Methane dynamics in the Baltic Sea: investigating concentration, flux and isotopic composition patterns using the coupled physical-biogeochemical model BALTSEM-CH 4 v1.0

. Methane (CH 4 ) cycling in the Baltic Sea is studied through model simulations that incorporate the stable isotopes of CH 4 ( 12 C-CH 4 and 13 C-CH 4 ) in a physical-biogeochemical model. A preliminary CH 4 budget identifies benthic release as the dominant CH 4 source, which is largely balanced by oxidation in the water column and to a smaller degree by outgassing. The contributions from land loads and net export to the North Sea are of marginal importance. Simulated total CH 4 emissions 15 from the Baltic Sea correspond to an average 0.04 g CH 4 m -2 y -1 , which can be compared to the calibrated sediment source of 0.3 g CH 4 m -2 y -1 . A major uncertainty is that spatial and temporal variations of the sediment source are not well known. Further, the coarse spatial resolution prevents the model to resolve shallow-water near-shore areas for which measurements indicate occurrences of considerably higher CH 4 concentrations and emissions compared to the open Baltic Sea. Modeling of stable CH 4 isotopes can help to constrain process rates; to our knowledge this is the first time that CH 4 isotopes have been 20 included in a physical-biogeochemical model. A large-scale approach is used in this study, but the parametrizations and parameters presented here could also be implemented in models of near-shore areas where CH 4 concentrations and fluxes are typically substantially larger and more variable. Currently, it is not known how important local shallow-water CH 4 hotspots are compared to the open water outgassing in the Baltic Sea.


