In Homework #2, Question 8, you were asked to calculate the concentration of car

Question

In Homework #2, Question 8, you were asked to calculate the concentration of carbon dioxide in the atmosphere in the year 2050 assuming we follow a "business-as-usual" model using 2010 data. Your calculation should have resulted in an approximate carbon dioxide concentration of 547 ppm (parts per million). You were then asked to calculate how much carbon would have to be removed from the atmosphere to return to a concentration of 350 ppm. That answer should have been approximately 418 gigatonnes, meaning that 418 gigatonnes of carbon would need to be removed from the atmosphere to return the concentration of carbon dioxide to 350 ppm. We will use this information in Questions 1 and 2 in Homework #3.

Current estimates show that terrestrial ecosystems (primarily plants and soils) absorb 3 gigatonnes of atmospheric carbon per year. The deep ocean absorbs roughly 2 gigatonnes of atmospheric carbon per year. The lithosphere absorbs 0.2 gigatonnes of atmospheric carbon per year. These 3 absorption rates sum up to the atmospheric carbon removal rate of 5.2 gigatonnes per year that we used in Homework #2.

In lecture, we discussed how modern climate change may affect the ability of natural carbon reservoirs to remove anthropogenic carbon from the atmosphere. Specifically, warming at high latitudes may reduce the strength of convection currents in the ocean by 60% thereby causing a potential decrease in the oceanic component of natural carbon removal by 60%. We also saw that higher precipitation rates and temperatures may increase chemical weathering rates and ultimately the lithosphere component of natural carbon removal by 50%. Climate-related changes in the ability of terrestrial plants and soils to absorb carbon from the atmosphere are not well understood, but models suggest that this reservoir may become saturated within the next 50 years (from 2016). That means the terrestrial reservoir of carbon may no longer remove atmospheric carbon by 2066.

Use the information above about how natural carbon reservoirs may be affected by climate change to calculate the year in which the atmospheric carbon dioxide concentration will return to 350 ppm.

Let's assume that the modified absorption rates for the lithosphere and ocean reservoirs do not take effect until the end of 2050. Let's also assume that we do not burn any fossil fuels after 2050.

Hint: Break the problem down into three majors steps.
1) Calculate the new rate of removal for the ocean reservoir and the lithosphere reservoir. The removal rate for terrestrial ecosystems will remain unchanged until after 2066. Add these removal rates together.
2) Calculate the amount of atmospheric carbon removed by 2066 using the combined removal rates for terrestrial ecosystems, the oceans, and the lithosphere. Subtract that value from 418 gigatonnes of carbon.
3) After 2066, only the ocean and lithosphere will absorb sufficient carbon. So, use the combined removal rate for the ocean and lithosphere to calculate the number of years to remove the remaining amount of carbon. Add this number to the year 2066.

Please type your answers out in the following format:

Assuming that modern climate change will affect natural carbon reservoirs, atmospheric concentrations of carbon dioxide will not return to 350 ppm until the year XXXX.

Explanation / Answer

So, basically you have to remove a total of 418gigatonnes of carbon dioxidem if we calculate from 2016 we have,

34yrs till 2050. Till 2050 as given in the question the modified rates do not come into affect. Hence, using the 5.2 gigatonnes per year rate,

Till 2050- 5.2*34yrs= 176.8 gigatonnes CO2 will be removed.

Now the new rate for ocean :

Reduced by 60%. That means only 40% of the current rate is into power.

New ocean rate- 0.4*2=0.8 gigatonnes per year

New rate for lithosphere:

Increased by 50%

New lithosphere rate- 0.5*0.2 =0.1, 0.1+0.2=0.3 gigatonnes per year

Terrestial rate is the same i.e, 3gigatonnes per year till 2066.

Hence for the 16 yrs (2050-2066) the total modified rate is 0.8+0.3+3=4.1gigatonnes per year

Amount of CO2 removed = 4.1*16=65.6 gigatonnes

Hence, total CO2 removed by 2066= 65.6+176.8=242.4 gigatonnes per year.

Remaining = 418-242.4= 175.6 gigatonnes

After 2066, only ocean and lithosphere will absorb. Hence, the rate is 0.8+0.3=1.1 gigatonnes/year

So, years to remove 175.6= 175.6/1.1=159.6 years

Adding to 2066= 2225.6

Hence, year 2225 and 6 months to reach 350ppm of CO2!

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