Carbon model worksheet 4 answers

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A schematic of the organic and inorganic components of the modelled carbon cycle.

http://www.noc.soton.ac.uk/jmodels/images/wiki/cmodel.jpg
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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