Introduction
Methane is the second-most important greenhouse gas after carbon dioxide (CO2), contributing up to 20% of the total radiative forcing (Etminan et al., 2016).Using top-down approaches (atmospheric observations and inverse modeling), the present-day global CH4 emissions have been estimated to be 576 Tg CH4 y -1 , whereas bottom-up approaches (process-based modeling of land surface emissions and data on anthropogenic emissions) yield a total of 737 Tg CH4 y -1 (Saunois et al., 2020).The causes of the discrepancy between the two methods are not well known, but is believed to mainly reflect uncertainties in estimates of natural emissionsin particular from wetlands, lakes, and running waters (Saunois et al., 2020).The global mean atmospheric CH4 level has increased by about 1000 ppb over the last two centuries (Ferretti et al., 2005).Projections of future development ranges from a gradual decrease to a massive increase depending on the development of anthropogenic emissions (Saunois et al., 2020).
It has been estimated that approximately half of the total CH4 emissions come from aquatic ecosystem sources, dominated by inland water ecosystems (Rosentreter et al., 2021).The total oceanic CH4 emissions, including diffusive and bubble-driven ebullitive fluxes, constitute a relatively small fraction amounting to ~6-12 Tg CH4 y -1 (Weber et al., 2019).Methane formation in sediments can be substantial, but aerobic and anaerobic oxidation processes efficiently remove CH4 both in the pore water and water column when oxidants (e.g., oxygen and sulfate), as well as, methanotrophic bacteria (Broman et al., 2020) are present.For that reason, near-shore areas (0-50 m water depth), shallow enough to allow CH4 to escape to the atmosphere before being oxidized, dominate the oceanic emissions despite representing a comparatively minor area (Weber et al., 2019).
In shallow, organic-rich sediments, CH4 emissions will increase in response to ocean warming due to increased biogenic CH4 production and decreased CH4 solubility, both of which promote seafloor ebullition (Borges et al., 2016).This notion was confirmed in a recent field study where exceptionally high CH4 emissions were reported from the coastal Baltic Sea at the end of a summer heat wave (~250 μmol m -2 day -1 , Humborg et al., 2019).
In the Baltic Sea, there are strong gradients in CH4 concentrations both from near-shore areas to open Baltic Sea surface waters (e.g., Humborg et al., 2019) and from surface to deep water (e.g., Schmale et al., 2010;Jakobs et al., 2013).Substantial parts of Baltic Sea deep waters are stagnant over extended periods in time, which in combination with high loads of organic material cause episodic anoxia (e.g., Carstensen et al., 2014).During stagnant anoxic periods, CH4 accumulates and reaches concentrations ranging from 1000 to 3000 nM (Jakobs et al., 2013;2014).This CH4 is, however, largely consumed by aerobic oxidation processes (MOX) when mixed into the redox zone at intermediate depths (Jakobs et al., 2013).Peak oxidation rates have consequently been observed in the redox zone where deep water enriched in CH4 is mixed with oxic water (Jakobs et al., 2013).Due to the special characteristics of deep water areas isolated from the atmosphere, and with transitions between oxic and anoxic conditions, the Baltic Sea is a unique and suitable system for studying key processes in CH4 cycling, in particular for investigating different oxidation pathways.
Surface water CH4 concentrations in the open Baltic Sea are typically about 3.5-5 nMonly slightly oversaturated compared to the atmosphere (Gülzow et al., 2013).In contrast, in shallow near-shore areas, observations indicate a very different situation, with CH4 concentrations ranging from 10 to 500 nM (Humborg et al., 2019;Myllykangas et al., 2020;Lundevall-Zara et al., 2021;Roth et al., 2022) with large temporal and spatial variations on small scales (e.g., Roth et al., 2022).Methane emissions to the atmosphere depend on the degree of oversaturation in the surface water, but also on wind speed and temperature (e.g., Wanninkhof, 2014).Estimated CH4 emissions from different near-shore sites in the Baltic Sea display a large range due to substantial variations in the parameters that control gas transfer across the air-sea interface (Humborg et al., 2019;Lundevall-Zara et al., 2021;Asplund et al., 2022;Roth et al., 2022;2023).Short-term and small-scale variations cause considerable challenges for empirical estimates of fluxes over larger scales and longer periods in time.
Different processes in the CH4 cycling do, however, produce certain "fingerprints" on the isotopic composition, similar to how the relative contributions of different atmospheric CH4 sources determine long-term trends of δ 13 CCH4a (Lan et al., 2021).This can be helpful when assessing process rates.Observations in the Baltic Sea show a pronounced 13 C-CH4 enrichment in the redox zone (Schmale et al., 2012;2016;Jakobs et al., 2013;2014;Gülzow et al., 2014), which is the result of a preferential oxidation of the lighter isotope.Similarly, CH4 emissions to the atmosphere can produce a 13 C-CH4 enrichment in the surface water because of a preferential outgassing of the lighter isotope (Knox et al., 1992).The isotopic composition of CH4 produced in sediments depends on the processes involved, i.e., CO2 reduction or acetate fermentation (Reeburgh, 2007; see also Sect. 2.3.5),but can then be modified by oxidation processes in the pore water (Chuang et al., 2019).
Models can be useful for identifying limiting processes and constraining budgets even though not all rates are well known, through sensitivity experiments on process rates and parameterizations, as well as on the influence of changes in forcing of the system.Methane cycling has previously been investigated in lake modeling studies (e.g., Lopes et al., 2011;Greene et al., 2014;Bayer et al., 2019).Furthermore, CH4 emissions from the Arctic shelf have been addressed by means of model simulations (Wåhlström and Meier, 2014;Malakhova and Golubeva, 2022).Wåhlström and Meier (2014) examined the sensitivity of CH4 emissions depending on riverine CH4 concentration, release rate from the sediments, and oxidation rate in the water column.None of the abovementioned models, however, included stable CH4 isotopes.In the present study, CH4 cycling and dynamics in the Baltic Sea are introduced into the coupled physical-biogeochemical Baltic Sea long-term and large-scale eutrophication model (BALTSEM), by expanding with state variables for both 12 C-CH4 and 13 C-CH4 concentrations (see Sect. 2.2).BALTSEM has previously been used in a similar approach where stable isotopes of dissolved inorganic carbon as well as dissolved and particulate organic carbon were included in the model in order to investigate constraints on process rates (Gustafsson et al., 2015).The motivation for implementing the CH4 modeling on a Baltic Sea scalewith considerable spatial differences in terms of e.g., water and sediment properties as well as production, respiration, and sedimentation patternswas utilizing the application of an already well-established model.BALTSEM has been described and validated in many publications, and it has been demonstrated that both physical (e.g., salinity, temperature, vertical mixing, lateral exchange, air-sea exchange) and biogeochemical (e.g., carbon and nutrient cycling and oxygen production/consumption) processes are largely described satisfactory (Gustafsson et al., 2012;2017;Savchuk et al., 2012).

Area description
The Baltic Sea is a semi-enclosed brackish sea, connected to the North Sea via the shallow and narrow Danish straits.The system is characterized by a pronounced horizontal salinity gradientgoing from the almost oceanic entrance area to the lowsaline northernmost sub-basinas well as a permanent salt dominated stratification, restricted water exchange with the North Sea, and long residence times (e.g., Stigebrandt and Gustafsson, 2003).As a result of strong stratification and long residence times, the central Baltic Sea is naturally susceptible to deep water de-oxygenation.Massively increased nitrogen (N) and phosphorus (P) loads from the early 1950s to the mid-1980s has caused a large expansion of de-oxygenated deep water areas (e.g., Gustafsson et al., 2012).The loads have declined substantially from the peak values in the 1980's (e.g., Kuliński et al., 2022), although oxygen conditions have not yet improved in the central Baltic Sea (Hansson and Viktorsson, 2021).

