Assignment

Earth's present atmosphere is theorized to have evolved from one based upon outgassing of the planet's interior.

Consider that period in Earth's history when outgassed water vapour has condensed to form a significant ocean. During this same period, suppose that there are only two mechanisms for removing CO₂ from Earth's atmosphere - namely photosynthesis and dissolution. (Note: CO₂ is dissolved into water through the process of dissolution.)

1. Given that the metal Calcium Oxide (CaO) is abundant in Earth's crust, and reacts with CO₂ according to the following chemical reaction

CaO(s) + CO₂(g) → CaCO₃(s),

provide a process-flow representation for this mechanism that removes CO₂ from Earth's early atmosphere. (Note: CaCO₃ forms as a precipitate - i.e., a solid that forms from a solution.)

2. Suppose the product of the mineral carbonation (carbonation is the process of dissolving carbon dioxide in liquid) reaction detailed in Question 1 above:

a. Precipitates at a rate of 2 cm/yr. How long will it take for a 0.5 m layer to accumulate?

b. Produces sediment that is compacted to a 4.5:1 ratio during lithification process - e.g., due to burial pressure. Determine the resulting thickness of the originally 0.5 m layer accumulated in Question 2(a).

c. Produces spheres of CaCO₃ with a radius of 2 mm.

i. Determine the corresponding terminal velocity (in m/s) of these spheres in water from v_T ≈ ( 151 r )^½, where r is the radius in m.

ii. Assuming and ocean depth of 2 km for an off-shore operation, calculate the settling time - i.e., the time it takes each of the spheres to descend through the ocean and settle out as sediment.

3. After the process of lithification completes, what is the resulting class and type of sedimentary rock? Obtain a photograph of a representative sample of this rock. (Note: Please attempt to provide an original photo. If you are unable to do so, please indicate your source. Note that you may be audited to prove originality.)

4. Enhance your Question 1 process-flow diagram to account for Question 3.

Over the past 400,000 years, but excluding the past 200 years, paleoclimatological evidence suggests that the concentration of CO₂, i.e., [CO₂], has barely exceeded 300 ppm.

5. Calculate the percentage reduction in the [CO₂] from volcanic-outgassing levels to this peak value of 300 ppm. (Note: Volcanic-outgassing levels for CO2 are provided in the "Appendix" below.)

Inspired by the results of Question 4, an interdisciplinary team undertakes to geoengineer the sequestration of CO₂ through very-large-scale mineral carbonation (VeLaMiCarb). (Geoengineering is a direct manipulation of the Earth system.) The VeLaMiCarb team's approach includes isolating the resulting precipitate (i.e., CaCO₃(s)), and ultimately burying it in underground vaults impermeable to groundwater.

6. Obtain [CO₂] versus time data for the past 5 years from the Mauna Loa Observatory. (Note that you can download a high-quality version of this graphical plot in various formats. See "Resources" below for access information.)

7. Using the graphical plot acquired in Question 6:

a. Estimate the current [CO₂] in ppm.

b. Estimate the annual increase in the [CO₂]. Include an annotated version of the plot in your solution that illustrates how this rate was calculated.

8. Based on your answer to Question 7(b), determine how long it will take the current value of [CO₂] to double. (This will subsequently be referred to as the "2x[CO₂] climate scenario".)

9. Suppose the EBCM-determined energy,¹ E_{2CO_2}, associated with this doubling of the [CO₂] is 1423.9 W/m². Estimate the temperature difference, resulting from the 2x[CO₂] climate scenario, using the Stefan-Boltzman Law T = (E_{2CO_2}/4σ)^1/4 - T0, where σ and T₀ are the constants 5.67x10-8 W/m2⋅K4 and 275.8 K, respectively.

¹ EBCM is a very simple climate model originally developed for NATS 1780 (Weather and Climate). Additional information is provided via the "Resources" below.

10. Rahmstorf (see "Resources" below) estimated that temperature differences account for sea-level changes according to the proportionality constant 3.4 mm/yr per °C. Using the temperature difference obtained in Question 9, estimate the change in sea level for the time span obtained as the answer to Question 8 - i.e., for the 2x[CO2] climate scenario.

11. Estimate the wavelength of maximum intensity corresponding to Earth radiating as a black body in the 2x[CO₂] climate scenario using Wien's Displacement Law, λ_max = w/T, where w = 2897 x 10-6 m•K.

12. In which part of the EM spectrum (below) is Earth radiating under the 2x[CO₂] climate scenario? What is the fate of this radiation?

13. Suppose the current estimate for the [CO₂], i.e., the answer to Question 7(a), corresponds to storage of 775 GtC in Earth's atmosphere. (1 GtC is a GigaTon of C.) If the intention of the geoengineered sequestration of CO₂ is to completely offset the effect of the 2x[CO₂] climate scenario, what should be VeLaMiCarb's target for C removal over the time frame dictated by your answer for Question 8 above? Explain.

14. It is stated that: "The VeLaMiCarb team's approach includes isolating the resulting precipitate (i.e., CaCO₃(s)), and ultimately burying it in underground vaults impermeable to groundwater." Why is groundwater isolation an important design consideration? (Hint: The rock type identified in Question 3 is highly susceptible to acid rain.)

15. Enhance your Question 4 process-flow diagram to account for the VeLaMiCarb approach.

16. Does this VeLaMiCarb initiative favour the importance of a systems-based approach? Explain.

17. Why might geoengineering, along the lines of the VeLaMiCarb initiative, become a necessity? Explain.

Attachment:- Assignment.pdf