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ER 102 Spring, 2010 Problem Set 9 Due April 8, 2010 J. Harte 1. Suppose that as a result of global warming, forest cover declines over the earth,...

I have questions on the first and 3rd questions of this problem set
1. Suppose that as a result of global warming, forest cover declines over the earth, reaching a low of 70% of current forested area. Assume the albedo of forest is 0.10, while that of the land cover that replaces it is 0.15. Further assume that the cloudiness and transmissivity of the sky above the former forested area is typical of Earth’s average (and thus has the same RA and TA as the atmosphere as a whole).

a. Using the multiple-scattering formalism, calculate the new albedo of the entire earth as a result of the albedo change accompanying this shift in land cover. (15 pts.)

b. Make a back-of-the envelope estimate of what the world-wide reduction in evapotranspiration (ET) would be if the ET rate from forest is twice that from the grassland or cropland that replaces it. Express your answer as a change in watts/m2 leaving Earth’s surface. (You will have to make some pretty bold assumptions here about what contribution forests make to present-day ET; state those assumptions clearly) (15 pts.)

c. Estimate the combined effect of the reduction in ET and the increase in albedo on Earth’s average surface temperature. (State any assumptions explicitly, but keep them as simple as possible.) Is this a negative or positive feedback to global warming? (20 pts.)

d. Describe qualitatively one other global climatic consequence that would likely result from the decline in forested area on Earth. (5 pts.)

3. The fraction of ultraviolet radiation incident on the top of the atmosphere that penetrates the stratosphere can be represented by an optical depth type formula of the form: I/Io = exp( m/mo), where m is proportional to the stratospheric ozone concentration. As you were told in class, 1% decrease in the stratospheric ozone concentration is expected to produce an increase of 2% in the transmitted UV.

a. Use this information to obtain the value of m/mo in the above formula (12 pts.)

b. Deduce from your answer to part a. the fraction of the incident UV that is being transmitted through the stratosphere. (6 pts)

ER 102 Problem Set 9 J. Harte Spring, 2010 Due April 8, 2010 1. Suppose that as a result of global warming, forest cover declines over the earth, reaching a low of 70% of current forested area. Assume the albedo of forest is 0.10, while that of the land cover that replaces it is 0.15. Further assume that the cloudiness and transmissivity of the sky above the former forested area is typical of Earth’s average (and thus has the same R A and T A as the atmosphere as a whole). a. Using the multiple-scattering formalism, calculate the new albedo of the entire earth as a result of the albedo change accompanying this shift in land cover. (15 pts.) b. Make a back-of-the envelope estimate of what the world-wide reduction in evapotranspiration (ET) would be if the ET rate from forest is twice that from the grassland or cropland that replaces it. Express your answer as a change in watts/m 2 leaving Earth’s surface. (You will have to make some pretty bold assumptions here about what contribution forests make to present-day ET; state those assumptions clearly) (15 pts.) c. Estimate the combined effect of the reduction in ET and the increase in albedo on Earth’s average surface temperature. (State any assumptions explicitly, but keep them as simple as possible.) Is this a negative or positive feedback to global warming? (20 pts.) d. Describe qualitatively one other global climatic consequence that would likely result from the decline in forested area on Earth. (5 pts.) 2. 1.a. The stratosphere contains ~ 300 Dobson units of ozone. Convert this to units of i. molecules/ cm 2 , ii. total moles of O 3 , iii. total mass of stratospheric O 3 in grams, iv. ppb(v) in the stratosphere. (12 pts.) b. Ozone is naturally created and destroyed at a rate of about 2 x 10 39 molecules per year. What is the residence time, in years, of O 3 in the stratosphere? (5 pts.) 3. The fraction of ultraviolet radiation incident on the top of the atmosphere that penetrates the stratosphere can be represented by an optical-depth-type formula of the form: I/Io = exp(-m/mo), where m is proportional to the stratospheric ozone concentration. As you were told in class, 1% decrease in the stratospheric ozone concentration is expected to produce an increase of 2% in the transmitted UV. a. Use this information to obtain the value of m/mo in the above formula (12 pts.) b. Deduce from your answer to part a. the fraction of the incident UV that is being transmitted through the stratosphere. (6 pts) 4. There are about 5x10 5 new skin cancers diagnosed each year in the US. (most of these are basal cell cancers that are easily treated if caught in time; the more deadly melanoma is fortunately only a small subset of these cancers). Knowing only the above, and assuming you are an average person: What is the probability that you will be diagnosed at least once with skin cancer during your lifetime? (10 pts.)
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