Midterm2000

Midterm2000 - ESM 203: Earth System Science Jeff Dozier...

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ESM 203: Earth System Science Midterm 2000 Jeff Dozier Assigned 7 November, due 10:00 a.m. 13 November Thomas Dunne ( either hardcopy or e-mail to Dozier) The Midterm Examination counts 25% of your course grade. Answer all four questions. The exam is open-book. You may use your notes, assigned readings, or other material. You may not use each other, so please do not discuss the exam with anyone else. You should refrain from even discussing course notes once you have downloaded or read the exam. Some of the questions are straightforward, and ask you essentially to re-explain what we covered in class. Others questions are more mature, and require you to apply what you have learned to something we did not explicitly teach you. Read the questions carefully and write short, focused answers. Some of the questions may tempt you to diverge into questions of history, policy, or ideology. Avoid this by concen- trating on the technical or management issue being raised. Try to be complete but concise. Do not bury your answer, which might be correct, too deeply. 1. Earth’s Surface Temperature Our old friend, the Harte Energy-Balance Model of Earth-Surface Temperature (from Consider a Spherical Cow ), can be used to investigate the effect of regional- scale deforestation. For reference, the equation for surface temperature is: 1/4 (3 3 2 ) 1.5 2 (3 2 ) pu l s ak k S L H W T fA σ −−− +  =   where S= 1.747 × 10 17 W Solar radiation intercepted by Earth W= 1.07 × 10 13 W Heat generated from nonrenewable energy sources L= 4.08 × 10 16 W Latent heat flux from surface H= 8.66 × 10 15 W Sensible heat flux from surface A= 5.101 × 10 14 m 2 Area of Earth’s surface σ = 5.67 × 10 –8 Wm –2 deg –4 Stefan-Boltzmann constant Note that the values for S, L, H, and W are integrated over the whole planet, rather than per square meter. The dimensionless parameters in the model are given in the following table: a p = 0.3 Planetary albedo k u = 0.18 Fraction of solar radiation absorbed in up- per layer of atmosphere k l = 0.075 Fraction of solar radiation absorbed in lower layer of atmosphere f= 0.95 Fraction of the infrared radiation emitted by the surface that is absorbed in the atmos- phere and then re-emitted from the upper atmosphere Suppose we deforest 20% of Earth’s land surface, and the deforested area subse- quently becomes degraded crop and rangeland. The deforested area has a higher al-
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2 bedo than the old forest: 25% vs. 15%. This change in surface albedo R S translates into a change in planetary albedo in a complicated way, because of multiple reflec- tions between the surface and atmosphere. An analysis of this effect comes up with the following equation to describe the relationship: 0.26 pS aR ∆= (a) 29% of Earth’s surface is land, and the deforestation raises the albedo of 20% of this area from 15% to 25%. What is the new value of a p ?
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Midterm2000 - ESM 203: Earth System Science Jeff Dozier...

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