View source for Carbon model worksheet 4 answers

[[Image:pfs -2.jpg|right|300px|thumb|A schematic of the organic and inorganic components of the modelled carbon cycle.]]
<span class=”plainlinks”>[http://www.noc.soton.ac.uk/jmodels/jnlp/C_Model.jnlp http://www.noc.soton.ac.uk/jmodels/images/wiki/cmodel.jpg]</span><br>
The article provides '''answers''' to the questions posed in the [[carbon model worksheet 4]].

==Worksheet answers==
# Try some different initial conditions (initial values of [CO<sub>3</sub><sup>2-</sup>]), to be produced as follows (keep all other variables at default values): (a) deep [DIC] = 2.20 Mol m-3; (b) deep [DIC] = 2.15 Mol m-3; (c) deep [DIC] = 2.30 Mol m-3; (d) deep [DIC] = 2.40 Mol m-3. What is the initial deep [CO<sub>3</sub><sup>2-</sup>] in each case? Does the model converge in each case? (i.e. does it homeostatically regulate [CO<sub>3</sub><sup>2-</sup>]?) Is the final value of [CO<sub>3</sub><sup>2-</sup>] always the same? [remember to reset initial conditions before making each change, so  previous changes are wiped clear] <br> <p style="color:#F00;">The steady-state (default) value of [CO<sub>3</sub><sup>2-</sup>] in the model deep ocean is ~100 μMol kg<sup>-1</sup>. The initial deep [CO<sub>3</sub><sup>2-</sup>]’s, after making the changes to [DIC], are, in each case: (a) ~140 μMol kg<sup>-1</sup> (b) ~170 μMol kg<sup>-1</sup> (c) ~70 μMol kg<sup>-1</sup> and (d) ~50 μMol kg<sup>-1</sup>. The model does converge back towards the steady-state value of ~100 μMol kg<sup>-1</sup> after each perturbation, and final values are more or less the same in each run. [NB. 1 μMol kg<sup>-1</sup> ≈ 1 mMol m<sup>-3</sup> = 0.001 Mol m<sup>-3</sup>].</p>
# The mechanism for carbonate compensation is supposed to involve changes in the lysocline depth in response to changes in [CO<sub>3</sub><sup>2-</sup>]. What, if any, changes do you see immediately after (a) doubling [CO<sub>3</sub><sup>2-</sup>]; (b) halving [CO<sub>3</sub><sup>2-</sup>]? [as produced, more or less, by the DIC changes for (b) and (d) in 1. above] <br> <p style="color:#F00;">Lysocline depths immediately after the changes are (a) a deepening to >4 km following a doubling of [CO<sub>3</sub><sup>2-</sup>]; (b) a shallowing to <1.5 km following a halving of [CO<sub>3</sub><sup>2-</sup>].</p>
# The return to the equilibrium state is governed by the balance between river inputs and burial outputs of CaCO<sub>3</sub> and POC. Examine the size of the CaCO<sub>3</sub> burial flux (a) immediately after doubling of deep [CO<sub>3</sub><sup>2-</sup>]; and (b) immediately after halving of deep [CO<sub>3</sub><sup>2-</sup>]. How does it compare to the river flux? <br> <p style="color:#F00;">The size of the CaCO<sub>3</sub> burial flux is (a) ~1 Gt C yr<sup>-1</sup> immediately after doubling of deep [CO<sub>3</sub><sup>2-</sup>], which exceeds the river flux of ~0.24 Gt C yr<sup>-1</sup>; and (b) ~0.1 Gt C yr<sup>-1</sup> immediately after halving of deep [CO<sub>3</sub><sup>2-</sup>], which is less than the river flux of 0.24 Gt C yr<sup>-1</sup>. 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].</p>
# 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 steady-state [CO<sub>3</sub><sup>2-</sup>]) following (a) doubling of [CO<sub>3</sub><sup>2-</sup>]; (b) halving of [CO<sub>3</sub><sup>2-</sup>]? 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? <br> <p style="color:#F00;">From visual inspection of the plots, it appears that it takes about 13 ky to return to steady-state after [CO<sub>3</sub><sup>2-</sup>] has been doubled, and somewhat greater than 20 ky to return to steady-state after [CO<sub>3</sub><sup>2-</sup>] 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).</p>
# The Paleocene-Eocene 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<sup>16</sup> m3 and 1 Gt C is equivalent to 8.33x10<sup>13</sup> Moles C. What effect do you see on the lysocline depth and [CO<sub>3</sub><sup>2-</sup>] 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? <br> <p style="color:#F00;">Adding 2000 Gt C into 135 x 10<sup>16</sup> m<sup>3</sup> equals a perturbation of about 0.123 Mol m<sup>-3</sup> (about 123 μMol kg<sup>-1</sup>) to the DIC concentration. Increasing deep [DIC] by this amount causes the lysocline depth to shallow to <1.5 km, and deep [CO<sub>3</sub><sup>2-</sup>] to decrease to <50 μMol kg<sup>-1</sup>, i.e. less than half its steady-state value. Carbonate compensation brings [CO<sub>3</sub><sup>2-</sup>] back towards its steady-state value of about 100 μMol kg<sup>-1</sup>, but does not do the same for deep [DIC]. The final value of deep [DIC] is nearly 2500 μMol kg<sup>-1</sup>, approximately 200 μMol kg<sup>-1</sup> higher than the value before the perturbation was made (~2300 μMol kg<sup>-1</sup>). The carbonate compensation feedback acts on [CO<sub>3</sub><sup>2-</sup>] and homeostatically regulates it, but does not necessarily regulate the other variables such as DIC.</p>
# 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 sea-level such that coral reefs that had been present for eons on the shelves were eroded following a fall in sea-level. Carry out experiments with the model initial conditions for deep ocean DIC and alkalinity to see how many Moles of CaCO<sub>3</sub> have to be added in order to drop the CCD by 1km. [dissolution of CaCO<sub>3</sub> adds DIC and alkalinity in a ratio of 1:2] <br> <p style="color:#F00;">Increasing deep [DIC] by 30 μMol kg<sup>-1</sup> and deep [Alk] by 60 μEquiv kg<sup>-1</sup> 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<sup>16</sup> m<sup>3</sup> gives the quantity of 4 x 10<sup>16</sup> Mol (i.e. 40 GMol) of CaCO<sub>3</sub> that would have to be added in order to drop the CCD by 1 km.</p>

