A developer in Amazonia has a plan to raise the levels of atmospheric oxygen by cutting down the rainforest and replacing it with a managed forest. The managed forest would be cut every 20 years, the cut trees would be sealed in plastic bags loaded with weights, and the bags would be dumped to the bottom of the ocean. What is the developer’s reasoning? Would the plan work? Why or why not? 3. In oxygen-depleted (anoxic) muds on the ocean f
PROBLEMS
6. 1 Short questions on the oxygen cycle
1. Comment on the following statement: “Destruction of the tropical rainforests, the lungs of the Earth, menaces the supply of atmospheric oxygen”
2. A developer in Amazonia has a plan to raise the levels of atmospheric oxygen by cutting down the rainforest and replacing it with a managed forest. The managed forest would be cut every 20 years, the cut trees would be sealed in plastic bags loaded with weights, and the bags would be dumped to the bottom of the ocean. What is the developer’s reasoning? Would the plan work? Why or why not?
3. In oxygen-depleted (anoxic) muds on the ocean floor, bacteria derive energy by using Fe2O3 and H2SO4 to oxidize organic material. The stoichiometry of the reaction is as follows (“CH2O” represents the organic material):
This reaction represents an important source of atmospheric oxygen. Why? Where do Fe2O3 and H2SO4 originate from? Comment on the role of the reaction in the oxygen cycle.
4. Hydrogen atoms are produced in the upper atmosphere by photolysis of water vapor and can then escape to outer space because of their light mass. This escape of H atoms is effectively a source of O2 to the atmosphere; explain why. The present-day rate of H atom escape to outer space is 5.4×107 kg H yr-1. Assuming that this rate has remained constant throughout the history of the Earth (4.5×109 years), calculate the resulting accumulation of oxygen. Is this an important source of oxygen?
5. Atmospheric O2 shows a small seasonal variation. At what time of year would you expect O2 to be maximum? Explain briefly. Estimate the amplitude of the seasonal cycle at Mauna Loa, Hawaii.
6. 2 Short questions on the carbon cycle
1. Does growth of corals (Ca2+ + CO32- → CaCO3(s)) cause atmospheric CO2 to increase or decrease? Explain briefly.
2. There are no sinks of CO2 in the stratosphere. Nevertheless, the CO2 mixing ratio in the stratosphere is observed to be 1-2 ppmv lower than in the troposphere. Explain.
[Source: Boering, K.A., et al., Stratospheric mean ages and transport rates from observa- tions of CO2 and N2O, Science, 274, 1340, 1996]
3. Humans ingest organic carbon as food and release CO2 as product. As the
bacteria 2Fe2O3 8H2SO4 15CH2O 4FeS2 15CO2 23H2O+ +→+ +
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world population grows, will increased CO2 exhalation from humans contribute to increasing CO2 in the atmosphere?
4. A consequence of global warming is melting of the polar ice caps. This melting decreases deep water formation. Why? Would this effect represent a negative or positive feedback to global warming? Briefly explain.
5. Comment on the statement: “Planting trees to reduce atmospheric CO2 is not an appropriate long-term strategy because the organic carbon in the trees will return to atmospheric CO2 in less than a century”.
6. 3 Atmospheric residence time of helium
Helium (He, atomic weight 4 g mol-1) and argon (Ar, atomic weight 40 g mol-1) are both produced in the Earth’s interior and exhaled to the atmosphere. Helium is produced by radioactive decay of uranium and thorium; argon is produced by radioactive decay of potassium-40 (40K). Both helium and argon, being noble gases, are chemically and biologically inert and are negligibly soluble in the ocean. Present-day atmospheric mixing ratios of helium and argon are 5.2 ppmv and 9340 ppmv, respectively.
1. Atmospheric argon has no sink and has therefore gradually accumulated since Earth’s formation 4.5×109 years ago. In contrast, atmospheric helium has a sink. What is it?
