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 In many continental margin sediments, a deep reaction zone exists which is separated from remineralization processes near the sediment surface. Here, methane diffuses upward to a depth where it is oxidized by downwardly diffusing sulfate. However, the methane sources that drive this anaerobic oxidation of methane (AOM) in the sulfate-methane transition zone (SMT) may vary among sites. In particular, these sources can be thought of as either (i) “internal” sources from in situ methanogenesis (regardless of where it occurs in the sediment column) that are ultimately coupled to organic matter deposition and burial, or (ii) “external” sources such as hydrocarbon reservoirs derived from ancient source rocks, or deeply buried gas hydrates, both of which are decoupled from contemporaneous organic carbon deposition at the sediment surface. Using a modeling approach, we examine the relationship between different methane sources and pore water sulfate, methane, dissolved inorganic carbon (DIC), and ammonium profiles. We show that pore water ammonium profiles through the SMT represent an independent “tracer” of remineralization processes occurring in deep sediments that complement information obtained from profiles of solutes directly associated with AOM and carbonate precipitation, i.e., DIC, methane, and sulfate. Pore water DIC profiles also show an inflection point in the SMT based on the type of deep methane source and the presence/absence of accompanying upward DIC fluxes. With these results, we present a conceptual framework which illustrates how shallow pore water profiles from continental margin settings can be used to obtain important information about remineralization processes and methane sources in deep sediments.
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 Both qualitative [Cowie and Hedges, 1994] and quantitative [Middelburg, 1989] observations suggest that under steady state conditions, organic matter reactivity decreases with increasing age. In sediments, where age increases with sediment burial, organic matter reactivity generally decreases with depth because more labile organic matter is preferentially remineralized near the sediment surface, leaving behind less reactive organic matter for subsequent decomposition with burial. Organic matter remineralization rates are therefore generally highest near the sediment-water interface and decrease in a near-continuous fashion with depth [e.g., Soetaert et al., 1996; Martin and Sayles, 2003; Jørgensen and Parkes, 2010]. In some marine sediments, however, profiles of pore water solutes such as O2, nitrate, and sulfate suggest the occurrence of this type of depth attenuation of remineralization processes in surface sediments, along with the existence of a deeper reaction zone. Additionally, these two zones are separated by distances ranging from approximately tens of centimeters to meters, where the occurrence of linear pore water profiles implies the existence of an intermediate no-reaction, diffusion-dominated zone [e.g., Goloway and Bender, 1982; Wilson et al., 1985; Niewöhner et al., 1998; Borowski et al., 1999; Berelson et al., 2005]. There are, however, several caveats to this explanation. For example, linear profiles can also be obtained when there are low rates of remineralization in this intermediate region as compared to higher rates in the overlying and underlying sediments [Burdige and Komada, 2011]. Similarly, curvature in sediment pore water profiles does not necessarily imply non-conservative solute behavior if there is significant pore-water advection, or if there are significant changes in diffusion coefficients with depth due to temperature and/or porosity variations [Lerman, 1977; Dickens, 2001].
 These factors notwithstanding, the causes of this apparent uncoupling between surface sediment remineralization processes and those in a deep reaction zone are not well understood and may vary among different sedimentary settings. For example, in some pelagic and hemipelagic settings, this can be the result of turbidite deposition and diagenesis [e.g., Goloway and Bender, 1982; Sørensen et al., 1984; Wilson et al., 1985]. Here the gravity-driven flow of relatively organic-rich continental margin sediments onto organic-poor sediments sets up a situation in which the subsequent burial and remineralization of organic matter in the turbidite results in a subsurface reaction front for aerobic respiration, denitrification, and metal redox cycling [also see a review in Burdige, 2006].
 In many other continental margin sediments, the apparent uncoupling is due to the occurrence of a deep reaction zone at the transition between sulfate-reducing and methanogenic sediments. In this sulfate-methane transition zone (SMT), sulfate concentrations go to zero as methane diffuses (or is advected) upward to the SMT where it is oxidized by downwardly diffusing sulfate, through a microbially mediated process termed anaerobic oxidation of methane, or AOM [Reeburgh, 2007; Knittel and Boetius, 2009]:
 In different continental margin settings, the depth of the SMT may vary from less than a meter below the sediment surface to ~10–20 m or more [Iversen and Jørgensen, 1985; Niewöhner et al., 1998; Borowski et al., 1999; Dickens, 2001; D'Hondt et al., 2002; Hensen et al., 2003; Berelson et al., 2005; Snyder et al., 2007; Knab et al., 2008; Chatterjee et al., 2011; Malinverno and Pohlman, 2011; and others]. The SMT not only represents a discrete zone of AOM activity, but is also an important site of iron sulfide mineral precipitation [Hensen et al., 2003; Borowski et al., 2013]. In addition, because AOM produces alkalinity, it can also be a site of extensive carbonate precipitation [Berelson et al., 2005; Meister et al., 2007; Snyder et al., 2007].
 Past studies of these systems have tended to focus on interpreting processes in the SMT by examining the concentration and isotopic composition of solutes directly associated with AOM and carbonate precipitation, i.e., dissolved inorganic carbon (DIC), methane, and sulfate (see references cited above). However, a number of fundamental questions remain, including the relationship between the origin of the methane that drives AOM and the resulting pore water profiles of associated solutes.
 Previously, we used a modeling approach to examine how pore water profiles of sulfate, methane, and DIC can be used to infer whether methane involved in AOM is produced locally by methanogenesis, or is introduced from a source at depth that is decoupled from ongoing organic matter degradation, such as geologic hydrocarbon reservoirs and/or deeply buried gas hydrate deposits [Burdige, 2011; Burdige and Komada, 2011]. Recent modeling efforts have also examined similar aspects of this problem [Chatterjee et al., 2011; Malinverno and Pohlman, 2011; Meister et al., 2013].
