Environmental Dynamics Homework 03

Based on results of the first assignment, I think these practice exercises are going to prove quite useful in developing your understanding of Environmental Dynamics. As was stated on the previous set of exercises, I don't expect that you will be able to recall the appropriate formulae from memory, but I do expect you will be able to locate them in appropriate reference material will a little bit of effort. In addition, I want to continue to encourage you to work together as a group - part of the philosophy of this program is to share expertise across disciplinary boundaries and that can't be done without working together.

This week, we will derive some interesting computations related to the global carbon cycle that I think will have some relevance as we continue to progress through the semester. The results of our computations this week will be useful to keep in mind as we proceed with our discussions of global change and the dynamic processes that effect those changes.

Simplified illustration of the global carbon cycle showing reasonable estimates of the quantities of carbon contained within each reservoir (in GT) and the relative fluxes of carbon between these reserovirs (in GT/y). Illustration taken from http://geosys.mit.edu/~chem/.

1. Assuming Earth is a sphere with diameter 12,756 km, calculate the volume of planet Earth in a) cubic kilometers (km³).

2. Earth's atmosphere extends outward from Earth's surface until it eventually more or less "dissolves" into space. However, let us assume that the bulk of Earth's atmosphere lies relatively close to the surface (say up to 7 km altitude). Using this assumption, calculate the volume of Earth's atmosphere in a) cubic km (km³).

3. According to the figures provided by Charles Keeling of the Scripps Institution of Oceanography, the concentration of CO₂ in the atmosphere is on the order of 380 ppmv (parts per million by volume). Using this figure, calculate the volume of carbon dioxide in the atmosphere in a) cubic kilometers (km³) and b) liters (L).

4. Each mole of CO₂ has a mass of 44 grams. Calculate the total mass of CO₂ in Earth's atmosphere in a) grams, b) kg, c) petagrams, d) gigatons. How does this compare to the value in the graphic above? Is it larger or smaller? Why? Provide a reasonably thorough explanation.

5. The Oceanic reservoir contains 38,500 GT of carbon. Assuming this carbon occurs primarily as dissolved CO₂, bicarbonate ion (HCO₃)^-, and carbonate ion (CO₃)^-2, estimate the concentration of total CO₂ (SCO₂) in the ocean in milligrams per liter (mg/L).

7. If all of the CO₂ in the atmosphere were to be transferred to the ocean reservoir, what percent increase in the quantity of carbon would occur?

8. Assuming all of the CO2 in the atmosphere is transferred to the ocean reservoir, recalculate the concentration of SCO₂ in the ocean in mg/L. Is this a significant change?