2. Show that the average source of argon to the atmosphere over Earth’s history is PAr = 1.5×107 kg yr-1.
3. Potassium-40 has no sources in the Earth’s interior and decays radioactively with a rate constant k = 5.5×10-10 yr-1. Hence the source of argon has decreased gradually since Earth’s formation. Let PAr(∆t) represent the present-day source of argon, where ∆t = 4.5×109 years is the age of the Earth. Show that
4. Observations in geothermal and bedrock gases show that the present-day sources of atmospheric helium and argon (kg yr-1) are of the same magnitude: PAr(∆t) ≈ PHe(∆t). Deduce the residence time of helium in the atmosphere.
6. 4 Methyl bromide
Methyl bromide (CH3Br) is the principal source of bromine in the stratosphere and plays an important role in stratospheric O3 loss. It is emitted to the atmosphere by a number of anthropogenic sources (agricultural fumigants, leaded gasoline…) and also has a natural source from biogenic activity in the ocean. There has been much recent interest in quantifying the relative magnitude of the anthropogenic vs. natural sources. This problem surveys some of the current understanding.
PAr ∆t( ) PAr
——————– k∆tk∆t( ) 1–exp——————————– = 0.23=
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1. Atmospheric lifetime of CH3Br
The main sinks for atmospheric CH3Br are oxidation in the atmosphere and uptake by the ocean. The lifetime of CH3Br against atmospheric oxidation is known with good confidence to be 2.0 years (see chapter 11). We focus here on determining the lifetime against uptake by the ocean and the implications for transport of CH3Br to the stratosphere.
1.1 The Henry’s law constant for CH3Br in seawater is
and the volume of the oceanic mixed layer is 3.6×1019 liters. Calculate the equilibrium fractionation nocean/ natm of CH3Br between the atmosphere and the oceanic mixed layer, where natm is the total number of moles of CH3Br in the atmosphere and nocean is the total number of moles of CH3Br in the oceanic mixed layer.
1.2 You should have found in question 1.1 that the oceanic mixed layer contains only a small amount of CH3Br compared to the atmosphere. However, ocean uptake can still represent an important sink of atmospheric CH3Br due to rapid hydrolysis of CH3Br(aq) in the ocean. The Figure below shows a 2-box model for CH3Br in the atmosphere-ocean system. The rate constant for hydrolysis of CH3Br(aq) is ko = 40 yr-1. The transfer rate constants for CH3Br from the atmosphere to the oceanic mixed layer, and from the oceanic mixed layer to the atmosphere, are k1 = 0.5 yr-1 and k2 = 22 yr-1. Show that the atmospheric lifetime of CH3Br against loss by hydrolysis in the oceans is τ= (ko + k2 ) / ko k1 = 3.3 years.
1.3 Could significant quantities of CH3Br be transferred from the oceanic mixed layer to the deep ocean? (That is, can the deep ocean represent a large reservoir for CH3Br, as it does for CO2?) Briefly explain.
1.4 By considering the sinks from both atmospheric oxidation and hydrolysis in
KH CH3Br aq( )[ ]
PCH3Br ———————————- 0.11M atm 1–= =
Atmosphere
Oceanic mixed layer
k1=0.5yr-1 k2=22yr -1
hydrolysis
ko=40yr-1
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the oceans, show that the overall atmospheric lifetime of CH3Br is 1.2 years.
1.5 Based on the answer to 1.4, and using a rate constant kTS = 0.14 yr-1 for transfer of air from the troposphere to the stratosphere, estimate the fraction of emitted CH3Br that enters the stratosphere and is thus active in O3 depletion.
2. A 2-box model for atmospheric CH3Br
We now use data on the tropospheric distribution of CH3Br to constrain the importance of the anthropogenic source. Observations indicate an interhemispheric ratio R = mN/mS = 1.3 for CH3Br, where mN and mS are the masses of CH3Br in the northern and southern hemispheres respectively. Let us interpret this ratio using a two-box model for the troposphere where the northern and southern hemispheres are individually well mixed and the transfer rate constant for air between the two hemispheres is k = 0.9 yr-1 (problem 3. 4). We assume that CH3Br is at steady state and is removed from the atmosphere with a rate constant k’ = 0.8 yr-1 (corresponding to a lifetime of 1.2 years, as derived in section 1 of this problem).