 Here we continue to examine this problem using an expanded version of the reactive-transport model described in Burdige and Komada  that also allows us to examine ammonium pore water profiles. Ammonium profiles that penetrate through the SMT have been reported in the literature [Borowski et al., 1996; Niewöhner et al., 1998; Borowski and Paull, 2000], but their relationship to methane biogeochemistry in deep sediments has not been fully explored. We address this knowledge gap by specifically linking the upward flux of methane to the SMT to processes that may also produce DIC and ammonium below the SMT. Specifically, we show that pore water ammonium profiles through the SMT represent an independent “tracer” of remineralization processes occurring in deep sediments that complement information obtained solely from profiles of DIC, methane, and sulfate. Through an examination of this problem using model sediment systems, we develop a conceptual framework that illustrates how surface pore water profiles can be used to obtain important information about remineralization processes and methane sources in deep marine sediments.
 In coastal or nearshore marine sediments, sulfate reduction and methanogenesis generally occur in the upper several meters or less of sediment [Burdige, 2006]. Methanogenesis occurs immediately below the zone of sulfate reduction, once pore water sulfate is completely, or near-completely, consumed [Reeburgh, 2007; Alperin and Hoehler, 2009], consistent with the “classic” biogeochemical zonation model [Claypool and Kaplan, 1974; Froelich et al., 1979]. Overall, the depth distribution of sulfate reduction and methanogenesis in this model is primarily driven by the deposition and burial of reactive particulate organic matter, and this methanogenesis is the primary source of methane for the AOM that occurs in the SMT. In such sediments, AOM generally represents less than ~30% of the total sulfate reduction [Reeburgh, 1983; Devol et al., 1984; Iversen and Jørgensen, 1985; Martens et al., 1998; Dale et al., 2008], and for coastal and nearshore sediments globally, an average value of ~12% appears to be reasonable [Henrichs and Reeburgh, 1987]. Thus in these sediments, sulfate reduction directly tied to the oxidation of reactive particulate organic matter generally dominates over AOM.
 In contrast, in some continental margin sediments, sulfate reduction over the entire sediment column may be dominated by AOM in the SMT. Here sulfate profiles are linear, or near-linear, from the sediment surface to the SMT, suggesting the dominance of diffusive transport of sulfate throughout the sediment column above the SMT [e.g., Niewöhner et al., 1998; Borowski et al., 1999; Berelson et al., 2005; Burdige, 2011]. However, the sources of the methane that drives AOM in these continental margin sediments are not well characterized. In the discussion below, we separate the methane sources broadly into those that we refer to as “internal” and “external.”
2.1 Internal Methane Sources for AOM in Continental Margin Sediments
 Much of the methane that drives AOM in continental margin sediments is not necessarily produced just below the SMT, as it is in many nearshore and coastal sediments. Rather, it may be produced in a deep zone of methanogenesis, some tens to hundreds of meters below the SMT. The causes of this relatively large spatial separation between the SMT and a deeper zone of active methanogenesis are not well understood [Wellsbury et al., 1997; Wallmann et al., 2006; Burdige, 2011; Archer et al., 2012], and discussion of this problem is beyond the scope of this paper. Nevertheless, regardless of this consideration, we can think of this deep in situ methanogenesis as ultimately being coupled to organic matter deposition at the surface and its subsequent burial. Furthermore, this methane is largely transported by vertical diffusion from its depth of production to its depth of consumption. We refer to this as an “internal” deep source of methane.
 In settings where methane is derived from such a deep internal source, there will be concomitant DIC production as well as ammonium and phosphate production during the complete remineralization of sedimentary organic matter by the consortium of anaerobes (i.e., hydrolytic, fermentative as well as methanogenic microbes) that mediate the process [Megonigal et al., 2003; Burdige, 2006]. The overall process by which this biogenic methane is produced can be expressed as
where Corg is reactive particulate organic carbon (also referred to here as POC), L2 is the molar amount of CH4 produced per mole of Corg oxidized, L3 is the molar amount of DIC (expressed here as CO2) produced per mole of Corg oxidized, and x:y:z is the C:N:P ratio of this organic matter (we also specifically define the N:C ratio of this material as rN:C [=y/x]; see Table 1 for a list of all abbreviations). If we approximate Corg as CH2O, then L2 = L3 = , although for Corg whose carbon oxidation state (ox) does not equal zero, L2 equals (4 − ox)/8 [Burdige, 2006], while L3 equals (4 + ox)/8 [Burdige and Komada, 2011]. For the sake of simplicity, this equation is not completely balanced because we have not specified the bulk H:C and O:C ratios of Corg. Partial remineralization of Corg may also occur in conjunction with complete remineralization and similarly lead to ammonium, DIC, and phosphate production along with production of a broad range of dissolved organic carbon (DOC) compounds in addition to CO2 [see, for example, Kujawinski, 2011]. However, expressing partial Corg remineralization with a defined stoichiometry such as that in equation (2) is difficult, because of the complexity of the different types of fermentation reactions observed in nature [e.g., Thauer et al., 1977], and because of the wide range of DOC compounds that can be produced during microbial remineralization.
Table 1. A List of Abbreviations Used in the Model Equations
Values of these parameters with the superscript “deep” are specifically for the organic matter undergoing remineralization by methanogenesis in deep sediments below the lower model boundary (e.g., see equations (5) and (6) and related discussions).
