The vertical stratification in each sub-basin is resolved by a variable number of horizontally homogeneous layers. The numbers of layers in the respective sub-basins increase over time because of both inflows from adjacent basins and instances of pycnocline retreat, as described below, but they are kept below maximum values by mixing of the two layers that require the least amount of energy to be merged (Gustafsson, 2000).

Flow dynamics through the straits that connect different sub-basins depends on the width of the strait compared to the internal Rossby radius, determining whether or not earth rotation influences the water exchange. In general, lateral exchange between sub-basins is forced by barotropic pressure gradients across the straits that depend on the sea level difference and wind set-up as well as by baroclinic pressure gradients caused by differences in stratification. In narrow straits, the water flow is influenced by frictional resistance and dynamical contraction due to the Bernoulli effect, while the transport through wider straits is further controlled by earth rotation effects (Gustafsson, 2000, 2003).

The dynamics of the mixed surface layer in each sub-basin is forced by wind stress and buoyancy fluxes but also depends on earth rotation, following Stigebrandt (1985). The pycnocline is eroded whenever the buoyancy flux is negative (e.g., if surface water density increases because of net evaporation, or by cooling when the water temperature is above the temperature for maximum density) or when the buoyancy flux is positive but the power generated by wind stress is sufficient to do work against the buoyancy forces. Pycnocline erosion means that the mixed surface layer becomes thicker and denser as a result of deep-water entrainment into the surface layer. If the power is not sufficient, the turbulent mixing becomes limited either by earth rotation or by buoyancy fluxes, leading to a pycnocline retreat and the formation of a new and shallower mixed surface layer. The thickness of the new surface layer will be determined either by the Ekman or Monin–Obukhov length scale – whichever is shorter (Stigebrandt, 1985).

Entrainment flows are further modified by the presence of sea ice (Gustafsson, 2003). Ice dynamics is based on a sea-ice model by Björk (1997) but adapted to the Baltic Sea following Nohr et al. (2009). Calculations for heating/cooling and evaporation at the sea, ice, or snow surface follow Björk (1997). About half of the incoming shortwave radiation is absorbed at the surface, while the remaining fraction attenuates exponentially using constant attenuation factors for water, ice, and snow.

Turbulent vertical diffusion in deeper layers below the mixed surface layer is parameterized as a function of stratification and mixing wind (Stigebrandt, 1987; Axell, 1998), representing the energy inputs from inertial currents and breaking internal waves. The model further includes dense gravity currents (i.e., deep-water inflows along the seafloor), where entrainment of surrounding deep water into the gravity currents depends on the bottom slope and friction as well as on the density difference between the gravity current and the surrounding water (Stigebrandt, 1987). Entrainment of surrounding water into gravity currents has the effect that the volume flow increases while at the same time density decreases, influencing at what depth the gravity current will be interleaved, i.e., the depth of neutral buoyancy. Deep-water inflows cause an uplift of the entire water column above the intrusion depth.

Biogeochemical processes are calculated using a nutrient–phytoplankton–zooplankton–detritus model set-up that closely follows Savchuk (2002) but that has been expanded with state variables representing, e.g., dissolved organic compounds and the inorganic carbon system (Gustafsson et al., 2014).

The biogeochemical module includes pelagic state variables for oxygen (O2); hydrogen sulfide (H2S); total alkalinity; dissolved inorganic carbon; nitrate + nitrite; ammonium; phosphate; dissolved silica; labile and refractory fractions of dissolved organic carbon (C), nitrogen (N), and phosphorus (P); particulate organic C, N, P, and silicon (Si); three functional groups of phytoplankton (representing diatoms, “summer species”, and diazotrophic cyanobacteria); and one bulk state variable for heterotrophs that represents zooplankton and other organisms that consume and mineralize phytoplankton and detrital matter. All pelagic state variables are subject to transport processes (vertical mixing and horizontal advection) as well as various biological and chemical transformation processes; source and sink terms for each state variable are computed in all water layers in each sub-basin. BALTSEM further includes sediment pools of C, N, P, and Si that are subject to mineralization and burial. The pelagic and benthic realms are coupled by sedimentation of organic matter and sediment–water exchange of dissolved inorganic compounds. Oxygen, CO2, and CH4 are exchanged at the air–sea boundary depending on solubilities, wind speed, and gradients between the sea surface and air of the respective gases.