==Other related pages==
* [[Carbon model|Carbon model overview]]
* [[Carbon model details]]
* [[Carbon model pros]]
* [[Carbon model cons]]
* [[Carbon model worksheet]]s
* [[Phosphorus model|Phosphorus model overview]]

==References==
* Archer ''et al.'' (1998). Dynamics of fossil fuel CO2 neutralization by marine CaCO3. ''Global Biogeochem. Cycles'' '''12''', 259-276.
* Chuck, A. ''et al.'' (2005). [http://www.blackwell-synergy.com/doi/full/10.1111/j.1600-0889.2005.00127.x?prevSearch=allfield%3A%28Chuck%29 The oceanic response to carbon emissions over the next century: investigation using three ocean carbon cycle models].  ''Tellus B''  '''57''', 70-86.
* Coxall, H. et al. (2005). Rapid stepwise onset of Antarctic glaciation and deeper calcite compensation in the Pacific Ocean. ''Nature'' '''433''', 53–57.
* Sundquist (1990). Influence of deep-sea benthic processes on atmospheric CO2. ''Phil. Trans. R. Soc. Lond. Ser. A'' '''331''', 155-165.
* Tyrrell, T. (1999).  [http://www.nature.com/nature/journal/v400/n6744/abs/400525a0.html The relative influences of nitrogen and phosphorus on oceanic primary production].  ''Nature'' '''400''', 525–531.
* Tyrrell, T. ''et al.'' (2007). [http://www.blackwell-synergy.com/doi/full/10.1111/j.1600-0889.2007.00290.x?prevSearch=allfield%3A%28Tyrrell%29 The long-term legacy of fossil fuels].  ''Tellus B''  '''59''', 664-672.
* Zeebe & Westbroek (2003). A simple model for the CaCO3 saturation state of the ocean: The “Strangelove,” the “Neritan,” and the “Cretan” Ocean”. ''Geochem. Geophys. Geosyst.'' '''4''', 1104, doi:10.1029/2003GC000538.

==External links==
* [http://en.wikipedia.org/wiki/Carbon Description of the chemical element carbon], [[Wikipedia]]
* [http://en.wikipedia.org/wiki/Carbon_cycle Description of the carbon cycle], [[Wikipedia]]
* [http://en.wikipedia.org/wiki/Phosphorus Description of the chemical element phosphorus], [[Wikipedia]]
* [http://en.wikipedia.org/wiki/Phosphorus_cycle Description of the phosphorus cycle], [[Wikipedia]]

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[[Category:Carbon model]]
[[Category:Phosphorus model]]
[[Category:Worksheet]]