Solutes and Solids
DIC (dissolved inorganic carbon)
Reactive particulate organic carbon (POC) in sediments
The bulk sediment diffusion coefficient for solute i (corrected for temperature and sediment tortuosity as discussed in Table 3)
A factor that converts solid phase concentration units to pore water solute concentration units [Burdige, 2006]
A function that inhibits the occurrence of methanogenesis when sulfate concentrations are above some threshold value [Burdige, 2011]
Grams dry weight (in units for reactive POC in sediments)
Upward flux of solute i at the lower model boundary
Rate constant for organic matter remineralization (i = OM) or AOM (i = aom)
Nitrogen:carbon ratio of organic matter undergoing remineralization
Moles of Corg oxidized, or DIC produced, per mole of sulfate reduced during sulfate reduction
 Expressing sulfate reduction in a similar fashion yields
where rC:S is the molar amount of Corg oxidized, or DIC produced, per mole of sulfate reduced. When Corg is approximated as CH2O, rC:S = 2 and in general, rC:S equals 8/(4 − ox) for Corg whose carbon oxidation state is ox [Burdige, 2006]. Analogous to methanogenesis, sulfate reduction is mediated by a consortium of hydrolytic, fermentative, and sulfate-reducing anaerobes.
2.2 External Methane Sources for AOM in Continental Margin Sediments
 Methane that is oxidized in the SMT may also be derived from a deep “external” source that unlike the internal sources described above, is decoupled from contemporaneous organic matter deposition at the sediment surface followed by remineralization and burial. External methane sources might include hydrocarbon reservoirs derived from ancient source rocks, or deeply buried gas hydrate deposits [see discussions and references in Burdige and Komada, 2011]. Furthermore, such an external methane source in a given sediment setting may actually have been produced elsewhere and subsequently migrated either laterally or vertically in the gaseous phase to its current location [e.g., Hein et al., 2006; Normark et al., 2006]. Relevant to this discussion is that both of these scenarios should result in a situation in which an external methane flux observed today (due to biogenic methane production in the past) is decoupled from ammonium or DIC production that may have occurred in the past along with the production of this methane. Although stable isotope measurements argue that deep methane sources are generally biogenic rather than thermogenic in origin [e.g., Bohrmann and Torres, 2006; Paull et al., 2008], discussions in Snyder et al.  suggest that there can also be some decoupling between upward fluxes of thermogenic methane and fluxes of DIC and ammonium.
 Decoupling of upward methane fluxes derived in this fashion from DIC and ammonium fluxes requires that the removal of methane from saturated sediment pore waters into a gaseous phase does not also result in significant removal of DIC and ammonium as CO2(g) and NH3(g), respectively. Support for this assumption stems in part from the fact that at the pH of sediment pore waters (~7–8.2), DIC and ammonium exist predominantly as HCO3− and NH4+ ions, versus aqueous CO2 or NH3, respectively (also see footnote b in Table 3) [Zeebe and Wolf-Gladrow, 2001].
Processes on the right-hand side of each equation are explained in brackets below each equation. Terms used in the equations are defined in Table 1.
[diffusion; Corg remineralization driven by sulfate reduction (equation (3)); and anaerobic oxidation of methane (equation (1))]
Reactive POC (G)
[advection driven by sedimentation; Corg remineralization driven by sulfate reduction (equation (3)); and Corg remineralization driven by methanogenesis (equation (2))]
Pore water methane (M)
[diffusion; Corg remineralization driven by methanogenesis (equation (2)); and anaerobic oxidation of methane (equation (1))]
Pore water DIC (C)
[diffusion; Corg remineralization driven by sulfate reduction (equation (3)); Corg remineralization driven by methanogenesis (equation (2)); and anaerobic oxidation of methane (equation (1))]
Pore water ammonium (N)
[diffusion; ammonium production associated with Corg remineralization driven by sulfate reduction (equation (3)); ammonium production associated with Corg remineralization driven by methanogenesis (equation (2))]
 Consistent with these arguments, studies of methane gas bubbles that form in shallow anoxic sediments [e.g., Martens and Klump, 1980; Martens and Chanton, 1989] show that these bubbles contain less than a few percent CO2. Gas bubbles at the seafloor derived from natural hydrocarbon seeps also contain ~10% to <1% CO2 [Leifer et al., 2006; Paull et al., 2008], although it is unclear whether this CO2 derives from the original underlying gas reservoir, or is produced in situ by processes occurring as the gas ascends from depth in the seabed to the seafloor. Finally, Claypool and Kvenvolden  report that CO2 is in general a “minor” or “trace” component of natural gas in marine sediments. Equally important though is the fact that if the methane in sediment systems such as those studied here is derived from methane gas that has migrated either laterally or vertically from its original source of production, then any DIC or ammonium that may have been produced along with this methane will likely have been “left behind.”
 In addition, hydrate formation is generally thought to exclude all dissolved ions such as, e.g., chloride [Bohrmann and Torres, 2006]. Thus, if biogenic methane produced by methanogenesis is trapped as solid hydrate, it is likely that HCO3− and NH4+ ions are similarly excluded from the hydrate structure. This exclusion means that when environmental conditions change and the hydrate becomes an active methane source in sediment systems such as those discussed here, there will be no accompanying upward flux of either DIC or ammonium.
3 Model Description and Analysis
 The model used here is a steady-state reactive transport model for sulfate (S), DIC (C), methane (M), ammonium (N), and reactive particulate organic carbon, or POC (G). The model equations are listed in Table 2, and the terms used in the equations are listed in Table 1. In this model, we assume that there is only one type of reactive POC undergoing remineralization, since having multiple pools of POC with different relativities undergoing remineralization (i.e., a multi-G model) does not affect the conclusions presented here.
 In the model, we further assume that porosity is constant with depth. The inclusion of variable porosity (due to sediment compaction) in reactive-transport model calculations over depth scales ranging from tens to a few hundred centimeters results in concentration differences, relative to constant porosity calculations, that differ by less than 15% over the entire calculated profiles [Lerman, 1977; Klump and Martens, 1989; Komada et al., 2013; D. Burdige, unpublished results]. Over longer depth (and timescales), the effects of variable porosity may be more significant [Dickens, 2001], especially if one is interested in specifically fitting the model to field data. In such cases, the equations used here can be adapted as necessary to account for compaction and variable porosity [Burdige, 2011].
