1. Please have a look at the corrected versions of lectures 18 and 19, and follow the method outlined in slides 20 through 23 of lecture 18. All parts of question 1 refer to a mixed layer at the surface of the ocean, which is essentially infinite laterally, and which does not chemically exchange with the underlying ocean at a significant rate (except for partsd, e and f where DIC export is assumed to be equal to DIC influx). This layer is at a constant temperature of 17.6°C.
a. Use global k of 10 cm/hr. Convert that to k in m/s. Your answer should be similar to that for 12.5 cm/hr in slide 20, lecture 18 (18.20)
b. Start with the “modern” seawater option using the upper left menu at https://biocycle.atmos.colostate.edu/shiny/carbonate/ and update this composition without changing alkalinity (2344 micromoles/kg) and temperature (17.6°C). The atmosphere averaged about 417 ppmv CO2 in 2021. What would be the dissolved inorganic carbon content (DIC) of the ocean in equilibrium with air in 2021, in units of micromoles/kg? And, using a density of 1 kg/liter of water, approximately what is DIC in units of micromoles/m3?
c. Continue to use https://biocycle.atmos.colostate.edu/shiny/carbonate/. If the mixed layer at the surface of the ocean has an average P(CO2) that is about 5.5 ppmv lower than the atmosphere (411.5), what is the total dissolved inorganic carbon content of the ocean at this lower P(CO2), in micromoles/kg? And micromoles/m3?
d. The difference between your answers to (b) and (c) approximates the current ΔC driving global CO2 uptake from the atmosphere into the oceans. Let’s assume this is a steady state, in which CO2 uptake from air is balanced by CO2 export from the surface ocean, so ΔC is approximately constant over years to decades. What is the corresponding steady state flux of CO2 into the ocean, in units of moles/m2/s?
e. Using your answer from (c), what is the corresponding steady state flux in moles per year over the entire global ocean?
f. And in Gt CO2/year?
g. OK, now let’s see if we can save the world. Let’s go back to modern seawater with P(CO2) of ~ 411.5 ppmv. Now holding DIC and temperature constant, determine the effect of instantaneously adding 5 milligrams (0.005 grams) of Ca(OH)2 per liter of seawater (1 kg/liter) to the surface ocean (mixed layer 10 m deep) using https://biocycle.atmos.colostate.edu/shiny/carbonate/. What is the resulting change in alkalinity? What is the resulting change in pH? What is the resulting change in Ωcalcite? What is the resulting P(CO2)?
h. The mixed layer with added alkalinity will take up CO2 from air. What would be the DIC in micromoles/kg in this layer with added alkalinity when it eventually reaches 417 ppmv CO2?
i. What is ΔC for the layer of seawater with added alkalinity in (g) relative to the same water with P(CO2) of 417 ppmv in (h), in micromoles/kg? In micromoles/m3?
j. Using k from (a) and ΔC from (i), what would be the resulting initial flux of CO2 from air into the mixed layer, in moles/m2/s? What is the ratio of this flux to the natural CO2 uptake into the ocean (answer to e)?
k. Adding 5 milligrams of Ca(OH)2 per liter of seawater to a well mixed surface layer 10 m thick, and ignoring natural CO2 uptake into the ocean (answers to (e) and (f)), following the method in slide 22, lecture 18, plot time, in days, versus the cumulative flux of CO2 from air into the surface layer in micromoles/kg. How many days will it take to produce seawater in the mixed layer with 411.5 ppmv CO2? (It might take forever to get to 417 ppmv CO2).
l. What is the pH when the seawater in the mixed layer reaches P(CO2) of 411.5 ppmv? What is Ωcalcite?
m. How many moles of CO2 have been added, per mole of Ca(OH)2 added? In one sentence, why is this ratio less than 2? How many tons of Ca(OH)2 would be required to remove one Gt CO2 from air?
n. If we rapidly add 5 milligrams of Ca(OH)2 per liter of seawater to a well mixed surface layer 10 m thick, and ignoring natural CO2 uptake into the ocean (answers to (e) and (f)), what fraction of the global ocean area would be required to remove 1 Gt CO2 in the year after addition? Take a long, hard look at slide 22 in lecture 18 before answering.
o. Unless we induce calcite precipitation, and/or downward diffusion and mixing reduces the dissolved Ca2+ content of the surface mixed layer to ambient seawater concentrations, this process will increase alkalinity in the local ocean area every time you do it. Let’s assume that calcite precipitation will not become a big problem until Ωcalcite is greater than 10. I realize that https://biocycle.atmos.colostate.edu/shiny/carbonate/ will not calculate results for alkalinity greater than 2500 micromoles/kg, but looking at your answers to (g) and (l) in order to make an educated guess, ignoring calcite precipitation, mixing and diffusion, could you add 5 milligrams of Ca(OH)2 per liter of seawater to the same area of the ocean in a second year, without driving Ωcalcite to a value > 10?