1- Let’s consider what the Earth would look like without horizontal energy trans
ID: 1661053 • Letter: 1
Question
1- Let’s consider what the Earth would look like without horizontal energy transport. Figure 3.9 in the textbook provides curves of insolation (the average flux received throughout the day on a horizontal surface) at several different latitudes. Using these values and the StefanBoltzmann law, determine the equilibrium temperature at: (a) The Equator at the start of February (b) 60º N at the start of February (c) Using the Internet, look up the daily average temperatures in February for Whitehorse, Yukon (60.7ºN) and Singapore (1.4ºN) as real-world proxies for the values you calculated above. NOTE: don’t forget to cite where you found the information!! If they are different from the values you calculated in (a) and (b), describe why.
2- One of the factors that will affect atmospheric thickness is temperature.
(a) Using the temperatures you found in Question 1, determine the atmospheric scale height at Whitehorse and Singapore in February.
(b) Do you think that the height of major atmospheric structures could change from pole to equator? Why or why not?
12 2 Noon 12 3 2 r solstice 4 10 Winter 12 1 10 5 Sotstice Horizon Sunset 9 7:30 4:30 PM. 10 A.M. 7:30 Sunrise 4:30 Figure 3.9 Insolation curves at various latitudes in the northern hemisphere as measured at the top of the atmosphere. Black lines mark the equinoxes and solstices. (Source: Strahler and Strahler, 1997, p. 44). Reprinted from Strahler and Strahler, Physical Geography, 1997, p. 44 with permission from John Wiley & Sons Ltd.Explanation / Answer
1)
The equilibrium temperature of a blackbody can be determined using the Stefan-Boltzmann Law;
sigma T^{4} = S_{i} (1-A)
Where sigma is the Stefan-Boltzmann constant (5.67 * 10-8 W/m2/K4) and T is the temperature
Si is the solar insolation and A is the albedo for earth (0.3)
a) During the start of February, as shown in the fig., Si at the equator is around 425 W/m2
Therefore,
5.67*10^{-8} * T^{4} = 425 (1-0.3)
T =left ( rac{297.5}{5.67*10^{-8}} ight )^{ rac{1}{4}}= 269 K
b) Similarly, during the start of February, as shown in the fig., Si at 60oN is around 50 W/m2
Therefore,
5.67*10^{-8} * T^{4} = 50 (1-0.3)
T =left ( rac{35}{5.67*10^{-8}} ight )^{ rac{1}{4}}= 158 K
c) The daily average temperatures during February for Whitehorse, Yukon is 10°F or 261 K
(Source: http://www.weatherbase.com/weather/weather.php3?s=46927&cityname=Whitehorse%2C+Yukon%2C+Canada)
The daily average temperatures during February for Singapore is 81°F or 300 K
(Source: http://www.holiday-weather.com/singapore/averages/)
d) These values are different from the ones calculated previously because of the greenhouse effect. The equilibrium temperature calculated using the Stefan-Boltzmann Law is simply the blackbody temperature of the earth surface and does not consider the impact of greenhouse effect imparted by the atmosphere.
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