 A Peclet number analysis [Boudreau, 1997] indicates that for the model parameters used here (Table 3), diffusion dominates over pore water advection driven by sedimentation, allowing us to safely ignore advection terms in the solute equations in Table 2. In sediment systems where advection driven by sediment compaction or by other processes (e.g., thermally driven fluid flow) is more significant [e.g., Luff and Wallmann, 2003; Buffett and Archer, 2004; Hensen and Wallmann, 2005], the model equations used here can again be modified as needed [Burdige, 2011].
Bulk sediment diffusion coefficients were determined using the modified Weissberg equation Ds = D°/[1 − ln(φ2)] [Boudreau, 1997], where D° is the seawater free solution diffusion coefficient. Values of D° were obtained from Schulz and Zabel  for an assumed bottom water temperature of 5°C. The free solution diffusion coefficient for DIC is a weighted average of the diffusion coefficients for HCO3−, CO32−, and aqueous CO2 based on their relative average composition (±1σ) in pore water DIC from Santa Monica Basin sediments (93.7 ± 2.8%, 3.8 ± 3.5%, and 3.5 ± 2.1%, respectively). Note that the bulk sediment diffusion coefficients for sulfate, methane, and DIC reported in Table 1 of Burdige and Komada  are incorrectly listed and in fact are seawater free solution diffusion coefficients.
 The upper boundary condition for the model equations specifies the sulfate, DIC, methane, and ammonium concentrations at the sediment-water interface (zero for methane and ammonium, and bottom water values for DIC and sulfate) and fixes the reactive POC concentration at the sediment surface (Go in Table 4). The lower boundary of the model is set to z = 400 cm. We chose this depth since it encompasses the SMT in the coastal and inner continental margin sediments we are most interested in examining here, but excludes the less well understood deep processes that ultimately represent the sources of methane, and perhaps DIC and ammonium at the lower boundary.
Table 4. Model Specific Parameters and Description of the Model Runs
Methane flux across lower model boundary from a deep external source without accompanying DIC and ammonium fluxes
Methane flux across lower model boundary from a deep internal source with accompanying DIC and ammonium fluxes
Methane flux across lower model boundary from a 1:1 mixture of a deep internal source and a deep external source with accompanying DIC and ammonium fluxes
Same as model run N4 but lower Go value
Same as model run N4 but higher Go value
Same as model run N4 but higher kOM value
Same as model run N4 but lower kOM value
Same as model run N4 but lower (=0.1 versus 0.143 in model run N4)
 We consider three sets of lower boundary conditions for M, C, and N. In the first case, we assume that there is no upward flux of methane across the lower model boundary (i.e., there is no deep external nor internal source of methane). This implies that ∂M/∂z = ∂C/∂z = ∂N/∂z = 0 at the lower boundary and is referred to here as the “no methane flux” lower boundary condition. In the second case, we prescribe an upward flux of methane across the lower model boundary (Jlb,m) that is supported by a deep external source
and because this methane originates from an external source, the DIC and ammonium fluxes at the lower boundary remain equal to zero. This is referred to as the “external methane flux” lower boundary condition. The third and final case is a situation in which there is an internal methane source below the depth of the model lower boundary. We specify the DIC and ammonium fluxes based on equation (2), rN:C, and the carbon oxidation state of the organic matter that is degraded in the deep sediments, i.e.,
 This is the “internal methane flux” lower boundary condition. One can think about this situation as one, for example, in which refractory organic matter escapes remineralization in the surface sediments, but is degraded by methanogenesis below the lower boundary of the model in response to increasing temperatures [Burdige, 2011]. However, as noted in section 2.1, this may not necessarily be the only explanation for the occurrence of such a deep zone of methanogenesis.
 Regardless of the choice of the lower boundary condition for solutes M, C, and N, for solute S we specify that ∂S/∂z goes to zero at the lower boundary. This lower boundary condition assumes that either all sulfate is consumed in the sediments above the lower boundary or that all reactive POC is consumed before complete sulfate reduction.
 The five model equations in Table 2 represent a set of coupled, nonlinear differential equations for which there is no analytical solution. A solution to this set of equations was obtained numerically using the method of lines technique with variable grid spacing [Burdige, 2011; Burdige and Komada, 2011]. In all model calculations, depth is positive downward, and therefore negative fluxes are upward, toward the sediment surface.
 Input parameters used in the model runs are listed in Tables 3 and 4. The sediment accumulation rates (ω) we used are within the range of values observed for nearshore to inner continental margin sediments [e.g., Middelburg et al., 1997]. The upward methane flux Jlb,M (0.2 mol m−2 yr−1) is consistent with fluxes reported by Berelson et al.  for sediments along the California/Mexican continental margin in water depths less than 1000 m. At these sites on the California/Mexican margin, methane fluxes of this magnitude result in SMT depths that range from ~100 to 200 cm, consistent with our model results (see section 4.3 and, e.g., Figure 1). In contrast, outer continental margin sediments have lower methane fluxes into the SMT and correspondingly deeper SMT depths. For example, at IODP site U11325 on the northern Cascadia Margin (water depth ~2200 m) the methane flux into the SMT is ~0.03 mol m−2 yr−1 with an SMT depth of ~5 m [Malinverno and Pohlman, 2011]. On the Blake Ridge (water depth ~2700 m), methane fluxes into the SMT are <0.01 mol m−2 yr−1 with an SMT depth of ~20 m [Borowski et al., 2000; Dickens, 2001; Burdige, 2011].
 In all model runs, ox was set equal to −0.7 [Burdige and Komada, 2011], and therefore the expected value of rC:S is 1.7. The organic matter undergoing remineralization in the surface sediments of these model runs was also assumed to have an rN:C value of 0.143 (C:N ratio = 7, which is a “typical” value for marine organic matter). In all but one model run, this same rN:C value was used for the organic matter undergoing remineralization that contributes to the deep internal methane source (see Table 4 and section 4.4 for more details).
