Assignment.

1. Evaporation removes the equivalent of 1.

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meter of water from the entire ocean every year. The ocean covers a surface area of 361,132,000 square kilometers. Calculate first the total mass of water that is evaporated over a year (A cubic meter of ocean water contains a mass of 1000 kg). The energy required to evaporate 1 kg of water is equal to 2.3×106 J. Calculate the energy that must be absorbed per square meter of ocean surface to provide this evaporation. How does this compare with the average rate at which solar energy is absorbed at the earth surface? (4 points)

2. Considering the energy balance of the present Earth with an albedo of 30%, we calculated in Chapter 13 that the Earth would have to radiate to space at an effective temperature of 255K (as in Box 13.2 in McElroy) in order to maintain energy balance. Suppose the albedo were to decrease to 27% due to the melting of the Arctic ice cap (white ice converted to darker ocean), what would the effective and surface temperature be in this case? Assume that the greenhouse effect in all cases would be efficient to raise the surface temperature by 33K with respect to effective temperature values. Discuss the implication. (4 points)

3. Residence times of Carbon. In Chapter 4, we briefly examined the carbon cycle. The figure below is a representation of the pre-industrial carbon cycle (with minor modifications from Figure 4.1 in the text). Reservoir contents are in units of Gigatonnes of Carbon (Gt C) and flows, indicated by arrows, are in units of Gt C per year (1 Gt = 109 tonnes =1012 kg). Note: By pre-industrial, we mean that in the flows and reservoirs are not significantly influenced by human activities as they have been since industrial times. (4 points)

a) The diagram is missing turnover from the sediment reservoir back to the atmosphere. Assume that sediments are returned to the atmosphere at a rate of 0.2 Gt of C/year. (i) Complete the diagram by adding this in; make sure the format is consistent with the rest of the diagram. (ii) Briefly explain the natural processes responsible for this direct movement of sedimentary carbon back to the atmosphere.

b) How long does it take the carbon in the sediment reservoir to get back to the land-ocean-atmosphere system? (Recall that residence time in this case would be Contents/output rate). Note that fossil fuels come from the sediment reservoir. Briefly explain the implications for how old our fossil fuel carbon is—i.e., on average how long have the fossil fuels we are tapping into today been “residing” in the sediments reservoir?

c) Through fossil fuel use, humans are significantly accelerating the rate at which the ancient carbon in the sedimentary reservoir is being returned directly to the atmosphere. Assume the human rate of sedimentary C ( atmosphere is 50 times that of the pre-industrial rate of 0.2 Gt C/ year. Calculate how much additional carbon humans are removing from the sediment reservoir and adding to the land-atmosphere-ocean system every year. Report your answer in tonnes (1 Gt = 109 tonnes).

d) Now let’s pretend that we have switched to a “zero-carbon” economy. In other words, pretend that humans have eliminated fossil fuels from their energy sources. Since the industrial revolution though, let’s say humans have added a total of 200 Gt C to the atmospheric reservoir (roughly corresponds to an increase of 280ppm CO2 to 390ppm CO2 today). Since we have “switched off” the human contribution from the sediment reservoir to the atmosphere, we can once again approximate the carbon cycle using the pre-industrial diagram above. How long will it take the additional 200 Gt C we added to the atmosphere to be removed from the atmosphere-land-ocean system and returned to the long-term sediment reservoir? Think about what this means for the long-tailed effects of our activities…this is how long it will take for us to return to pre-industrial levels of CO2 if we were to stop burning fossil fuels right now!

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