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Appendix
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Model Description
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To assess potential relationships between the benthic foraminiferal derived
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productivity and the CM events, we use an updated version of the box model developed by
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Diester-Haass et al. [2009] and Lefebvre et al. [2010]. This box model contains four
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reservoirs for the global ocean (low latitude surface ocean, low latitude thermocline, high
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latitude surface ocean, deep ocean) and one for the atmosphere. It calculates the budgets of
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carbon, alkalinity, phosphorus and dissolved oxygen in the ocean reservoirs, and those of
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carbon dioxide and oxygen in the atmosphere. The carbon isotope budget (13C values) is also
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calculated for each reservoir, as well as carbonate speciation. Biological productivity in the
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surface oceanic reservoirs is driven by phosphorus inputs to these reservoirs; the model only
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predicts export production (i.e., the productivity corresponding to the amount of organic
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matter that escapes oxidation in the surface reservoirs and is transferred to the thermocline or
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the deep ocean).
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Inclusion of an oxygen budget is new compared to the previous version of the model
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[e.g., Diester-Haass et al., 2009, Lefebvre et al., 2010]. It is a relatively classical description
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of the oxygen cycle, with production of O2 in the atmosphere or the surface ocean, transport
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of O2 through ocean circulation and consumption of O2 when organic matter is oxidized in the
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thermocline and the deep ocean. More details on this module can be found in Lefebvre
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[2009].
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Input and output fluxes of carbon, alkalinity, phosphorus, and oxygen to/from the
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ocean-atmosphere system are calculated from a geochemical sub-model [Diester-Haass et al.,
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2009; Lefebvre, 2009] which takes into account the volcanic release of CO2 (assumed to be
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constant through time for the present study), weathering of silicate and carbonate rocks,
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weathering of old organic carbon (kerogen) from sedimentary rocks, and organic carbon
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deposition from both land and marine sources. In the treatment of silicate rock weathering we
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distinguish between basalts and other silicates (granites), for which separate weathering rate
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laws are used [Lefebvre, 2009; Lefebvre et al., 2010; Grard et al., 2005; Dessert et al., 2001,
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2003]. Both rates increase with runoff (linear relationship), temperature (exponential
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relationship) and soil CO2 partial pressure (power law with 0.3 exponent, soil pCO2 being
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related to atmospheric pCO2 through terrestrial productivity, using the approach of Volk,
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1987). They are both proportional to a mechanical weathering factor mech, used to take into
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account the dependence of chemical weathering on changes in physical erosion. The value of
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mech is derived from reconstructed accumulation rates of terrigenous sediments [Wold and
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Hay, 1990]. For this study, we used a relative flux of terrigenous sediments of 0.25 at middle
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Miocene times compared to today, a value comparable to that used by Wallmann [2001]. The
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weathering rate law for carbonate rocks assumes that the water draining carbonate rocks is
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saturated with respect to calcite. It depends on temperature and soil pCO2. Kerogen
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weathering is assumed to be proportional to runoff and to vary with physical erosion as
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mech0.3, but no direct temperature dependence is considered in the standard version of the
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model. Outcrop areas of all types of rocks are taken as proportional to the land area.
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Carbonate deposition occurs as coral reef formation on the shelf and as rain of calcite
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or aragonite on all the seafloor above the respective compensation depths. Coral reef
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formation is proportional to shelf area and varies with the saturation ratio of surface seawater
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with respect to calcite. Carbonate rain rates vary proportionally to biological productivity.
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Lysoclines for calcite and aragonite are calculated as a function of the CO3= concentration in
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the deep oceanic box and a correction proportional to productivity is made to obtain the
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compensation depths. The areas above these compensation depths are obtained from the
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hypsometric curve. Organic deposition in the sediment is proportional to the fraction of the
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produced organic matter not decomposed in the water column and reaching the seafloor in
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each reservoir and, hence, also depends on the hypsometric curve. Organic deposition on land
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is prescribed as in Diester-Haass et al. [2009] to linearly increase from 2.31012 mol/yr to
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3.31012 mol/yr between 19 Ma and 16 Ma, then remaining constant between 16 Ma and 14
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Ma, and finally decreasing back to the original value between 14 and 12 Ma. As discussed by
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Diester-Haass et al. [2009], such an increase produces a long-term excursion in the 13C
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record similar in amplitude and phase to the Monterey excursion of the Middle Miocene.
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Since the weathering rates on land as well as the carbonate equilibrium constants and
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solubilities in the ocean depend on temperature, the geochemical model is coupled to an
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energy balance model [François and Walker, 1992] that evaluates mean surface temperature
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in 18 equidistant latitude bands. Runoff on land in each latitude band is evaluated from the
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parameterization developed in the same study.
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Besides carbon, weathering and deposition fluxes also bring or remove alkalinity,
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phosphorus and oxygen (O2) to or from the ocean. Alkalinity is brought to the ocean through
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silicate and carbonate weathering and is removed through carbonate deposition, the ratio
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between alkalinity and carbon being dictated by the stoichiometry of the
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weathering/deposition reactions [e.g., François and Walker, 1992]. Phosphorus is assumed to
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be provided to the ocean mainly through silicate weathering, its input flux associated with
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weathering is thus taken as proportional to total (basalt+granite) silicate weathering. It is
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removed from the ocean through organic carbon and carbonate deposition. As François and
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Walker [1992], we use a constant C:P ratio of 1000:1 for carbonates. By contrast, the C:P
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ratio of buried organic matter is assumed to vary linearly with the oxygenation level of the
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ocean reservoir in which the deposition occurs [Van Cappellen and Ingall, 1996], the C:P
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ratio reaching 200:1 in well oxygenated waters ([O2]>0.20 mol m-3) and 4000:1 in anoxic
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waters ([O2]<0.05 mol m-3). The O2 budget is only calculated for the atmosphere, the
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thermocline and the deep ocean reservoirs. Indeed, in the surface ocean reservoirs, dissolved
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oxygen is assumed to be in equilibrium with atmospheric O2. The source and sink of
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atmospheric O2 correspond respectively to deposition of organic carbon (ocean + land) and
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kerogen weathering. O2 is transported through ocean circulation from the surface to the
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thermocline and deep water reservoirs, where it is consumed by organic matter
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remineralisation in the water column. The remineralized fraction of organic matter settling
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from the above reservoir increases linearly with dissolved oxygen concentration, from 0.02 in
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anoxic waters to 1 in oxygenated waters (same [O2] thresholds as above).
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References
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Dessert, C., B. Dupré, J. Gaillardet, L. M. François, and C.J. Allègre (2003), Basalt
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Diester-Haass, L., K. Billups, D.R. Gröcke, L. François, V. Lefebvre, and K. C. Emeis
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