Phytoplankton growth depends on water temperature and is further limited by light and nutrient availability (Savchuk, 2002). Light penetration in water in the biogeochemical module is calculated as a function of the biogeochemical state. The phytoplankton groups assimilate dissolved inorganic C, N, and P according to fixed Redfield ratios while at the same time producing oxygen, but they also take up an excess of dissolved inorganic carbon, which is transformed into dissolved organic carbon, representing extracellular production (Gustafsson et al., 2014). The cyanobacteria group is able to fix atmospheric N when ammonium and nitrate become limiting. The diatom group is the only phytoplankton group that requires dissolved silica. Loss terms for phytoplankton include natural mortality, grazing by zooplankton, and sinking. Dead phytoplankton are converted into detrital C, N, P, and Si according to their elemental stoichiometry.

Heterotroph/zooplankton growth depends on the grazing rate, which is regulated by water temperature and food concentration (phytoplankton and detritus), as well as the respective availability of different food sources (Savchuk, 2002). Grazing is in addition strongly inhibited at low oxygen concentrations. Fractions of each food source that are not digested are instead assigned to detritus pools in accordance with the stoichiometry of the food sources. Zooplankton have elemental stoichiometry that differs from their food sources; growth thus becomes limited by the element in relative shortage, while carbon and nutrients in excess of zooplankton stoichiometry are excreted. Zooplankton biomass decreases by natural mortality and excretion; dead zooplankton are converted into detrital C, N, and P according to their elemental stoichiometry.

Phytoplankton and detritus sink through the water column; phytoplankton that are not lost by grazing or natural mortality in the water column settle on the seafloor where their constituents are assigned to sediment pools of C, N, P, and Si according to their elemental composition. Temperature-dependent leaching converts a fraction of the detritus into dissolved organic C, N, and P as well as dissolved silica in the water column, while the remainder is either consumed by zooplankton in the water column or it settles on the seafloor where it is assigned to the respective sediment pools. Organic carbon and nutrients in the water column are mineralized either by means of zooplankton respiration (dissolved inorganic carbon) and excretion (ammonium and phosphate) or by temperature-dependent oxidation of dissolved organic compounds; these processes also consume oxygen. Nitrification converts ammonium into nitrate while consuming oxygen. Heterotrophic and chemolithoautotrophic denitrification processes represent loss terms for nitrate. In the absence of both oxygen and nitrate, organic matter is instead oxidized by sulfate, which also leads to hydrogen sulfide production. Sulfide can be oxidized by either oxygen or nitrate (i.e., chemolithoautotrophic denitrification); sulfide oxidation thus represents loss terms for either oxygen or nitrate.

The sediment compartment in each sub-basin can be described as a series of horizontal terraces with a resolution of one terrace per 1 m water depth; the area of each terrace is a function of the hypsographic curve for the respective sub-basins. Sediment state variables are not vertically resolved on the individual terraces but instead formulated as pools of bioavailable C, N, P, and Si that have been deposited on the different terraces – representing the “active” (i.e., not permanently sequestered) top layer of sediments (Savchuk et al., 2012). The carbon and nutrients in phytoplankton and detritus that settle on the terraces are added to the respective sediment pools. A fraction of the sediment pools is permanently sequestered and thus removed from the biogeochemical cycling, while the remaining fraction undergoes temperature-dependent mineralization into inorganic carbon and nutrients that can again be released to the water column.

