar radiation in the clear-sky case and in the total to evaluate the effect of couds on the radiation budget. To do that, click on the "expert mode" link in the upper right corner of the window. We will first average all the data over time to look at the annual average. In the expert mode window type the following line of text below the text which is already present in the window:

    [T] average

Now click the "OK" button to the right of the expert window. This tells the software to average the data over all time slices. Each point in space is averaged separately. View this field to look at the annual average total reflected shortwave radiation. Do the same with the clear-sky field. As with the albedo fields, a comparison between the total and clear-sky data highlights the role of clouds in the short wavelength budget.

Now return to expert mode and continue typing underneath the first line you entered:

    Y cosd mul

This multiplies every grid point in space by the cosine of the latitude angle (Y is the latitude angle in degrees, and cosd is a calculation of cosine when the angle is given in degrees). We need to do that so that our grid points will be properly weighted with respect to the geographical areas they represent as there are more grid points per unit area in the high latitudes than in the tropics. Then type:

    [X Y] average

Cick the "OK" button again. The viewer will return a single number just below the expert window (in bold letters). That number is the amount of reflected shortwave energy averaged over the entire globe in W/m2. Do the same operation with clear-sky shortwave radiation.

Task 2: Record the global annual averages for both the total and clear-sky shortwave radiation. (Results) How do you explain the difference between these numbers in relation to cloud cover? If cloud cover increases, how will this difference change? (Discussion)

C. Total long wavelength Earth radiation

Open a new browser window with the total longwave radiation dataset (hold the apple/command key down when you click here). In the expert mode calculate the annual mean outgoing longwave (that is, type "[T] average" and click OK). In the other window, go back to the view of the global mean reflected radiation. Display the figures side-by-side.

Task 3:

D. Total net radiation

The net radiation is the difference between the radiation coming into the Earth from the sun and the energy radiated by the Earth to space. For the planet as a whole what comes in must equal what goes back out; however, more radiation comes in at the tropics than goes out in these latitudes and more is radiated from the higher latitudes (north and south of the tropics) than comes in. This difference provides the energy to drive the circulation of the atmosphere and ocean.

Task 4: Calculate the global annual average net radiation (use the expert mode again). (Results) What percentage of incoming solar radiation at the top of the atmosphere (So/4 = 342 Wm-2) is the global annual average net radiation? (Results) (You should find one value for global annual average net radiation using the same technique as in Section B.)

E. Cloud Forcing

In order to try to understand how clouds affect the Earth's radiation budget, ERBE scientists calculated the difference between the clear-sky fields and the total fields. The result is often referred to as cloud-forcing. The fields in this dataset show how much clouds affect the amount of radiation available to Earth by comparing the data from the same locations during cloudy and non cloudy days. This calculation cannot be done in some places due to insufficient data.

Go to the annual average net cloud forcing dataset. Here you can see that clouds may locally warm or cool a given region. The degree of cloud cover at given location is necessary but not sufficient to determine the cloud forcing. Compare the region over the western tropical Pacific (near Indonesia and northern Australia) to the North Pacific (between Japan and Alaska), two areas with extensive cloud cover.

Task 5: What is the net cloud forcing in these two areas? (Results) How does this relate to the balance between shortwave reflection and longwave emission? (Discussion)

F. The Greenhouse Effect

The Stefan-Boltzmann Law relates the amount of longwave radiation emitted by a black body to its temperature. Thus we can calculate the effective temperature of Earth as determined by its total longwave radiation emitted into space, and compare it with the surface temperature. To do that let us go back to the total longwave radiation dataset (you might want to close all other windows first).

In the expert mode we can calculate the temperature corresponding to the outgoing longwave radiation by first dividing by the Stefan Boltzmann constant and then taking the square root of the result twice. We do that as follows:

    5.67E-08 div
    sqrt sqrt
    273.15 sub
    X Y 1 SM121

This code converts the results to °C and add some smoothing in space. View the results in colors and contours.

