Calculate how long it would take for a perturbation of the atmosphere that is pr
ID: 106550 • Letter: C
Question
Calculate how long it would take for a perturbation of the atmosphere that is produced by instantaneous release of all available fossil fuel reserves (i.e. 3700 Gt) into Earth’s atmosphere and surface spheres to decrease to 5% (0.05) of its original size by returning to the geosphere. Hint – you need to consider which residence time is appropriate to apply this problem (Residence times for C is procided blow). You also only need to consider the amount of carbon added to the system, not the total amount. The equation may help for this question A(t) = A0 * e(-t/)
Reservoir
Stock (Gt
C)
Input flux (Gt C/yr)
Output flux (Gt
C/yr)
Residence time (yr)
Atmosphere
597
190.2
190.2 =
120 + 70 +0.2
3.14
Surface Ocean
900
171.8
171.8
1.11
Deep Ocean
37,100
101.2
101.2
367
Land Vegetation (+ Soils)
2,300
120
120
19.2
Marine biota
3
50
50 = 39 + 11
0.06 ~ 20 days
Surface Spheres relative to the Geosphere
40,897
0.2
0.2
204,000
Reservoir
Stock (Gt
C)
Input flux (Gt C/yr)
Output flux (Gt
C/yr)
Residence time (yr)
Atmosphere
597
190.2
190.2 =
120 + 70 +0.2
3.14
Surface Ocean
900
171.8
171.8
1.11
Deep Ocean
37,100
101.2
101.2
367
Land Vegetation (+ Soils)
2,300
120
120
19.2
Marine biota
3
50
50 = 39 + 11
0.06 ~ 20 days
Surface Spheres relative to the Geosphere
40,897
0.2
0.2
204,000
Explanation / Answer
For this problem the residence time of land vegetation (+soils) is considered to be more appropriate because fossil fuels are taken from the ground and they are mainly formed due to degradation of dead and decaying matter.
The stock Gt C value for land vegetation is =2300 and the residence time is =19.2yrs.
This data shows that the residene time of fossil fuels in land vegetation is 19.2yrs.
The release of all available fossil fuels=3700Gt
Now dividing the available fossil fuels by Gt value of land vegetation,we get
=(3700/2300)=1.6086
The amount of carbon added in case of land vegetation due to fossil fuels=10 petagrams of carbon
The half life period of carbon must also be considered which is -0.693.
The value of t is 5730 for carbon.
Substituting the values in the formula,we get
A(t)=Ao*e(-t/t)
A(t)=1.6086*e(-(-0.693)/5730)=1.6087
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