"Back of the envelope" problem set on carbon management

We've been exploring strategies to reduce the excess CO₂ that is entering, and staying, in the atmosphere, currently estimated to be approximately 3.3 gigatons of carbon annually.

Keep in mind that I have intentionally framed this problem in largely technological terms. There are other potential ways of thinking about the climate change problem -- most of which lie outside the scope of the course.

Environmental studies is characterized by the recognition that there are multiple valid ways for viewing an issue. This material is designed to help you frame environmental science problems in ways that will enable you to think wisely about them and to solve them. In this section of the course, we want you to think carefully about the order of magnitude of the numbers involved in human impacts on the carbon cycle. This material is presented not because the authors are convinced (and want to convince you) that active carbon management technologies are required. We do want you to recognize the importance of the orders of magnitude involved in this issue. If you really think that the key to solving the climate change problem is to change patterns of human consumption in the United States then make sure that your thinking is consistent with reasonable calculations of possible impacts. Again, to be clear --you can argue that the root of all environmental problems lies in modern attitudes towards consumption and that until those attitudes are changed we will just experience crisis after crisis. It is not our intention to tell you that your views are wrong. What we do want, however, is for your to make arguments that are qualitatively defensible with "order of magnitude arguments:.

Here are some opportunities to explore these issues.

STATE ALL ASSUMPTIONS. Feel free to look data up! At the beginning of each problem, list all the data you used or estimated and where relevant indicate where you got the data from.

(1) The Bush administration has proposed to reduce CO₂ output from 183 metric tons of carbon-equivalents per million dollars of GDP to 151 metric tons of carbon-equivalents per million dollars of GDP in 2012. If you are interested in reading some details of the voluntary compliance agreements that the administration has recently announced signing, see http://www.epa.gov/newsroom/headline_021203a.htm

Figure out how much carbon the US is likely to be emitting in 2012 given a reasonable assumption of GDP.

How much carbon is the US likely to be emitting in 2012 if carbon efficiency doesn't change (again assume a reasonable GDP growth rate)?

How much carbon is that per person?

How much carbon would be emitted worldwide if all humans emitted this much carbon?.

(2) Estimate how much carbon the US could conserve if all vehicles in the United States were fueled with hydrogen fuel cells. Assume no CO₂ is released during the production of hydrogen.

(3) Estimate how much of the earth's primary productivity would need to be directed towards carbon mitigation using terrestrial sinks in order to stabilize atmospheric carbon at 400 ppm in 100 years assuming that CO₂ outputs stay constant. Assume that every gigaton of excess carbon that remains in the atmosphere contributes another 0.4 ppm to the global average. This assumption relies on the assumption that the current ratio of total outputs (~7.1 Gt) to atmospheric increases (3.3. Gt) stays the same. Now do the same calculation while changing one parameter of your choice (e.g. amount of CO₂ released). Explain why you changed the parameter you chose in the way you did.

(4) Current US demand for electricity is 12 TW. 88% of that electricity is generated by fossil fuels. Estimates of carbon dioxide outputs from electricity generated from gas is 5-6 GtCO₂ per 10 TW electricity, from oil is 7-8 GtC O₂ per 10 TW electricity and from coal is 9-10 GtCO₂ per 10 TW. If all electricity in the US was generated by nuclear fission, how much CO₂ per year could the US save?

(5) Maximum conversion efficiencies for photovoltaic cells are 15% (15% of sunlight can be converted to electricity). The average solar flux is 0.6 W m². Given the US electricity needs stated above, how much land mass would be required to generate all the U.S.'s energy needs? If the entire population consumed energy at the rate that people in the US do, what percentage of primary productivity would need to be directed towards energy production (assuming all electricity is generated from sunlight)?

(6) How much energy is expended per skier at a typical downhill ski facility? Think carefully about the assumptions that you make in doing this problem and state them. For example, are you picturing a typical ski facility in Virginia or Utah? Do some research to figure out as much as you can about the energy demands of snow making and chair lifts. Iπm interested in comparing some of your numbers on this subject in class.

(7) How much carbon dioxide do Bates College students release into the atmosphere each year through their travel to study abroad?