According to the Stefan-Boltzmann law, the amount
of radiation emitted over a unit area during a unit time (i.e., the
object's irradiance) is a function of the object's temperature. As
the object's temperature increases, the irradiance increases; as the
temperature decreases, the irradiance decreases.
Stefan-Boltzmann Law
E* = sT4
where E* = the blackbody irradiance [in W m-2]
s = 5.67x10-8 W m-2 deg-4 (Stefan-Boltzmann constant)
T = the temperature of the radiating body [in degrees K]
This law states that the amount of energy radiated per unit time from a unit surface area of a blackbody is proportional to the fourth power of the absolute temperature of the object.
In this lesson, the student will calculate the approximate irradiance during a day at an ARM/CART extended facility. The calculated irradiance then will be compared to the measured values at the station.
Objectives
Stefan-Boltzmann Law
E* = sT4
where E* = the blackbody irradiance [in W m-2]
s = 5.67x10-8 W m-2 deg-4 (Stefan-Boltzmann constant)
T = the temperature of the radiating body [in degrees K]
This law states that the amount of energy radiated per unit time from a unit surface area of a blackbody is proportional to the fourth power of the absolute temperature of the object.
In this lesson, the student will calculate the approximate irradiance during a day at an ARM/CART extended facility. The calculated irradiance then will be compared to the measured values at the station.
Objectives
- To calculate the hourly irradiance of the earth at a site given the near-surface air temperature of the site.
- To compare the calculated values of irradiance with those measured by instruments at the site.
- It is best to use data from a clear, calm day for this activity.
| PROCEDURE 1. On your writing paper or lab notebook, create a four-column, 24-row table. Label the rows by the hours of the day starting at midnight and ending at 11 PM. Label the columns "Time", "Air Temperature (in degrees Celsius)", "Calculated Irradiance (in Watts per square meter)" and "Measured Irradiance (in Watts per square meter)". Put a title at the top of the table and include the date of the data. 2. Write the hourly ARM air temperature data in the appropriate column. Make sure the data are in degrees Celsius. 3. Use the Stefan-Boltzmann Law to calculate the hourly irradiance during the day. Write these calculations in the proper location in the table. Assume that the ground is radiating as a blackbody. Assume that the ground's effective temperature is equal to the ARM air temperature. Remember to convert the temperatures to Kelvin before calculating irradiance. 4. Write the hourly ARM upwelling longwave radiation measurements in the final column of the table. 5. Graph the calculated and measured irradiances on the graph paper, using different colors for each. Be sure to label your axes, title your graph and include a legend. QUESTIONS 1. How does the calculated irradiance for the earth change during the day? When is the irradiance the highest? When is it the lowest? 2. How do the calculated and measured irradiances compare to one another? Is one always higher than the other? If so, which one? What could account for the differences you found? 3. If an observing network does not have enough money to purchase instruments to measure upwelling terrestrial radiation directly, would you approve scientists using the air temperature data to calculate this variable as an alternative to direct measurement? If so, do you think there will be occasions when these values will not be accurate? If so, under what circumstances? |
PREREQUISITES
Blackbody Irradiance Longwave radiation Terrestrial radiation Upwelling CORE CURRICULUM SKILLS APPLIED IN THIS LESSON
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