Hydrogeochemical models can reflect the complex web of early diagenetic processes in marine sediments. Of particular interest regarding to methane cycling within marine sediments, the formation of methane hydrate and processes in the transition zone between sulphate reduction and methanogenesis have been studied in great detail [e.g., Davie and Buffett, 2001; Hensen and Wallmann, 2005; Wang and van Cappellen, 1996]. Additionally, rates of sulphate reduction, methanogenesis, and organic matter degradation have been modeled [Sivan et al., 2007; Wallmann et al., 2006 and references therein], but the modeling of early diagenetic remineralization of organic matter has often been limited to the upper few centimeters of marine sediments [Boudreau, 1996; Luff et al., 2000; Luff and Wallmann, 2003; Wang and van Cappellen, 1996]. More advanced models of microbial respiration and organic matter degradation have resolved complex microbial mechanisms involved in the anaerobic degradation of organic matter [Jin and Bethke, 2003; Jin and Bethke, 2005; Wirtz, 2003]. So far, most of the applied models have focused on isolated hydrogeo- or biochemical reactions that are only part of a complex web of reactions evolving into a multicomponent and multiphase system. Reactions are interrelated due to reaction products and reactants that are involved at different steps of process chains.
 The modeled sediment columns are composed of 50 cells (“generic reactors”), each. The generic 1.7 l reactor is filled with an aqueous solution of present-day chemical seawater composition [Nordstrom et al., 1979], and with sediments of defined mineral composition according to sediments from ODP Leg 112, Sites 679, 680, 681, 682, and 688, and Leg 201, Site 1231 [Shipboard Scientific Party, 2003; Suess et al., 1988]. Equilibrium species distribution and coupled mass transfer that results from reactions in the modeling reactor are calculated byusing the PHREEQC (version 2) program [Parkhurst and Appelo, 1999].Calculations are based on mass action laws that include all species of Ca, Mg, Na, K, Al, Fe, Si, Cl, C, S, N, P, H2O, and their corresponding equilibrium constants. Species, mass-action equations, and equilibrium constants are listed in the thermodynamic database “wateq4f.dat” [Parkhurst and Appelo, 1999] and Table S2.8 of the auxiliary material. The reaction kinetics of organic carbon remineralization are integrated into the set of equilibrium reactions by defining the type and the amount of remineralized organic matter in a certain time step. The accumulation of the organic matter metabolites (e.g., CH4, CO2, and H2) leads to the development of new inorganic equilibrium conditions in the system.
 The modeled sediment column is 495 m thick (representing the zone crucial for early diagenetic reactions), and is subdivided into fifty 10-m-thick cells (Tables S2.2–S2.7). Each cell is an original reactor (expressed as representative volume (RV); 1.7 l = 10 m · 0.013 m · 0.013 m) and contains 1 l of pore water (V(aq)) and 1.89 kg of solid sediment. Hence, the average porosity (ϕ) is 0.59 and the average specific weight of solids (ρ(s)) is 2.7 kg l−1. The model design displays a growing sediment column [cf. Arning et al., 2011, Figure 1b]. Initially, equilibrium calculations are performed on one sediment cell that is overlain by five cells containing seawater. At a second time step, the first cell is instantaneously buried to a depth of 10 m. The time step for each cell (Tables S2.2–S2.7) is calculated from the sedimentation rate (Tables S2.2–S2.7) [Shipboard Scientific Party, 2003; Suess et al., 1988]. Freshly deposited sediments at the sediment-water interface form the second cell in the growing sediment column. After 50 time steps the modeled sediment column consists of 50 cells and represents the upper 495 m of the investigated sites. Once all calculations have been completed, the mineral assemblage and pore waters of the first cell (from the first time step) shift from the sediment-water interface to the base of the modeled sediment column at a depth of 485 to 495 m below seafloor (mbsf).
