# Carbon model worksheet 4 answers

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The article provides **answers** to the questions posed in the carbon model worksheet 4.

## Worksheet answers

- The steady-state (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 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}]. - 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 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] - From visual inspection of the plots, it appears that it takes about 13 ky to return to steady-state after [CO
_{3}^{2-}] has been doubled, and somewhat greater than 20 ky to return to steady-state after [CO_{3}^{2-}] 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). - 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 steady-state value. Carbonate compensation brings [CO_{3}^{2-}] 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 [CO_{3}^{2-}] and homeostatically regulates it, but does not necessarily regulate the other variables such as DIC. - 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 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.

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