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Laboratory 3: Net Radiation at Earth's Surface

Laboratory 3: Net Radiation at Earth’s Surface [54 marks]

Due Date: The beginning of the next lab period. Hand in a typed and stapled lab assignment.

Calculator, paper, and pencil (please bring these)

One shortwave sensor and one infrared thermometer (provided by your TA)


To learn about energy inputs and outputs for different materials/situations on campus; to learn how to measure and calculate net radiation;

to understand the factors that influence net radiation; to practice simple mathematical computations; and to practice writing a lab report.

References: Chapter 4 – Atmosphere and Surface Energy Balances pages 90-113 (4th ed.) or pages 84-109 (3rd ed.)

Format: A typed report using a standard 11-point font type, 2.5 cm margins, figure and table captions, and references where appropriate. Check the formatting and proof-read for errors before printing. Note that when you are working with numbers for this lab, you should use all available digits for calculations, but the final result should be reported only to two places after the decimal. A Word document and an Excel spreadsheet are provided on CuLearn to help you with formatting. Refer to the Sample Lab Write-up available on CuLearn for an example lab submission.


No system will operate without some sort of energy supply. For the earth-atmosphere system, the sun provides more than 99.8% of the energy needed for life and life-supporting processes on the earth, to maintain the circulation of the atmosphere and oceans, etc.

The energy budget of the earth-atmosphere system, or of a parking lot, or of a single blade of grass is

the balance between energy gained and energy lost – hence it is called the “Radiation Balance”.

o Energy is transferred (e.g., from Sun to Earth or from Earth to Space) by radiation. Hence it is
also called Radiation Flux (“flux” means movement or change).
The result – the “Net radiation” – is the total radiation in minus the total radiation out.

o When there is an energy surplus, energy is available to increase temperatures, melt snow or ice, or evaporate water.
o When there is an energy deficit, the surface cools, water freezes, or vapour condenses.

In physical geography, we often need to determine the net radiation budget at the surface of the earth at a particular place or time. For example, you may want to find out why arctic plants grow in special places in Ontario, so you want to know if the sites have a different radiation balance from the surrounding regions.

In this lab, you will measure and calculate the radiation budget of a variety of terrestrial surfaces here on campus. The radiation budget of these surfaces will vary depending on the microclimate of the area as influenced by surface properties, time of day, and general weather conditions.

The Radiation Balance Equation (Equation 1 - below) describes the net radiation as the sum of all the radiation inputs and losses.
Each term in this equation has units of watts per square meter (W m-2). A watt is a unit of power equal to one joule of energy per second, in other words, a rate of energy transfer over time. We need

the surface area over which this energy is transferred; hence, the area is standardized to 1 m2 so that it may be easily scaled up as required.

The radiation balance equation consists of five variables (all in units of W m-2):

1. Net radiation (Rn): A measure of the sum of radiation inputs minus radiation losses at the surface.
2. Incoming solar (shortwave) radiation (K ): The radiation emitted from the sun that reaches the

Earth’s surface.

3. Outgoing solar (shortwave) radiation (K ): The radiation emitted from the sun that is reflected from the Earth’s surface.

4. Incoming infrared (longwave) radiation (L ): The radiation emitted from clouds, water vapour and other gases in the atmosphere that is directed towards the Earth’s surface.

5. Outgoing infrared (longwave) radiation (L ): The radiation emitted from the Earth’s surface.

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Net radiation (Rn) is equal to the difference between the incoming and outgoing shortwave (solar) radiation (K and K ) plus the difference between the incoming and outgoing longwave (infrared) radiation (L and L ). This can be expressed mathematically as:

Rn = K - K + L - L (1)

In theory, you may measure all of the variables and calculate the net radiation using Equation 1. In reality, it is not always possible to measure all four variables. It is usually easy enough to directly measure the incoming shortwave radiation (K ). There may, however, be instances when you do not have explicit measures of outgoing solar radiation (K ), incoming infrared radiation (L ), or outgoing infrared radiation (L ). In these cases, it may still be possible to indirectly determine the values if other key information is provided (Table 1).

Table 1. Equations for calculating outgoing solar radiation (K ), incoming infrared radiation (L ), and outgoing infrared radiation (L ) variables from the net radiation equation (Equation 1).

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Example of a net radiation calculation

An Excel spreadsheet has been provided on CuLearn in which you may set up the relevant formulas to calculate three of the input variables for the net radiation equation as well as the final net radiation value. This example calculation may be used to ensure that you have the formulas set up correctly before you move on to calculating the Cases provided below.

Scenario A:

Month, time, and weather:

June, midday, no cloud

Solar radiation measured at surface (K ):

850 W m-2

Surface material and temperature:

dry, sandy soil at 30 C

Sky temperature:

5 C

1. Incoming solar radiation (K ): given as 850 W m -2

2. Outgoing solar radiation (K ):

From Table 1 below, a mid-range

K = α K

= 0.30 × 850 W m

= 255 W m-2

3. Outgoing longwave radiation (L ):

albedo value for dry sandy soil is 30% or 0.30.


The longwave radiation flux density emitted from a surface is given by the Stefan-Boltzmann Law:


= 0.95 × (5.67 × 10-8 W m-2 K-4) × (303 K) 4

= 454 W m-2

4. Incoming longwave radiation (L ):

L = σTSKY4

= 0.6 × (5.67 × 10-8 W m-2 K-4) × (278 K) 4

= 203 W m-2

5. Combine all terms to compute net radiation (Rn):

We can now insert the above values in Eqn. 1.

Rn = K - K + L - L

= (850 – 255 + 203 – 454) W m-2

= 344 W m-2

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5. Explain three ways that emergency space blankets (ultra thin plastic sheets with a reflective metallic coating often found in first-aid kits) help keep you warm. Remember to include appropriate references for the resources that you used. (3 marks)

Part 2) Energy budget calculations for areas around Ottawa [19 marks]

Answer questions 6-11 and present your answers in your typed lab report. Handwritten work will not be marked and all values should be reported to two places after the decimal. One-word answers are unacceptable.

6. Calculate the net radiation for the following four cases either by hand or by using Excel. When consulting Table 2 for albedo constants, use middle-of-range values. You are required to calculate one of the Cases during the lab section. Show all calculations for this Case in your lab report, as well as the values for the other three Cases (12 marks).

Case A: December, midday, cloudless, and a fresh snow cover. K = 375 W m-2. Sky temperature

= -31 C. A temperature probe you have installed near the top of the snowpack records a value of -12 C.

Case B: June, midnight, and overcast. The cloud base temperature is 11 C. The temperature of the sandy soil is 16 C.

Case C: June, midnight, cloudless, and very dry with a sky temperature of 5 C. There is a sandy soil at a temperature of 25 C.

Case D: July, midday, and cloudless over Meech Lake. Surface temperature of the lake is 25 C.

K = 900 W m-2. The sky’s temperature is 6 C.

7. Explain why K↓ is so different between Cases B and D? (1 mark)

8. Compare Cases B and C. Are these surfaces experiencing a net energy loss or gain? Which surface is closer to a net energy equilibrium (influx ≈ outflux) and why? (3 marks)

9. For Case A, will the bright sunshine cause the snow to melt? Explain. (2 marks)

10. In the example of a net radiation calculation on page 4, the net energy surplus is used to heat the sandy soil. What energy-consuming process is likely at work in Case D? (1 mark)