3.4 Now let’s apply similar logic to the ocean. The surface area of the ocean is

Question

3.4 Now let’s apply similar logic to the ocean. The surface area of the ocean is about 3.6 × 1014 m2, and net photosynthesis averages 1.3 × 1014 g C d–1. The average depth of the ocean is about 3800 m, and for purposes of this calculation we can assume that the marine analogue the hypolimnion, which we will call the sub-thermocline water, has a thickness of about 3600 m. Assume that the bottom water of the ocean has a dissolved oxygen concentration of 10 g O 2 m–3 when initially formed and that its residence time is 500 years. Assume furthermore that 10% of the organic carbon produced by marine algae is exported to the sub-thermocline water. Assuming that all the organic carbon exported to the sub-thermocline water is oxidized there, what would you expect the average dissolved O2 concentration to be in the sub-thermocline water? Now let’s imagine that the formation of oceanic bottom water is slowed due to a global warming and that the residence time of seawater in the sub-thermocline water increases to 1000 years. What would the average concentration of dissolved O2 in the sub-thermocline water become under these conditions?

Explanation / Answer

Given:Surface area of ocean=3.6*1014m2

average depth of ocean=3800 m

Now volume of ocean water= surface area* depth of ocean

=3.6*1014m2*3800m

=136.8*1016m3

Given:Average depth of sub-themocline water=3600 m

Then depth of bottom water=3800-3600=200 m

Given Residence time of bottom water=500 years

Dissolved oxygen in the bottom water per m3 of ocean water=10gO2m-3

Total amount of dissolved oxygen in the bottom water= total volume of bottom water*10gO2m-3

=3.6*1014m2*200m*10gO2m-3=7.2*1017gO2

Given: Residence time of bottom water=500 years

Now,

Residence time= total amount of oxygen / rate of input or output of O2

500=7.2*1017gO2/rate of inputor output

Rate of input/ouput=7.2*1017/500=1.44*1015gO2/year

Given: 10% of organic carbon of bottom water is exported to the sub thermocline water

10% of 1.44*1015gO2/year

=0.144*1015 gO2 exported to sub thermocline water

Average dissolved concentration of O2 in subthermocline water=??

Residence time of subthermocline water=1000 years

Residence time=Amount of dissolved oxygen/Rate of input to the subthermocline water

1000 years=Amount of dissolved oxygen/0.144*1015gO2year-1

=6.94*10-15gO2 is dissolved in the sub thermocline water

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