Nutrient cycling and release from the sediments is strongly coupled with oxygen concentration in the overlying water. During oxic conditions, mineralized N is released in the form of nitrate, but an oxygen-dependent fraction of the nitrate is lost by denitrification. A fraction of the mineralized P is retained in the sediments during oxic conditions, representing phosphate bound to, e.g., iron oxides. The retention capacity of P is further regulated by salinity, representing a proxy for both sulfate concentration and iron availability (Savchuk et al., 2012). During anoxic conditions in the overlying water, mineralized N is released in the form of ammonium. At the same time, mineralized P cannot be retained in the sediments during anoxic conditions; instead, previously sequestered phosphate is released to the water column, representing reduction of metal oxides that are thus unable to bind phosphate. During oxic conditions, sediment mineralization consumes oxygen in the overlying water; during anoxic conditions, the sediments release hydrogen sulfide to the overlying water, representing sulfate reduction.

The meteorological forcing includes 3-hourly wind data, air temperature, cloudiness, air pressure, and precipitation. Model forcing for the hydrodynamic module also includes observed daily mean sea level in the Kattegat as well as monthly mean river runoff to each sub-basin. Further, the model forcing includes monthly mean loads of inorganic and organic carbon and nutrients and alkalinity from land (point sources and river loads) and the atmosphere. Daily profiles of salinity and temperature (i.e., stratification), as well as concentrations of all biogeochemical state variables (Table A1), define the conditions at the open boundary between the northern Kattegat (sub-basin 1; Fig. S1) and the Skagerrak (open ocean). Monthly mean atmospheric partial pressures of CO2 and CH4 comprise the atmospheric boundary conditions for the respective gases. The model forcing is further detailed in Appendix B.

An initial model run over the period 1970–2000 started with initial profiles for the different state variables based on observations when possible or on fitted values. The initial model run was then used as a spin-up for a series of model runs covering the period 2001–2020 that are performed to examine the sensitivity of, e.g., CH4 concentration and isotopic composition depending on process parameterizations (Sect. 4.1).

Isotope values of CH4 are expressed in δ13C units (‰) relative to the Vienna Peedee Belemnite (VPDB) standard (Hoffman and Rasmussen, 2022): 1δ13C=RsampleRstd-1⋅1000, where Rsample and Rstd represent the 13C/12C ratios of a sample and the VPDB standard, respectively.

Isotopic fractionation α during different processes (e.g., oxidation, air–sea exchange) in the CH4 cycling can be expressed as 2α=RARB, where RA and RB represent 13C/12C ratios of compounds A and B.

Fractionation can also be expressed in δ13C units using Eqs. (1) and (2): 3α=δA1000+1/δB1000+1. Alternatively, fractionation is often expressed as ε values (Zeebe and Wolf-Gladrow, 2001): 4ε=δA-δB≈α-1⋅1000. In the model description below, both α and ε values are used to describe fractionation during different processes.

The CH4 flux (FCH4) between water and air is calculated according to 5aFCH4=kCH4eq-CH4w,5bCH4eq=K0pCH4a, where k (m s-1) is the transfer velocity, CH4eq is the equilibrium concentration with the atmosphere, K0 (nM atm-1) is the CH4 solubility, pCH4a (atm) is the partial pressure of CH4 in air, and CH4w (nM) is the CH4 concentration in surface water.

The solubility is calculated as a dimensionless Bunsen coefficient (β) according to Wiesenburg and Guinasso (1979): 6lnβ=A1+A2100/TK+A3lnTK/100+SB1+B2TK/100+B3TK/1002, where A1, A2, A3, B1, B2, and B3 are constants and TK is temperature (K).

Then, β is converted to K0 (nM atm-1) according to 7K0=PSβRTS×106, where PS=101325 Pa atm-1 represents a unit conversion from Pa to atm, R=8.314 m3 Pa K-1 mol-1 is the molar gas constant, and TS=273.15 K is the standard temperature.