Now open the JONES surface temperature climatology dataset. These temperature data were carefully compiled from land station measurements and from ship observations made from 1854 through 1994.

Task 6:

We can use these temperatures to calculate the amount of longwave radiation emitted from the Earth's surface, and compare that to the ERBE measurements of what is emitted into space. Go back to the longwave radiation dataset and in the expert mode replace the Stefan Boltzmann calculation with a calculation of the annual averaged longwave radiation using "[T] average" as described before. Then go to the Jones surface temperature dataset and use the Stefan Boltzmann Law to calculate the longwave radiation emitted from the surface assuming that surface emissivity is 1 (not accurate, but sufficient for our purpose). To do that, type the following into the expert window:

    273.15 add
    dup mul dup mul
    5.67E-08 mul
    [T] average

The command "dup" duplicates the data which is then multiplied by the original using "mul". This is done twice to create the 4th power of temperature in K.

Task 7: Compare the annual averaged longwave radiation coming from the surface with that going out to space. Which is larger? What does the difference represent? Where is the effect (difference) largest. Where is it smallest?

III. Hands-on Experiments

A. Black and white "blackbodies"

In the previous section, you used the Stefan-Boltzmann law to calculate the effective temperature of a planet heated by the sun. The same reasoning applies to ordinary paper heated by a lamp. In this experiment you will use a desk lamp, a two channel thermometer and two pieces of paper, one black and one white. Both pieces of paper can be treated as black bodies with different albedos. Calculated albedos are written on the pieces of paper. You will do the experiment on both pieces of paper at the same time under the same conditions. Tape one of the thermometer sensors to each piece of paper. Place the papers close to each other under the desk lamp and turn the lamp on. You will find that the temperatures of both papers immediately rise. Why? After a few minutes, the temperatures stop growing and stay constant, which means the papers have reached an equilibrium state. Now write down those steady state temperatures. Why is there a big difference? Use the Stefan-Boltzmann law to calculate the energy emitted by the lamp in two ways: one using the thermal equilibrium of the white paper, the other for the black paper. Are they the same?

B. Radiative energy spectrum from different light sources:

It is often very useful to describe a light-emitting body in terms of its emission spectrum, that is, the partitioning of energy among the different frequencies (or wavelengths) composing the light. For example, the sun emits most of its energy in the visible part of the spectrum, centered on wavelengths around 500 nm (green). This means that its emission spectrum shows a bump at these wavelengths, where its brightness is at a maximum. A spectroscope is a device that allows you to see the spectrum of the incoming lights. Point the spectroscope at two different light sources, a fluorescent light (ceiling light) and a halogen light (desk lamp). You will notice that the different colors are not present at the same brightness. Sketch a qualitative spectrum plot (intensity versus wavelength) for each light sources. Make sure to label both axes and use the spectral chart to convert the colors to wavelengths in microns. Compare the two spectra. Are both continuous? Where are peak intensities?


  1. NASA ERBE Climatology
  2. JONES surface temperature climatology
  3. The Earth Radiation Budget Experiment.
  4. The NASA Educational Resources website - the Trading Card page (click on Earth's radiation budget).
  5. JPL Quick-Look at ERBS site.
  6. A NASA Fact Sheet on ERBE.

Lab Report Instructions

Write a lab report (as per the Lab Report Format) summarizing the major findings of your investigation. In addition, explain the following questions in your discussion section:

  1. Discuss the effect of clouds on the earth's radiation balance. Include in your answer their net (overall) effect, their regional and seasonal effects (give examples) and how different types of clouds in different regions affect the balance.
  2. Discuss the greenhouse effect as it is expressed in the difference between the longwave radiation emitted from the Earth's surface and that emitted from the top of the atmosphere. In answering this question relate to the annual-average picture. Address regional differences and explain what factors govern variations in the greenhouse effect as best as you can from the material you have studied in class and in the lab.

Report the results of your hands-on experiments.

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Updated July 9, 2007
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