2.1 If the source of CH3Br were exclusively anthropogenic and located in the northern hemisphere, show that R would have a value of 1.9, higher than observed.
2.2 The discrepancy may be explained by the natural biogenic source of CH3Br in the oceans. Assume that this biogenic source is equally distributed between the two hemispheres, as opposed to the anthropogenic source which is exclusively in the northern hemisphere. In order to match the observed value of R, what fraction of the global source must be biogenic?
2.3 Is the finding that the ocean represents a major source of CH3Br contradictory with the finding in question 1.2 that the ocean represents a major sink? Briefly explain.
[To know more: Penkett, S.A., et al., Methyl bromide, in Scientific Assessment of Ozone Depletion: 1994, chap. 10, World Meteorological Organization, Geneva, 1995]
6. 5 Global fertilization of the biosphere
We apply here the box model of the nitrogen cycle presented in Figure 6-3 to examine the possibility of global fertilization of the biosphere by human activity over the past century.
1. What is the residence time of nitrogen in each of the reservoirs of Figure 6-3?
2. Consider a “land reservoir” defined as the sum of the land biota and soil reservoirs. What is the residence time of nitrogen in that reservoir? Why is it so much longer than the residence times calculated for the individual land biota and soil reservoirs?
3. Human activity over the past century has affected the nitrogen cycle by
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cultivation of nitrogen-fixing crops and application of industrial fertilizer to crops (increasing the land biofixation rate from 110 Tg N yr-1 to 240 Tg N yr-1), and by fossil fuel combustion (increasing the nitrogen fixation rate in the atmosphere from 5 Tg N yr-1 to 30 Tg N yr-1). Estimate the resulting percentage increases over the past century in the global nitrogen contents of the land biota reservoir and of the ocean biota reservoir. Conclude as to the extent of global fertilization of the Earth’s biosphere by human activity.
[To know more: Vitousek, P.M., et al., Human alteration of the global nitrogen cycle: sources and consequences, Ecol. Appl., 7, 737-750, 1997]
6. 6 Ocean pH
The surface ocean is saturated with respect to CaCO3 (this saturation is indeed necessary for the formation of sea shells). Calculate the pH of the surface ocean for present-day conditions (PCO2 = 365 ppmv) using the observed seawater Ca2+
concentration [Ca2+] = 0.01 M and the carbonate equilibria:
(H)
(1)
(2)
(S)
Equilibrium constants are KH = 3×10-2 M atm-1, K1 = 9×10-7 M, K2 = 7×10-10 M, KW = 1×10-14 M2, KS = 9×10-7 M2.
6. 7 Cycling of CO2 with the terrestrial biosphere
Consider the following global cycle of carbon between the atmosphere, the terrestrial vegetation, and the soil. Reservoirs are in units of Pg C (1 petagram = 1×1015 g) and flows are in units of Pg C yr-1.
1. The three reservoirs “ground vegetation,” “tree leaves,” and “tree wood” represent collectively the “terrestrial vegetation reservoir.” The flow rate of atmospheric CO2 into this terrestrial vegetation reservoir represents the net primary productivity (NPP) of the terrestrial biosphere. Calculate the lifetime of carbon in the terrestrial vegetation reservoir against transfer to the litter and soil.
2. Tree leaves eventually fall to produce litter. What is the dominant fate of carbon in the litter? What fraction is incorporated into the soil?
3. Acid rain causes a decrease of microbial activity in the litter and in the soil. How is atmospheric CO2 affected?
H2OCO2 g( ) CO2 H2O⋅⇔
CO2 H2O⋅ HCO3 – H++⇔
HCO3 – CO3
2- H++⇔
CaCO3 s( ) Ca 2+ CO3
2-+⇔
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6. 8 Sinks of atmospheric CO2 deduced from changes in atmospheric O2
Measurement of the long-term trend in atmospheric O2 has been used to determine the fate of fossil fuel CO2 in the atmosphere and the relative importance of uptake by the ocean and by the biosphere. We describe here the principle of the method.