 In our previous work [Burdige and Komada, 2011], we used pore water property-property plots [Berner, 1977, 1980] to analyze model results and infer information about remineralization processes occurring in the sediments [also see, for example, similar plots in Dickens and Snyder, 2009; Chatterjee et al., 2011]. This approach is based on the observation that a plot of ∆C versus ∆S (where ∆ indicates the concentration difference relative to bottom water values) is often linear if DIC production is strongly coupled to bacterial sulfate reduction. The slope of the line through these data (d∆C/d∆S) is related to rC:S according to
 In a similar fashion, sulfate and ammonium concentrations are related to rN:C according to [Burdige, 2006]
 To further examine remineralization processes occurring in these model sediments, we also calculated pore water gradients and diffusive fluxes above and below the SMT. Pore water gradients were calculated using the slopes of the best fit lines through the appropriate linear portions of the model data, and diffusive fluxes were then calculated with Fick's first law [Burdige, 2006], using the porosity value and bulk sediment diffusion coefficients given in Table 3.
4 Model Results and Discussion
4.1 No Methane Flux at the Lower Model Boundary, No Methane Source Within the Model Domain
 In model run N1, POC loading is low (Table 4) and reactive POC is depleted before pore water sulfate, preventing the occurrence of methanogenesis. This model also assumes that there is no upward methane flux at the lower model boundary. Model depth profiles decrease (sulfate or reactive POC) or increase (DIC, ammonium) in exponential-like fashions (Figure 1). These trends are broadly consistent with field results from many nearshore sediments [Burdige, 2006]. Applying equations (7) and (8) to property-property plots of the data from this model run returns the input values of rC:S and rN:C [Burdige and Komada, 2011].
4.2 No Methane Flux at the Lower Model Boundary, Methane Production Within the Model Domain
 Model run N2 also uses the “no methane flux” lower boundary condition, but has a higher carbon loading as compared to model run N1 (Table 4). This results in complete sulfate depletion in the sediments along with the occurrence of in situ methanogenesis just below the SMT at ~80 cm (Figure 1). Overall, model-derived methane and sulfate profiles are concave up and down, respectively, although the methane gradient just below the SMT and the sulfate gradient just above the SMT are both linear (not shown here, but see Figure 5 in Burdige and Komada ). Profiles such as these are also observed in nearshore sediments (see discussions in the beginning of section 2 as well as specific examples in, e.g., Martens and Berner , Alperin et al. , Martens et al. , and Dale et al. ). In this model run, ammonium and DIC profiles also are both concave down, due to the production of these solutes in association with sulfate reduction, methanogenesis, and, in the case of DIC, AOM.
 In our earlier work [Burdige and Komada, 2011], we observed that the ∆C:∆S property-property plot of these model results returns the value of rC:S for organic matter oxidation coupled to sulfate reduction, despite the occurrence of AOM in the model sediments along with DIC production by methanogenesis. This then led to the important conclusion that the internal cycling of methane by the coupling of in situ methanogenesis and AOM does not lead to deviations in the value of rC:S such as those seen in many continental margin sediments [e.g., Jahnke, 1990; Berelson et al., 2005]. The simplest explanation for this observation is that the sum of these two reactions (AOM and methanogenesis) is stoichiometrically indistinguishable from sulfate reduction coupled to organic matter oxidation [also see Jørgensen and Parkes, 2010], despite the fact that the major zones of methane production and consumption in the sediments are spatially separated.
 We now expand this observation to ammonium production in these model sediments. Here we similarly see that a ∆N:∆S property-property plot using model run N2 results returns the rN:C value for sulfate reduction using equation (8) (Figure 2), despite the fact that ~20% of the ammonium in these model sediments is actually produced in association with methanogenesis below the depth of sulfate reduction. A ∆N:∆C property-property plot with these model results also yields this same value of rN:C (not shown). These observations therefore indicate that the tight coupling between methanogenesis and AOM that “masks” DIC production by methanogenesis in ∆C:∆S property-property plots [Burdige and Komada, 2011] also extends to ammonium production associated with methanogenesis.
4.3 Methane Flux Across Lower Model Boundary From Internal and External Sources, No Methane Production Within the Model Domain
 The next three model runs (N3–N5) have the same reactive POC flux to the sediment surface as model run N1 and have pore water ammonium, DIC, and sulfate profiles that show slight curvature near the sediment surface due to the remineralization of this material. At the lower boundary, these three model runs have identical upward methane fluxes, but the fluxes are partitioned into different deep processes/sources (Table 4). These differences result in contrasting DIC and ammonium pore water profiles, particularly at depth.
 Because these runs are identical with respect to the POC flux to the sediment surface and the magnitude of the methane flux across the lower model boundary, they have identical methane and sulfate pore water profiles, and in all cases, the SMT is situated at ~120 cm (Figure 1). While the sulfate and methane gradients into the SMT appear linear, a careful examination of these profiles within the SMT [see Burdige and Komada, 2011,Figure 7] indicates that the model profiles show the type of curvature and overlap in this transition zone that is commonly seen in field data [e.g., Martens and Berner, 1974; Reeburgh, 2007; Knab et al., 2008].
 Model run N3 uses the external methane flux lower boundary condition, where one can think of the methane flux as perhaps coming from a relict gas hydrate deposit with no associated DIC or ammonium flux. Model run N4 uses the internal methane flux boundary condition where the methane flux comes from a deep internal source and therefore there are associated DIC and ammonium fluxes. Finally, model run N5 represents an intermediate case between N3 and N4 in which half of the methane comes from an external source and the other half comes from a deep internal source. This division is purely arbitrary, chosen for the sake of this example.
