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HW1_F11 - Assuming that an energy balance holds between...

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Homework 1 Geog 210a Due: October 6, 2011 Problems from text : 2.2.7, 2.2.13, 2.3.6, 2.3.9, 2.5.3, 2.5.9, 2.6.5, 2.6.6, 2.6.13, 2.6.18, 2.7.6, 2.7.7, 2.7.13, 2.7.15, 2.7.21, 2.8.5, 2.8.7, 2.8.13, 2.8.14, 2.9.3, 2.9.9, 2.9.12 DV Problems : 1. The radiative equilibrium temperature of the Earth (T p ) can be determined knowing the balance between the incoming solar radiation (E s ) absorbed by the Earth and its thermal emission (E t ). The net incoming solar radiation is E s = S d (1- α ) π R 2 where R is the Earth's radius (6371 km), α is its planetary albedo (0.3) and S d is the "solar constant". The solar constant can be determined knowing the luminosity or radiant output of the sun (L o =3.9x10 26 W) and the spherical shell over which that radiant energy is dispersed (S d = L o /(4 π D 2 ); where D is the mean Earth-Sun distance = 1.5x10 11 m). The thermal emission for a blackbody Earth is equal to E t = 4 π R 2 σ T p 4 where σ is the Stefan-Boltzmann constant (=5.67x10 -8 W m -2 K -4 ) and the temperature is in Kelvin.
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Unformatted text preview: Assuming that an energy balance holds between incoming solar radiation and out-going longwave energy, derive the functional relationship for T p to all of the other variables in the system and then calculate the equilibrium temperature of the Earth. Assuming all of the other parameters are constant, determine the derivative of T p with respect to solar luminosity. If the solar output varies by 1%, what are its effects upon the radiative equilibrium temperature of the Earth? 2. Help the lazy professor write the final HW. Write an instructive, yet creative, question that you think that someone should be able to complete in less than 20 minutes. Discuss what points covered in class are used in your question and address how you will examine them. Give a complete answer for the question. Remember use only material covered in this homework. Present the question and its answer on a single, separate sheet of paper....
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