1. We first examine the O2:CO2 stoichiometry of the individual CO2 sources and sinks.
1.1 The mean stoichiometric composition of fossil fuel burned is CH1.6 (1 part carbon for 1.6 parts hydrogen). We view fossil fuel combustion as a stoichiometric reaction where CH1.6 is oxidized by O2 to yield CO2 and H2O. Show that 1.4 moles of O2 are consumed per mole of CO2 emitted by fossil fuel combustion.
1.2 How many moles of O2 are produced per mole of CO2 taken up by the biosphere?
1.3 Is any O2 produced or consumed when CO2 dissolves into the ocean as CO2.H2O/HCO3-/CO32- ?
2. We are now equipped to use the method. Observations from July 1991 to July 1994 (3 years) indicate a 3.2 ppmv increase in atmospheric CO2 and a 8.8 ppmv decrease in atmospheric O2. Global fossil fuel combustion during this period was 6.3×1012 kg C yr-1.
2.1 If fossil fuel were the only process affecting CO2 and O2 concentrations during the 1991-1994 period, by how much would these concentrations have changed?
Atmosphere 760
Ground vegetation
15
110
10
1800
5
3
Tree leaves 40
22
22
Tree wood 630
25
22
3 11
51
litter
Soil
60
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2.2 From the observed trends of atmospheric CO2 and O2, determine the fraction of CO2 emitted from fossil fuel combustion over the 3-year period that (a) was taken up by the biosphere, (b) dissolved in the oceans, (c) accumulated in the atmosphere.
[Source: Keeling, R.F., et al., Global and hemispheric CO2 sinks deduced from changes in atmospheric O2 concentrations, Nature, 381, 218-221, 1996.]
6. 9 Fossil fuel CO2 neutralization by marine CaCO3
We saw in chapter 6 that a fraction f = 28% of CO2 emitted by fossil fuel combustion remains in the atmosphere once full equilibration with the ocean is achieved. We examine here how dissolution of calcium carbonate (CaCO3) from the ocean floor can reduce f over longer time scales.
1. Explain qualitatively how dissolution of CaCO3 from the ocean floor increases the capacity of the ocean to take up atmospheric CO2.
2. We assume that CaCO3 on the ocean floor was in equilibrium with oceanic CO32- in preindustrial times. Ocean uptake of fossil fuel CO2 has since disrupted this equilibrium by decreasing CO32- levels. Dissolution of CaCO3 is a slow process, taking place on a time scale of several thousand years. By that time we will most likely have exhausted all our fossil fuel reserves. We consider a “final” state several thousand years in the future when equilibrium between CaCO3 and oceanic CO32- has finally been reachieved. Show that the oceanic CO32-
concentration in this final state is the same as in preindustrial times. [Note: the oceanic Ca2+ concentration is 10-2 M, sufficiently high not to be affected significantly by enhanced dissolution of CaCO3 from the sea floor].
3. Show that
4. Global reserves of exploitable fossil fuel are estimated to be 5×1018 g C. Show that if all the exploitable fossil fuel were emitted to the atmosphere as CO2, the increase in the mass of HCO3- in the ocean when the “final” state is achieved would be 10×1018 g C. Assume as an approximation that all the emitted CO2 enters the ocean (we will verify the quality of this approximation in the next question).
5. Infer from questions 3 and 4 the fraction of added fossil fuel CO2 that remains in the atmosphere in the “final” state where all exploitable fossil fuel has been emitted to the atmosphere and full reequilibration of the ocean with CaCO3 on the sea floor has been achieved. The “initial” preindustrial state is defined by a total mass of HCO3- in the ocean of 38×1018 g C and PCO2 = 280 ppmv. Ignore
PCO2,final PCO2,preindustrial —————————————
HCO3 –
[ ]final
HCO3 –
[ ]preindustrial
———————————————–
2
=
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any net uptake of carbon by the biosphere.
[Source: Archer, D.H., et al., Dynamics of fossil fuel CO2 neutralization by marine CaCO3, Global Biogeochem. Cycles, 12, 259-276, 1998.]