 In all three model runs, the DIC profiles are largely linear between the surface zone of organic matter remineralization (upper ~20–30 cm) and the SMT (Figure 1). The DIC profiles also show an inflection point at the SMT, as seen in field data [Berelson et al., 2005; Harrison et al., 2009]. The magnitude of the upward DIC flux above the SMT (JC+) as well as the degree of inflection of the profiles in the SMT depends on two quantities: (i) the magnitude of the upward methane flux below the SMT (JM−) which is oxidized to DIC by AOM near the SMT (and which is identical in all three of these model runs), and (ii) the magnitude of the upward DIC flux below the SMT (JC−) from any deep remineralization processes (N4 > N5 > N3 = 0). Equally important is the observation that the ratio of the upward DIC and methane fluxes into the SMT from below (JC−/JM−) allows one to distinguish between different sources of methane at depth in these model sediments (Table 5).
Table 5. Solute Fluxes (Units: mol m−2 yr−1) Above and Below the SMT for Model Run N3–N10a
Fluxes were calculated as discussed in the text using Fick's first law, and positive fluxes are downward. Pore water gradients above the SMT were determined by linear least squares of the model data from 60–100 cm (N3–N5 and N10), 80–120 cm (N6), 75–115 (N7), 100–120 (N8), and 80–90 cm (N9). Below the SMT, this fitting was done with model data from 140–180 cm (N3–N5 and N10), 160–200 cm (N6–N8), and 120–130 cm (N9).
Specific details about the parameters used in each model run can be found in Table 4.
For model run N3, the predicted value of JC + : JS + is based on the stoichiometry of AOM (equation (1)). For model runs N4 and N6–N10, it is the value of rC:S for sulfate reduction of Corg with a carbon oxidation state of −0.7, given the observed coupling of methanogenesis and AOM “looking” like sulfate reduction (see the text for details). For model run N5, the 1:1 split in the sources of the upward flux of methane into these model sediments implies that this predicted ratio is the average of the previous two values.
For model runs N4 and N6–N10, the predicted value of JN + : JC + is the value of rN:C for the Corg undergoing remineralization by methanogenesis at depth. For model runs N4–N9 = 0.143 (C:N ratio = 7) while for model run N10 = 0.1 (C:N ratio = 10). For model run N5, the 50:50 split in the sources of the upward flux of methane into the SMT of these model sediments (and the fact that methane derived from an external source is assumed to not have an accompanying ammonium or DIC flux) implies that this predicted ratio is given by
where the numerator is the upward flux of ammonium from the deep sediments (see equation (6)) and the denominator is the sum of the upward methane flux (oxidized to DIC by AOM at the SMT) plus the additional upward DIC flux that accompanies deep methane production (see equation (5)).
For model run N3, the predicted value of the ratio JC−:JM− is zero since there is no upward DIC flux that accompanies the methane flux. For model runs N4 and N6–N10 the predicted value is L3/L2 (see equations (2) or (5)). For model run N5, the 1:1 split in the sources of the upward flux of methane and their impact on the upward flux of DIC at depth in these model sediments implies that this predicted ratio is the average of the previous two values.
For model run N3, the predicted value of the ratio JN-:JC- is zero since there is no upward ammonium flux that accompanies the methane flux. For the remaining model runs, the only process producing DIC and ammonium below the SMT is methanogenesis (see equation (2)). Hence, the predicted value of this ratio is . For model runs N4–N9 = 0.143 (C:N ratio = 7) while for model run N10 = 0.1 (C:N ratio = 10).
Ratios of Fluxes Into the SMT (From Above and Below)
 For model runs in which there is a deep source of ammonium (model runs N4 and N5), the ammonium profiles are highly linear below the surface zone of organic matter remineralization and through the SMT into the methane-containing sediments (Figure 1). This is also evidenced by the similarity in the JN− and JN+ values for each run (Table 5), and their agreement with the appropriate Jlb,N values in Table 4. In addition, linear ammonium profiles only occur when there is deep ammonium production in the sediments, as opposed to the situation in which there is no deep source of ammonium in conjunction with the deep methane source (model run N3). The linearity of the ammonium profiles across the SMT in model runs N4 and N5 coupled with the inflection in the DIC profiles implies that the ammonium:DIC flux ratios above and below the SMT (i.e., JN +/JC + and JN −/JC −) provide complementary information about processes occurring in the sediments. This point is discussed in further detail in section 4.4.
 In model run N3, the ∆S:∆C property-property plot shows slight curvature with different slopes (and hence apparent rC:S values) at high and low −∆S values [see Burdige and Komada, 2011, Figure 8]. This curvature highlights the difficulty in the simple interpretation of such property-property plots when multiple processes affect pore water profiles over differing depth intervals [Burdige and Komada, 2011]. For these reasons, in the remainder of the discussion, we will examine pore water gradients and fluxes above and below the SMT as more robust indicators of processes occurring in these model sediments.
 For run N3, the ratio of the upward DIC flux to the downward sulfate flux above the SMT JC +/JS +) is essentially 1 (Table 5), as predicted by the stoichiometry of AOM in equation (1). For similar reasons, the ratio of the diffusive fluxes of methane and sulfate into the SMT (JM −/JS +) is also 1 (Table 5).
 In model run N4, the fluxes of methane, DIC, and ammonium at the lower boundary are stochiometrically linked since they originate from deep methanogenesis (see equations (2), (5), and (6)). The upward DIC flux above the SMT (JC+) therefore consists of DIC produced directly by methanogenesis at depth as well as DIC produced by AOM in the SMT when the upward methane flux is oxidized. Since this methane is produced by an internal source, JC +/JS + is again identical to the predicted value of rC:S for DIC production by sulfate reduction (Table 5).