 The active transportation processes considered in this model are 1) the one-dimensional molecular diffusion of aqueous species, and 2) the burial of solids (including methane hydrate) and aqueous species, according to the observed sedimentation rate, which also represents advection. Porosity changes that occur within the upper few meters and toward greater sediment depths [Shipboard Scientific Party, 2003; Suess et al., 1988] cannot be resolved by the model, hence compaction flow and advection are not incorporated. Diffusion enables the transportation of dissolved species between all cells during sediment deposition and burial. A mean diffusion coefficient (0.86 · 10−9 m2s−1) for all aqueous species is calculated from diffusion coefficients (corrected for tortuosity) according to Giambalvo et al. .
 The upper boundary is defined as a constant concentration boundary (overlying seawater). The lower boundary is defined as a closed boundary for diffusion in models designed for Sites 679, 682, 688, and 1231. For the Sites 680 and 681, our model defines the lower boundary as a constant one with regard to water influx from subsurface brine [Kastner et al., 1990]. Diffusive exchange between seawater and pore water takes place at the sediment-water interface, between each newly deposited sediment cell and the lowermost cell containing seawater.
 Temperature increases linearly throughout the modeled sediment column consistent with the geothermal gradient (Tables S2.2–S2.7) [Shipboard Scientific Party, 2003; Suess et al., 1988]. A constant pressure (Tables S2.2–S2.7, calculated as hydrostatic pressure according to water depth and 250 m of sediments) was selected for calculations of gas solubility because of software limitations, as the effect of varying the total pressure on aqueous species distribution and associated solid phases is minor (cf. Table S2.1).
 Secondary minerals and gas phases (Tables S2.2–S2.7) are not present at the beginning of the equilibrium calculations but are by default allowed to form and react during the model run. Saturation indices (SI; SI = log(IAP/K) with IAP the ion activity product and Kthe equilibrium constant) with respect to the mineral phases of interest are initially set to 0 except for dolomite, siderite, and Ca-rhodochrosite (Tables S2.2–S2.7). Supersaturation for these carbonates is assumed due to phosphate adsorption onto calcium carbonate, in accordance with observations by Raiswell and Fisher  and Warren . Equilibrium phases that are not present within the used database wateq4f.dat, such as those for struvite, carbonate fluorapatite (CFA), Ca-rhodochrosite, and CH4-hydrate, are defined separately (Table S2.8).
 Given in situ pressure and temperature conditions, sediments of Sites 682, 688, and 1231 are within the gas hydrate stability zone [e.g., Sloan, 1998, and references therein]. Therefore, methane hydrate is defined as an additional equilibrium phase in these model scenarios. The equilibrium constant for methane hydrate is calculated from Gibb's free energy (ΔG = 5.736 kJ mol−1) of the methane dissolution reaction: CH4 · 6H2O(s) = CH4(aq) + 6H2O, pressure (P = 10 MPa), and temperature (T = 279.55 K) after Lu et al. .
 Input parameters that define primary and secondary equilibrium phases and physical boundary conditions are given in Tables S2.2–S2.7 of the auxiliary material. A detailed description of the physical and chemical considerations and the calculation scheme of the applied model are given in Arning et al. .
3.2. Model Calibration and Organic Matter Remineralization
 Measured pore water alkalinity profiles (Figures 3b and 6b) are used for calibration. The release of CO2 from the organic matter and its subsequent dissolution influences pore water alkalinity. To calibrate the model, the amount of organic matter (simplified as (CH2O)x(NH3)y(H3PO4)z) that can be converted in each representative volume at each time step (Figures 3a and 6a) is readjusted until the modeled alkalinity profiles of investigated sites match measured alkalinity profiles (Figures 3b and 6b).
Figure 3. (a) Amounts (mmol and wt.%) and rates (mmol m−3 yr−1) of organic matter remineralized in each representative volume (RV) of the shelf and lower slope sites, as well as measured total organic carbon (TOC) content (wt.%). (b) Modeled and measured alkalinity profiles of the shelf and lower slope sites. (c) Modeled and measured ammonia concentration profiles of the shelf and lower slope sites. Grey dots: modeled data, diamonds: measured data. Measured pore water concentration data are taken from Suess et al. . Red numbering indicates sedimentary units according to Suess et al. .
