Understanding the PETM using Carbon Isotopes

Environmental Science
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Question description

Question 2: Understanding the PETM using carbon isotopes 

Around 55 Myr ago, global temperatures increased by 5-9˚C over 1-10 thousand years, and the δ13C of the ocean’s carbon (as recorded by benthic foraminifera) decreased by 3‰. The cause of the Paleocene-Eocene Thermal Maximum (PETM) was initially thought to be a sudden increase in volcanic activity. Some scientists now believe that it was caused by a massive injection of methane to the atmosphere from methane hydrates in marine sediments (the methane was subsequently oxidized to CO2). Carbon isotope data offer a way to test these hypotheses, since volcanic COhas very different δ132 a C than methane. In the problems below, we’ll consider only the carbon in the ocean and atmosphere. Assume that just prior to the PETM, the atmosphere held 2,000 GtC, and the ocean held 38,000 GtC. Because there’s so much more carbon in the ocean than in the atmosphere, and because most of the ocean’s carbon is in the deep ocean, the δ13C of deep waters (again, recorded by benthic foraminifera) can be taken as the δ13C of the combined ocean-atmosphere carbon reservoir. 

a) Volcanic carbon dioxide δ13C is –5‰. The average δ13C of the climate system before the PETM was –1.45‰. The magnitude of change during the PETM was δ13C was –3‰. Use the following isotopic mass balance equation to calculate how much volcanic carbon would have to be added to the climate system at the start of the PETM in order to produce the isotopic change observed. MX is the mass of carbon at time X, (δ13C)X is the δ13C at time X. 13C during PETM (F) = 13C before PETM (0) + 13C added (A) (δ13C)M = (δ13C)M13FF 00 + (δC)AMA b) Modern volcanic CO2 fluxes are ~80 MtC per year (Morner and Etiope, 2002). 

b) Assume that the PETM carbon release occurred over 10,000 years. Using your answer from #1, by what factor would volcanic emissions have to increase to reach the implied fluxes for the PETM if volcanic CO2 was the sole source of the additional carbon?

 c) The average δ13C of methane is –60‰. What mass of carbon from marine methane hydrates would have to be added to the climate system to cause the observed isotopic change? The estimated mass of carbon stored as marine methane hydrates today is 500 to 2,500 Gt.

I am having trouble on c. I got 3.45% on a, and 2.752 on b. I am quite sure they are both wrong

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