Carbon model worksheet 4 answers
Worksheet answers

Try some different initial conditions (initial values of [CO_{3}^{2}]), to be produced as follows (keep all other variables at default values): (a) deep [DIC] = 2.20 Mol m3; (b) deep [DIC] = 2.15 Mol m3; (c) deep [DIC] = 2.30 Mol m3; (d) deep [DIC] = 2.40 Mol m3. What is the initial deep [CO_{3}^{2}] in each case? Does the model converge in each case? (i.e. does it homeostatically regulate [CO_{3}^{2}]?) Is the final value of [CO_{3}^{2}] always the same? [remember to reset initial conditions before making each change, so previous changes are wiped clear]
The steadystate (default) value of [CO_{3}^{2}] in the model deep ocean is ~100 μMol kg^{1}. The initial deep [CO_{3}^{2}]’s, after making the changes to [DIC], are, in each case: (a) ~140 μMol kg^{1} (b) ~170 μMol kg^{1} (c) ~70 μMol kg^{1} and (d) ~50 μMol kg^{1}. The model does converge back towards the steadystate value of ~100 μMol kg^{1} after each perturbation, and final values are more or less the same in each run. [NB. 1 μMol kg^{1} ≈ 1 mMol m^{3} = 0.001 Mol m^{3}].

The mechanism for carbonate compensation is supposed to involve changes in the lysocline depth in response to changes in [CO_{3}^{2}]. What, if any, changes do you see immediately after (a) doubling [CO_{3}^{2}]; (b) halving [CO_{3}^{2}]? [as produced, more or less, by the DIC changes for (b) and (d) in 1. above]
Lysocline depths immediately after the changes are (a) a deepening to >4 km following a doubling of [CO_{3}^{2}]; (b) a shallowing to <1.5 km following a halving of [CO_{3}^{2}].

The return to the equilibrium state is governed by the balance between river inputs and burial outputs of CaCO_{3} and POC. Examine the size of the CaCO_{3} burial flux (a) immediately after doubling of deep [CO_{3}^{2}]; and (b) immediately after halving of deep [CO_{3}^{2}]. How does it compare to the river flux?
The size of the CaCO_{3} burial flux is (a) ~1 Gt C yr^{1} immediately after doubling of deep [CO_{3}^{2}], which exceeds the river flux of ~0.24 Gt C yr^{1}; and (b) ~0.1 Gt C yr^{1} immediately after halving of deep [CO_{3}^{2}], which is less than the river flux of 0.24 Gt C yr^{1}. They do agree qualitatively with the schematic. [NB. The constancy of the burial flux during the first 5 ky is an artefact of the model construction, which prevents the lysocline from being so shallow as to lie within the surface or middle boxes].

In the scientific literature the carbonate compensation time is suggested to be somewhere between 6 and 14 thousand years, and so is relatively rapid from a geological perspective. Calculate the approximate compensation times (times to return to steadystate [CO_{3}^{2}]) following (a) doubling of [CO_{3}^{2}]; (b) halving of [CO_{3}^{2}]? Is it the same in response to halving as to doubling? How does the carbonate compensation time in this model compare to the literature values?
From visual inspection of the plots, it appears that it takes about 13 ky to return to steadystate after [CO_{3}^{2}] has been doubled, and somewhat greater than 20 ky to return to steadystate after [CO_{3}^{2}] has been halved. These durations are not dissimilar to the literature carbonate compensation times of 614 thousand years. It should be noted, however, that the system returns asymptotically to equilibrium and so it is in fact meaningless to talk about a response time unless it is precisely defined. In practise it is necessary to use some sort of more quantitative metric, such as the time to remove 90% of the original perturbation, or the efolding response time (the latter is more commonly used).

The PaleoceneEocene Thermal Maximum is thought to have been caused by the injection of a massive amount of carbon (~2000 Gt) into the system, probably from methane clathrates. The volume of the ocean is 135x10^{16} m3 and 1 Gt C is equivalent to 8.33x10^{13} Moles C. What effect do you see on the lysocline depth and [CO_{3}^{2}] if you add all that carbon to the DIC reservoir of the deep sea? What effect does carbonate compensation have on the response of the system?
Adding 2000 Gt C into 135 x 10^{16} m^{3} equals a perturbation of about 0.123 Mol m^{3} (about 123 μMol kg^{1}) to the DIC concentration. Increasing deep [DIC] by this amount causes the lysocline depth to shallow to <1.5 km, and deep [CO_{3}^{2}] to decrease to <50 μMol kg^{1}, i.e. less than half its steadystate value. Carbonate compensation brings [CO_{3}^{2}] back towards its steadystate value of about 100 μMol kg^{1}, but does not do the same for deep [DIC]. The final value of deep [DIC] is nearly 2500 μMol kg^{1}, approximately 200 μMol kg^{1} higher than the value before the perturbation was made (~2300 μMol kg^{1}). The carbonate compensation feedback acts on [CO_{3}^{2}] and homeostatically regulates it, but does not necessarily regulate the other variables such as DIC.

At the Eocene/Oligocene boundary the lysocline/CCD fell rapidly by about 1 km. One hypothesis is that this was caused by a fall in sealevel such that coral reefs that had been present for eons on the shelves were eroded following a fall in sealevel. Carry out experiments with the model initial conditions for deep ocean DIC and alkalinity to see how many Moles of CaCO_{3} have to be added in order to drop the CCD by 1km. [dissolution of CaCO_{3} adds DIC and alkalinity in a ratio of 1:2]
Increasing deep [DIC] by 30 μMol kg^{1} and deep [Alk] by 60 μEquiv kg^{1} causes the lysocline to fall by about 1 km, so that its initial value is 3.4 km (compared to its steadystate value of 2.4 km). Multiplying by the ocean volume of 135 x 10^{16} m^{3} gives the quantity of 4 x 10^{16} Mol (i.e. 40 GMol) of CaCO_{3} that would have to be added in order to drop the CCD by 1 km.