The transfer velocity k is calculated according to Wanninkhof (2014) and converted from cm h-1 to m s-1: 8k=0.251U102660Sc⋅0.013600, where U10 (m s-1) is the wind speed at 10 m height and Sc is the Schmidt number for CH4 (Wanninkhof, 2014): 9Sc=A+BT+CT2+DT3+ET4, where A, B, C, D, and E are constants and T is temperature (°C).

The atmospheric CH4 level has increased from around 800 ppb to almost 1900 ppb over the last 2 centuries (see Fig. S2). In the different model runs, the atmospheric CH4 levels according to the RCP4.5 scenario were used (Fig. S2). The mixing ratio is expressed as mole fraction of dry air (ppb) and is thus identical to the CH4 partial pressure, pCH4a (natm).

The fractionation of a gas during transfer between air and water depends on two fractionation processes – gas dissolution and molecular gas transfer. The fractionation αeq during dissolution of CH4 in water is defined as (Knox et al., 1992) 10αeq=RCH4eq(d)RCH4eq(g), where RCH4eq(d) and RCH4eq(g) represent the ratios of the heavy and light CH4 isotopes between the equilibrium concentrations of CH4 in dissolved (d) and gas phase (g), respectively. Experiments by Fuex (1980) indicate that the heavy CH4 isotope is more soluble than the lighter isotope (although the lighter isotope initially dissolves faster), with a fractionation during dissolution amounting to approximately αeq=1.00033.

A difference in the molecular transfer rates of heavy and light CH4 isotopes results in further fractionation defined as (Knox et al., 1992) 11αk=k13CH4k12CH4, where k13CH4 and k12CH4 represent the transfer rates of the heavy and light isotope, respectively. Experiments by Knox et al. (1992) indicate a preferential exchange of the light isotope, with a fractionation during gas transfer of approximately αk=0.9992. Measurements from stagnant wooded swamps point to a reduced gas exchange but also a considerably more pronounced kinetic fractionation in waters with insoluble organic surface films (Happell et al., 1995). Surface films are, however, not taken into account in BALTSEM-CH4 v1.0.

The 13C–CH4 flux between water and air, F13CH4, is calculated based on Holmes et al. (2000): 12F13CH4=kαkK0pCH4aRatmαeq-13CH4w, where Ratm is the 13C/12C ratio of atmospheric CH4, and [13CH4w] is the surface water concentration of 13C–CH4.

In the model runs, the atmospheric δ13CCH4 is set to a constant -47 ‰.

Measurements in Swedish low-order streams (Strahler stream order 1–4) indicate a median CH4 concentration of approximately 6.7 µgCL-1 – corresponding to 560 nM – but with substantial variations between individual streams (Wallin et al., 2018). As opposed to CO2 concentrations that generally declined with increasing stream order, there was no such clear relation between stream order and median CH4 concentration, although the lowest median concentration (3.6 µgCL-1, corresponding to 300 nM) was reported for the largest streams (Wallin et al., 2018).

CH4 produced in freshwater sediments and wetlands is presumed to mainly result from acetate fermentation (see Sect. 2.3.5), with isotope values typically ranging from -65 ‰ to -50 ‰ (Whiticar et al., 1986; Quay et al., 1988). However, both CH4 oxidation and outgassing cause 13C enrichment in the residual CH4 pool. This means that an increasing isotope value is expected, as outgassing and oxidation processes gradually modulate both CH4 concentrations and isotopic composition in streams and rivers along their routes toward the sea. Measurements in a subtropical river network in Australia indicate surface water δ13CCH4 values ranging from -57 ‰ to -47 ‰ (Atkins et al., 2017), i.e., values close to or lower than the atmospheric δ13CCH4 (see Sect. 2.3.2). Similarly, measurements in an urbanized river system in Scotland indicate δ13CCH4 values ranging from -60 ‰ to -47 ‰ (Gu et al., 2021).