 This result further extends our previous observations [Burdige and Komada, 2011] that when methane is produced by in situ methanogenesis driven ultimately by the downward burial of organic matter from the sediment surface, the internal recycling of this methane by AOM masks this methanogenesis in certain pore water properties. Specifically here this occurs even if there is large spatial decoupling between the zones of sulfate reduction and methanogenesis. Again, while the model used here does not explicitly define the location of the zone of deep methane production, conceptually, it clearly occurs well below the lower boundary of the model calculations (see section 3 for details).
 In a similar fashion, in model run N4, the ratio JN +/JC + above the SMT returns the value of rN:C for ammonium production associated with sulfate reduction, despite the fact that ~20% of the ammonium in these model pore waters is actually produced at depth in association with methanogenesis (Table 5). Thus, the linkage between deep methanogenesis and AOM impacts pore water ammonium profiles in the same way that it affects sulfate and DIC profiles, regardless of whether methanogenesis occurs immediately below the SMT (i.e., model run N2), or at much greater depths in the sediments as in model run N4 (see both model runs in Figure 1).
 Finally, for model run N5, the ratio JC +/JS + is essentially identical to that predicted when 50% of the DIC is produced by AOM driven by an external methane source, and the remaining 50% produced by what we can think of as “apparent” sulfate reduction, i.e., internal methanogenesis coupled to AOM (Table 5). Similar trends are seen when examining JN +/JC + above the SMT, due to the differing relationship between deep ammonium production and deep methane sources and methanogenesis in this model run (Table 5).
4.4 Linking Surface Remineralization Processes and Deep Reactions
 To examine the interplay between organic matter remineralization processes in the surface sediments and deep methanogenesis, we carried out a series of model runs that independently adjusted either Go (model runs N6 and N7) or kOM (model runs N8 and N9) with all other parameters fixed at the values used in model run N4 (Table 4).
 Figure 3 illustrates the impact on sediment profiles of changing the value of Go with all other input parameters kept constant at model run N4 values. When Go increases from 2 to 10 mg C gdw−1 the depth range over which organic matter remineralization occurs in the surface sediments does not change significantly, because the e-folding depth for remineralization is approximately ω/kOM which is constant for all three runs. However, since more sulfate is consumed as Go increases, the SMT systematically moves upward. Below ~50 cm, all sulfate profiles are linear and essentially parallel to one another since their slopes in this region (JS+ in Table 5) are determined by the upward methane flux which is constant in all three model runs (Table 3). Similarly, as Go increases, the methane profiles also shift upward and are parallel to one another. For DIC and ammonium, increasing Go increases the amount of curvature in the profiles near the sediment surface, although again below ~50 cm, these profiles are parallel, with (DIC) or without (ammonium) inflection points at the SMT. Fluxes above and below the SMT for model runs N6 and N7 are therefore essentially the same as those from model run N4 (as are their associated flux ratios).
 Figure 4 illustrates the impact on sediment profiles of changing the value of kOM with all other input parameters kept constant at model run N4 values. Decreasing the value of kOM results in a significant increase in the depth over which organic matter remineralization occurs, since as noted above, the e-folding depth for remineralization is roughly given by ω/kOM. However, pore water sulfate depth profiles are impacted in an opposite sense since decreasing kOM results in the SMT shoaling from ~140 cm (kOM = 0.03 yr−1 in model run N8) to ~100 cm (kOM = 0.001 yr−1 in model run N9).
 The contrasting responses in sulfate and reactive POC occur in part because diffusive exchange with bottom waters is very effective in replenishing sulfate being consumed near the sediment surface for larger kOM values. In a more general sense, the relationship between kOM and the depth of the SMT seen in Figure 4 can be explained as follows. The downward sulfate gradient (in Figure 5) is given by
and is constant for a fixed upward methane flux (see Figure 5 for the definition of these symbols). Although a mathematical expression for δS is not easily defined, based on an examination of the original 1-G model for sulfate reduction [e.g., see Berner, 1980, equations (6-20)–(6-24)], we might expect δS to increase as kOM decreases. We base this on the fact that in this model, the difference in the sulfate concentration between the sediment surface and the asymptotic value at depth is inversely related to kOM (assuming here that reactive POC rather than sulfate limits sediment sulfate reduction in the 1-G model). As δS increases, the numerator of equation (9) will decrease and in order to maintain a constant sulfate gradient, zSMT must also decrease. Therefore, as kOM decreases, zSMT will decrease. These results are consistent with the model findings of Meister et al.  who examined the depth of the SMT as a function of POC reactivity as defined by the reactive continuum [Boudreau and Ruddick, 1991] or power law [Middelburg, 1989] models.
 In these results, we also see that with a decrease in kOM not all of the reactive POC in the surface sediments is consumed by sulfate reduction, and the model results predict that some methanogenesis will occur in the depth region just below the SMT (as opposed to occurring strictly at some greater depth in the sediments below the lower boundary of the model). Evidence for this can be seen in the reactive POC profile of model run N9 (kOM = 0.001 yr−1), where significant POC consumption occurs below the SMT (Figure 4). In addition, in this same model run the upward flux of methane into the SMT (JM− = −0.236 mol m−2 yr−1 in Table 5) exceeds the value of Jlb,M in Table 4 (equal to −0.2 mol m−2 yr−1), again implying the occurrence of methanogenesis below the SMT but above the lower model boundary in this model run. This occurrence is likely a result of an interplay between (i) changes in the depth scales of POC remineralization by sulfate reduction in the surface sediments, (ii) changes with depth in pore water sulfate concentrations due to this remineralization, and (iii) the sulfate flux needed to oxidize the upward methane flux from depth. For the model conditions used here, the transition between complete and partial consumption of surficial reactive POC by sulfate reduction occurs between kOM values of 0.001 and 0.003 yr−1 (i.e., model runs N9 and N4). However, a more rigorous analysis of this problem would likely indicate that this transition is also a function of a number of other parameters, including Jlb,m, Go, and ω.
