Chapter 7 · Carbon in the Low-Temperature Environment

Problem 1

During glacial times, the p(CO₂) of the atmosphere dropped sufficiently to cause the CO₃²⁻ concentration in ocean surface waters to increase as much as 40 µmol/kg (Spero et al., 1997). Assuming that the effect of CO₃²⁻ concentration on δ¹³C values of foraminifera carbonate from Orbulina universa is given by Δ(δ¹³C)/(CO₃²⁻ µmol/kg) = −0.006, how much would the δ¹³C value of this species change between a glacial–interglacial cycle? [Printed units read mmol/kg; Spero et al. (1997) works in µmol/kg.]

[Worksheet constructed.]

Problem 2

Assuming that there are 5,000·10¹⁵ g of fossil fuels yet to be burned and that present consumption is 5.4·10¹⁵ g/yr (about 44 trillion pounds of CO₂),

1. How much does the δ¹³C value of the atmosphere change annually if all of the products of burning go into the atmosphere? What is wrong with this calculation?
2. What will the δ¹³C value of the atmosphere be when all of the available fossil fuels are burned? Assume that half will go into the shallow ocean, with the appropriate fractionation between CO₂(g) and dissolved HCO₃⁻.

[Worksheet constructed, for part (a); the reservoir numbers are those used in the printed answer.]

Problem 3

Explain how the δ¹³C value of C₃ plants changes under conditions of intense water stress.

Problem 4

There are three major crustal reservoirs of carbon: carbonates, organic carbon in sediments, and crystalline rocks. If the δ¹³C values of carbonates and organic carbon were −1 and −28‰, respectively (instead of the estimates given in Table 1), what would be the δ¹³C value of average crystalline rocks? Assume the abundances in Table 1 and a mantle value of −6‰.

[Worksheet constructed; the abundances are those used in the printed answer (Table 1).]

Problem 5

Biogenic methane can have a Δ¹³C value greater than 50‰ relative to organic matter. Carbonates with the lowest and highest δ¹³C value samples are related to methane. Explain how carbonates with superhigh and superlow δ¹³C values can form as a result of methanogenesis.

Problem 6

Derive a simple two box model for the shallow-deep ocean system, including the two reservoirs and input and output fluxes. The input flux to the shallow ocean is riverine. Transfer between the two reservoirs is accomplished by a slow flux associated with diffusion. A more rapid transfer from the shallow to the deep ocean is accomplished by the biological pump. Outputs from both shallow and deep ocean are sedimentation of carbonates and organic matter (separate fluxes). (See Kump, 1991, for more details.) Use the following parameters:

Problem 7

Figure 7.15 shows how the δ¹³C values of shallow and deep oceans change with time if the biological pump is suddenly “shut off.” (Productivity stops.) Sketch δ¹³C-vs-time curves for deep-ocean and shallow-ocean carbonates for the following conditions (some of these may not be geologically reasonable, but never mind!):

1. Decreased burial, constant productivity
2. Decreased burial and decreased productivity
3. Decreased productivity, constant burial

(Hint: keep the box model for Problem 6 in mind; see Holser, 1997, for further discussion.)

Problem 8

Explain, in one or two sentences for each entry, the δ¹³C values of the following carbonates and why they have those values:

1. deep marine limestones
2. shallow marine limestones
3. freshwater limestones
4. soil carbonates
5. diagenetically altered marine carbonates

Problem 9

The atomic weight of carbon reported in a typical periodic table is 12.0107 amu. Given that the ¹³C/¹²C ratio of VPDB is 0.0112372, what is the δ¹³C value of “typical” carbon as defined by the periodic table (¹²C = 12 amu; ¹³C = 13.003354838 amu)?

[Worksheet constructed.]