As a first approximation, it will be assumed that the riverine CH4 concentration (CH4riv) is 100 nM and that δ13CCH4=-50 ‰ in rivers entering the Baltic Sea.

Methane concentrations in open North Sea surface waters are highly heterogeneous, but generally above the solubility equilibrium with the atmosphere. Observations indicate a range from 3 to 30 nM (Bange et al., 1994; Rehder et al., 1998; Osudar et al., 2015). This heterogeneity has been suggested to partly be a result of the westward transport of surface waters originating from the Kattegat and Skagerrak (Rehder et al., 1998). Closer to the coasts where both rivers and coastal sediments can be significant regional sources of CH4, concentrations are usually considerably higher (Scranton and McShane, 1991; Rehder et al., 1998; Upstill-Goddard et al., 2000; Grunwald et al., 2009; Osudar et al., 2015), but large fractions appear to be removed within estuaries before reaching the open sea (Upstill-Goddard et al., 2000; Grunwald et al., 2009). Measurements from the southern central North Sea indicate concentrations close to (but higher than) the equilibrium (Scranton and McShane, 1991; Bange et al., 1994; Rehder et al., 1998).

As a first approximation, it will be assumed that the CH4 concentration is 5 nM and that δ13CCH4=-47 ‰ in North Sea water entering the Baltic Sea.

There are two primary methanogenic pathways for biologically mediated CH4 production – CO2 reduction and acetate fermentation (Reeburgh, 2007): 13CO2+4H2→CH4+2H2O,14CH3COOH→CH4+CO2. CO2 reduction is dominant in the sulfate-depleted zone of marine sediments, whereas acetate fermentation is dominant in freshwater sediments. Both pathways may, nevertheless, occur in both marine and limnic environments (Whiticar et al., 1986). Methanogenesis in marine environments is assumed to predominantly occur in anoxic sediments, whereas the presence of oxygen and/or sulfate generally prevents large-scale methanogenesis in the water column. In anoxic sediments, sulfate can be used as an oxidant during mineralization of organic matter or can be consumed by sulfate-mediated oxidation of CH4. The sediment depth of sulfate depletion and the main zone of methanogenesis depend strongly on location and sedimentation rate. Measurements in the Baltic Sea area indicate sulfate depletion depths in a range of centimeters to meters (Jørgensen et al., 1990; Slomp et al., 2013; Myllykangas et al., 2020).

The default sediment source is set to 50 µmolm-2d-1, which is a fitted value that reproduces deep-water CH4 observations reasonably well. The impact from the sediment source is further explored in different sensitivity experiments (Sect. 4.1).

Isotope values of CH4 from biogenic sources are typically in a range from -110 ‰ to -60 ‰ (Whiticar et al., 1986), depending on the methanogenic substrate and mechanisms (i.e., CO2 reduction vs. acetate fermentation). The fractionation during CO2 reduction is typically ε>95 ‰, while the range in fractionation during acetate fermentation is ε∼40 ‰–60 ‰ (Whiticar, 1999).

Measurements from anoxic deep water in the central Baltic Sea show isotope values of -84 ‰ and -71 ‰ in the Gotland and Landsort deeps, respectively (Jakobs et al., 2013). Deep water in the Bornholm Basin shows isotope values of approximately -70 ‰, and deep water in the Arkona Basin shows isotope values ranging from -69 ‰ to -63 ‰ (Gülzow et al., 2014). Measurements by Roth et al. (2022) indicate a value of approximately -67 ‰ for the sediment source in shallow areas with oxic conditions in the water column. Furthermore, measurements by Egger et al. (2017) indicate surface sediment pore water δ13C–CH4 values of approximately -80 ‰ in the Landsort Deep (451 m b.s.s.), -70 ‰ in the Bornholm Deep (87 m b.s.s.), and -60 ‰ in the Little Belt (37 m b.s.s.).

