Carbon model worksheet 4 answers

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A schematic of the organic and inorganic components of the modelled carbon cycle.
The article provides answers to the questions posed in the carbon model worksheet 4.

Worksheet answers

  1. The steady-state (default) value of [CO32-] in the model deep ocean is ~100 μMol kg-1. The initial deep [CO32-]’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 steady-state 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].
  2. Lysocline depths immediately after the changes are (a) a deepening to >4 km following a doubling of [CO32-]; (b) a shallowing to <1.5 km following a halving of [CO32-].
  3. The size of the CaCO3 burial flux is (a) ~1 Gt C yr-1 immediately after doubling of deep [CO32-], 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 [CO32-], 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]
  4. From visual inspection of the plots, it appears that it takes about 13 ky to return to steady-state after [CO32-] has been doubled, and somewhat greater than 20 ky to return to steady-state after [CO32-] has been halved. These durations are not dissimilar to the literature carbonate compensation times of 6-14 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 e-folding response time (the latter is more commonly used).
  5. Adding 2000 Gt C into 135 x 1016 m3 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 [CO32-] to decrease to <50 μMol kg-1, i.e. less than half its steady-state value. Carbonate compensation brings [CO32-] back towards its steady-state 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 [CO32-] and homeostatically regulates it, but does not necessarily regulate the other variables such as DIC.
  6. 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 steady-state value of 2.4 km). Multiplying by the ocean volume of 135 x 1016 m3 gives the quantity of 4 x 1016 Mol (i.e. 40 GMol) of CaCO3 that would have to be added in order to drop the CCD by 1 km.

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