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 Remineralized organic matter in the models (Redfield-CH2O) designed for Sites 680, 681, 682, 688, and 1231 is assumed to be primarily of marine origin, with a minor contribution from terrestrial input. This organic matter is defined with an approximate Redfield stoichiometry of C:N:P equal to 100:15:1 [Redfield, 1958]. In the model for site 679, organic matter of marine origin is converted in Holocene period to upper Miocene sediments (5 to 235 mbsf), whereas in older sediments (245 to 495 mbsf) mixed marine/terrestrial organic matter (C:N:P = 100:12:1) is converted. In our model, the organic matter is considered as a whole, and reaction rates are included by converting different amounts of Redfield-CH2O in each time step. It has to be noted, that the stoichiometry of the remineralized organic matter is an approximation as in organic matter landing on the seafloor the Redfield ratio did not be necessarily conserved. The good fit between measured and modeled ammonia concentration profiles (Figure 3c, except for sites 680 and 681; see explanation in section 4.2) support our assumptions of organic matter composition.
 Rates of organic carbon remineralization at Sites 681, 680, 679, and 682 are comparable (Figure 3a). Some higher rates are only modeled in the Quaternary sediments of the shelf sites 681 and 680. Organic carbon remineralization at Site 679 is relatively constant, whereas at Site 682 most organic carbon was remineralized during the middle Miocene period. The amounts of remineralized organic carbon are twice as high in the Miocene sediments of site 682 compared with the Miocene sediments of Site 679. Organic carbon remineralization was suppressed in Site 682 sediments older than the Miocene period. By far most organic carbon was remineralized within the Quaternary sediments of Site 688 (up to 3.2 wt.%). The most inactive site is the open ocean Site 1231 with less than 0.05 wt.% of organic matter remineralized (Figure 6a). To calculate rates and carbon amounts for Miocene sediments, the calibrated models were run for less time steps covering sediment depths from the Miocene period.
 The diffusive flux J [mol/(m2 · s)] of HCO3−, dissolved CO2, and dissolved CH4into the sulphate-methane transition zone (SMTZ) is calculated from the modeled pore water profiles using Fick's first law:
where φ is porosity (−), Dsed is the specific diffusion coefficient in pore space of a sediment (m2/s), and dc/dx is the concentration gradient (mol/(m3 · m)).
 Dsed can be calculated as:
with Dsw diffusion coefficient in solution [m2/s] taken from Schulz  and θ2 tortuosity (estimated from porosity φ: θ2 = 1 − ln(φ2) [after Boudreau, 1997]. The fluxes are calculated for the present-day and the Miocene situation. It is not meant that these fluxes are continuous over time.
 Mass accumulation rates of total organic carbon (MARTOC) (g/(cm2 · kyr)) are calculated following the equation developed by van Andel et al. :
where TOC is total organic carbon (%), SR is the mean sedimentation rate (cm kyr−1), WBD is wet bulk density (g/cm3), and PO is porosity (%). Using mass accumulation rates, dilution effects by inorganic compounds can be excluded, and the data can be interpreted in terms of changes in sediment supply and thus primary productivity. From MARTOC we can calculate the primary productivity (PP) (g/(cm2 · kyr)):
where EPis the export production (%). In the present-day high productivity area on the Peruvian shelf, 10% of primary productivity from the photic zone of the ocean reaches the seafloor [Fossing, 1990]. High alkalinity in the pore water of lower slope sites (Figure 3b) suggests high organic matter remineralization on these sites, as well. We, therefore, assume that 10% of the primary productivity has constantly reached the seafloor at the shelf and lower slope sites off the coast of Peru. It has to be noticed that this is an approximation.