As a first approximation, the sediment CH4 source in the model is assumed to have a δ13C–CH4 value of -80 ‰ or -60 ‰ in sediments underlying anoxic or oxic water, respectively. This value will then be adjusted in different sensitivity experiments (Sect. 4.1).

In aerobic CH4 consumption by methanotrophic processes, CH4 and oxygen are consumed while CO2 and water are produced: 15CH4+2O2→CO2+2H2O. The oxidation rate, WCH4_O2 (nM d-1), is parameterized as Monod functions of both CH4 (nM) and O2 (µM) concentrations (Van Bodegom et al., 2001; Greene et al., 2014): 16WCH4_O2=vWCH4_O2CH4hCH4+CH4O2hO2+O2, where vWCH4_O2 (nM d-1) is the potential maximum aerobic oxidation rate; [CH4] (nM) and [O2] (µM) are CH4 and O2 concentrations; and hCH4 (nM) and hO2 (µM) are “half-saturation” concentrations for CH4 and O2, respectively.

Aerobic oxidation of CH4 is also included as an O2 sink term in the model, consuming 2 mol O2 for each mol of consumed CH4 (Eq. 15). Furthermore, both aerobic and anaerobic CH4 oxidation are included as sources of dissolved inorganic carbon in the model, producing 1 mol of dissolved inorganic carbon for each mol of consumed CH4 (Eqs. 15 and 17, respectively).

Observations from the Gotland and Landsort deeps in the Baltic Proper indicate oxidation rates in the range 0.1–4 nM d-1 depending on location and season (Schmale et al., 2012, 2016; Jakobs et al., 2014). The parameters in Eq. (16) are set to default values of vWCH4_O2=8 nM d-1, hCH4=60 nM, and hO2=100 µM. These are fitted values that produce CH4 concentrations and oxidation rates that reproduce observations fairly well (see Sect. 3.1). In Sect. 4.1, the influence of modified values of vWCH4_O2, hCH4, and hO2 will be addressed in different sensitivity experiments.

AOM is typically assumed to be mediated by sulfate, although other oxidants such as nitrate, nitrite, and also iron and manganese oxides could be used as well (Myllykangas et al., 2020). The stoichiometry for sulfate mediated AOM can be written (Hoehler et al., 1994) as 17CH4+SO42-→HS-+HCO3-+H2O. The ratios of sulfate and chlorine concentrations in the Baltic Sea are close to the oceanic ratio (Kremling, 1972), which means that the sulfate concentration [SO42-] in the Baltic Sea can be approximated as 18SO42-≈SO42-ocS35, where S is the salinity and [SO42-]oc=0.0282 mol kg-1 is the sulfate concentration in sea water (S=35) (Dickson et al., 2007). Thus, sulfate concentrations in the Baltic Sea are orders of magnitude higher than CH4 concentrations. For that reason, CH4 oxidation by sulfate, WCH4_SO4 (nM d-1), is parameterized as a function of CH4, whereas the sulfate concentration is assumed not to be limiting in the water column: 19WCH4_SO4=vWCH4_SO4CH4hCH4+CH4. Since sulfate is assumed not to be limiting, other potential oxidants during AOM are not accounted for in the model.

Observations from the anoxic deep waters of the Gotland and Landsort deeps in the Baltic Proper indicate oxidation rates of <0.1 nM d-1 (Jakobs et al., 2014). The maximum anaerobic oxidation rate is set to a default value of vWCH4_SO4=0.1 (nM d-1).

There is preferential oxidation of 12C–CH4 compared with the heavier 13C–CH4, causing fractionation during the process. The oxidation of 13C–CH4 is thus computed according to 20W13CH4_O2=αoxiRCH4WCH4_O2, where αoxi is the fractionation during CH4 oxidation, RCH4 is the 13C/12C ratio of CH4, and WCH4_O2 is the CH4 oxidation rate (Eq. 16). Using Eq. (16), Eq. (20) can be rewritten as 21WCH4_O2≈αoxivWCH4_O213CH4hCH4+CH4O2hO2+O2. Observations indicate a wide range of fractionation during CH4 oxidation (e.g., ε∼4 ‰–30 ‰, Whiticar (1999); ε∼16 ‰–54 ‰, Chan et al., 2019b). Based on observations from the central Baltic Sea by Jakobs et al. (2013), the default fractionation is set to 12 ‰, which corresponds to αoxi=0.988 in Eq. (20). The influence of fractionation during CH4 oxidation is addressed by sensitivity experiments in Sect. 4.1.