 While model run N8 (kOM = 0.03 yr−1) yields fluxes and flux ratios that are essentially identical to those for model run N4 (Table 5), the same is not entirely true for model run N9 (kOM = 0.001 yr−1). In this model run, the downward sulfate flux into the SMT is greater than that seen in the other model run (0.25 versus ~0.2 mol m−2 yr−1; see Table 5) since processes in the SMT now include the direct remineralization of surficial sediment organic matter by sulfate reduction in addition to AOM that results from methane production at depth. This occurrence may then also explain why the ratio JM −/JS + is slightly less than 1 in model run N9 (Table 5), since some of the sulfate diffusing into the region of the SMT is directly consumed by organic matter remineralization.
4.5 Linking Pore Water Fluxes With the C:N Ratio of Organic Matter Undergoing Remineralization
 The highly linear ammonium profiles through the SMT in model runs N4–N9 as compared to model run N3 (Figures 1, 3, and 4) are similar to deep ammonium profiles from continental margin sediments with analogous linear sulfate profiles above the SMT [Borowski et al., 1996; Niewöhner et al., 1998; Borowski and Paull, 2000]. In addition, in shallow sediment profiles (<1 m) from inner continental margin sites [Bender et al., 1989; Prokopenko et al., 2006; Komada et al., manuscript in preparation], pore water ammonium profiles show gradients that are similar in magnitude to those observed in these model sediments above the SMT (i.e., JN+ in Table 5). Overall, this suggests the potential usefulness of the conceptual framework presented here in providing information about remineralization processes occurring in deep marine sediments. The similarity in the values of JN−/JC− for model runs N4 and N5 is of interest since it provides information strictly about the stoichiometry of methanogenesis in the deep sediments, regardless of whether there is also some methane in the upward flux from an external methane source.
 These observations also appear to hold for model run N10 (Figure 6), in which we use model parameters that are identical to model run N4, but assume that the C:N ratio of the organic matter undergoing methanogenesis at depth is more depleted in nitrogen than that undergoing remineralization in the surface sediments (1/rN:C = 7; Table 4). This assumption is not necessarily unreasonable, since more refractory organic matter is generally depleted in nitrogen relative to more reactive organic matter [e.g., Burdige, 1991] and organic matter undergoing remineralization at depth in sediments might be expected to be less reactive than that being remineralized near the sediment surface.
 In model run N10, the ammonium profile is linear through the SMT, and the slope (i.e., the upward ammonium flux) of the model profile (both above and below the SMT) is lower than that of model run N4 because of these differences in C:N ratios (Table 4). Again, the values of JN− and JN+ agree well with the value of Jlb,N for this model run (compare values in Tables 5 and 4).
 Application of these model results to field data also requires additional considerations if one wants to use similar fluxes obtained from field data to examine the C:N ratio of the organic matter undergoing remineralization in deep sediments. For example, when the DIC and ammonium fluxes below the SMT for these model runs are taken at face value, their ratio (JC−/JN−) might suggest the remineralization of very nitrogen-rich organic matter at depth in these model sediments (Table 6). In fact, a more accurate representation of the C:N ratio of this material must also account for carbon that is remineralized and partitioned into the upward methane flux (i.e., (JC− + JM−)/JN−).
Table 6. Predicted C:N Ratio of the Organic Matter Undergoing Remineralization at Depth in the Model Sediments Based on Solute Fluxes as Compared to the Actual Valuesa
Actual C:N ratio
All fluxes are taken from Table 5. The actual C:N ratio listed here is 1/rN:C for the organic matter undergoing remineralization by methanogenesis at depth (see sections 3 and 4.4 for more details).
 At the same time, since this methane flux is oxidized by AOM in the SMT, in model runs N4 and N6–N10, the ratio of the upward DIC and ammonium fluxes just above the SMT (i.e., JC+/JN+) accurately represents the C:N ratio of the organic matter undergoing remineralization at depth (see discussions of similar phenomena in Burdige and Komada ). However in model run N5, this approach fails because half of the upward methane flux is derived from an ancient source, resulting in a predicted C:N ratio of the organic matter undergoing remineralization at depth that is too carbon rich.
 These observations highlight the fact that the correct interpretation of these model observations requires that the results be examined within the context of the conceptual model presented here, paying close attention to sources of methane at depth, and their relationship to deep DIC and ammonium production. Similar considerations also need to be taken into account in the interpretation of analogous fluxes and flux ratios obtained with field pore water data.
 The results presented here show that pore water ammonium profiles through the SMT represent an independent “tracer” of remineralization processes occurring in deep sediments that complement information obtained from profiles of solutes directly associated with AOM and carbonate precipitation, i.e., DIC, methane, and sulfate. Specifically, linear ammonium profiles through the SMT result from deep ammonium production associated with in situ methanogenesis at depth, while pore water DIC profiles show an inflection point in the SMT based on the type of deep methane source and the presence/absence of accompanying upward DIC fluxes. Overall, these modeling results provide a conceptual framework that illustrates how pore water profiles within the uppermost few meters of the sediment column can be used to obtain important information about remineralization processes and methane sources in deep marine sediments.
 However, a complete quantitative interpretation of field pore water data using this modeling approach also requires the inclusion of carbonate precipitation in model equations such as those presented here. Its occurrence will impact both the shape of the pore water profiles as well as the interpretation of pore water property-property plots and calculated solute diffusive fluxes [e.g., Berelson et al., 2005; Snyder et al., 2007; Burdige and Komada, 2011]. Quantifying carbonate precipitation will require independent results such as pore water Ca2+ profiles, as well as isotopic tracers of DIC and/or methane sources [e.g., Chatterjee et al., 2011].
 This work was supported by the following grants from NSF (Chemical Oceanography Program): OCE-115562 (to DJB) and OCE-1155764 (to TK). We thank two anonymous reviewers for providing us with comments that greatly improved an earlier version of this manuscript. We also thank Jerry Dickens, whose review of another of our manuscripts motivated the work presented here.