Adjusting the potential maximum rate of MOX (vWCH4_O2) by ±50 % (tests 1 and 2) has a large influence on CH4 concentrations (Fig. S6), where decreased vWCH4_O2 (test 1) leads to substantially higher CH4 concentrations, and increased vWCH4_O2 (test 2) leads to lower CH4 compared with the standard model run. Since the MOX rate in addition to vWCH4_O2 depends on CH4 concentration, the changed CH4 concentration in itself will further modify the shape of the MOX profile (CH4 oxidation also consumes O2, but the influence on O2 concentration is small compared with the influence on CH4 concentration, since O2 and CH4 typically differ by orders of magnitude). The modified shapes of the MOX profiles also influence the δ13C–CH4 profiles, with changed depths of the intermediate deep-water peak as well as changed peak values. Adjusting the potential maximum rate of AOM (vWCH4_SO4) has a comparatively minor influence on both the CH4 concentration and the isotopic composition because of the low anaerobic oxidation rates (not shown).

Adjusting the half-saturation values for CH4 oxidation (hCH4 and hO2) by ±50 % (tests 3–6) influences the MOX rates and thus both the CH4 concentration and the isotopic composition (Figs. S7 and S8). These parameters alter the dynamics within a relatively small range close to their respective values. Thus, the MOX rate is most sensitive to changes of hCH4 where the CH4 concentration is close to 60 nM and, similarly, most sensitive to changes of hO2 where the O2 concentration is close to 100 µM (Table 1). At high concentrations compared with the values of hCH4 and hO2, we do not expect a large impact by adjusting these constants. On the other hand, at low concentrations compared with the constants, the sensitivity to changed values of hCH4 and hO2 is expected to be similar to changing the potential maximum rate constant (vWCH4_O2).

In these particular experiments, CH4 dynamics is more sensitive to changes in hO2 than hCH4, and the reason for this is the relatively large water volume where the O2 concentration is close to hO2, while the CH4 concentration, on the other hand, is only close to hCH4 in a comparatively narrow band at intermediate depths. The modified CH4 dynamics is, however, transferred to other depths by turbulent diffusion and vertical internal circulation (“old” water mixing into the intruding new deep water), which means that altered CH4 concentrations, δ values, and MOX rates are (more or less) apparent throughout the entire water column.

Adjusting the fractionation during CH4 oxidation by ±4 ‰ (tests 7 and 8) has no influence on CH4 oxidation rates and concentrations but a relatively strong (and predictable) impact on δ13C–CH4 values throughout the entire water column (Fig. S9).

As indicated in Sect. 4, it is expected that the isotopic composition of the sediment source differs between different locations depending on the degree of oxidation in the pore water. The rate of CH4 release is also expected to depend on the balance between benthic CH4 production and oxidation. Adjusting the δ13C–CH4 value of the sediment source by ±10 ‰ during oxic conditions (tests 9 and 10) has no influence on CH4 oxidation rates and concentrations but a strong (and predictable) impact on δ13C–CH4 profiles (Fig. S10).

In experiments where the rate of CH4 release from the sediments source was adjusted by ±50 ‰ during oxic conditions (tests 11 and 12), strong impacts are apparent for both the CH4 concentration and isotopic composition throughout the water column. Deep-water MOX rates are, however, less sensitive, since the rates in these cases depend more on O2 concentration – which is very similar between the two experiments (not shown) – than on CH4 concentrations (Fig. S11).