The model
BALTSEM is a process-based coupled physical-biogeochemical 1D-model that divides the Baltic Sea into thirteen sub-basins that are horizontally homogenous, but with a high (~1 m) vertical resolution (Fig. S1).The standard model includes pelagic state variables for salinity, temperature, oxygen (O2), hydrogen sulfide, total alkalinity, dissolved inorganic carbon, nitrate, ammonium, phosphate, dissolved silica, labile and refractory fractions of dissolved organic carbon (C), nitrogen (N), and phosphorus (P), particulate organic C, N, P, and Si (biogenic Si), three functional groups of phytoplankton (representing diatoms, 'summer species', and diazotrophic cyanobacteria), and one bulk state variable for heterotrophs (representing all processes that mineralize organic matter).All pelagic state variables are subject to transport processes (vertical mixing and horizontal advection between sub-basins) as well as various biological and chemical transformation processes.BALTSEM In this study, a new expanded version of the model, BALTSEM-CH4 v1.0, with state variables for both 12 C-CH4 and 13 C-CH4 is presented for the first time.BALTSEM-CH4 v1.0 is an expansion of BALTSEM v9.5 (Gustafsson et al., 2023).Source code, model forcing, boundary conditions, and initial profiles are archived on Zenodo at https://doi.org/10.5281/zenodo.10037197.
Figure 1 illustrates processes involved in CH4 cycling that are included in the model.The model (prior to the inclusion of CH4) has been described and validated in detail in earlier publications (see Gustafsson et al. (2017) and references therein); this will not be repeated here.A list of all state variables (Table A1) is included in Appendix A. Further, the model forcing is briefly described in Appendix B.
This study focuses on the modeling of stable CH4 isotopes: The CH4 sources (i.e., land load and sediment release), boundary conditions (i.e., atmospheric CH4 and CH4 at the model boundary), transport and transformation processes (i.e., CH4 oxidation and air-sea exchange), as well as the isotopic fingerprints associated with these processes are described in Sect.

Isotopic fractionation
Isotope values of CH4 are expressed in δ 13 C units (‰) relative to the Vienna Peedee Belemnite (VPDB) standard (Hoffmann and Rasmussen, 2022): Here, Rsample and Rstd represent the 13 C/ 12 C ratios of a sample and the PDB standard, respectively.
Isotopic fractionation α during different processes (e.g., oxidation, air-sea exchange) in the CH4 cycling can be expressed as: Here, RA and RB represent 13 C/ 12 C ratios of compounds A and B.
Fractionation can also be expressed in δ 13 C units using Eq. 1 and 2: Alternatively, fractionation is often expressed as ɛ values (Zeebe and Wolf-Gladrow, 2001): In the model description below, both α and ɛ values are used to describe fractionation during different processes.

Air-sea exchange
The CH4 flux (FCH4) between water and air is calculated according to: where k (m s -1 ) is the transfer velocity, CH4eq the equilibrium concentration with the atmosphere, K0 (nM atm -1 ) the CH4 solubility, pCH4a (atm) the partial pressure of CH4 in air, and CH4w (nM) the CH4 concentration in surface water.
β is then converted to K0 (nM atm -1 ) according to: where PS = 101325 Pa atm -1 represents a unit conversion from Pa to atm, R = 8.314 m 3 Pa K -1 mol -1 is the molar gas constant, and TS = 273.15K is the standard temperature.
The transfer velocity k is calculated according to Wanninkhof (2014) and converted from cm hour -1 to m s -1 : Here, U10 (m s -1 ) is the wind speed at 10 m height and Sc is the Schmidt number for CH4 (Wanninkhof, 2014): Here, 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 two centuries (see Fig. S2).In the different model runs, the atmospheric CH4 levels according to the RCP 4.5 scenario were used (Fig. S2).The mixing ratio is expressed as mole fraction of dry air (ppb) and thus identical to the CH4 partial pressure, pCH4a (natm).

Fractionation during gas transfer and dissolution
The fractionation of a gas during transfer between air and water depends on two fractionation processesgas dissolution and molecular gas transfer.The fractionation αeq during dissolution of CH4 in water is defined as (Knox et al., 1992): Here, 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, result in further fractionation defined as (Knox et al., 1992): Here, 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 13 C-CH4 flux between water and air, F13CH4, is calculated based on Holmes et al. (2000): Here, Ratm is the 13 C/ 12 C ratio of atmospheric CH4, and [ 13 CH4w] is the surface water concentration of 13 C-CH4.
In the model runs, the atmospheric δ 13 CCH4 is set to a constant -47‰.

River loads
Measurements in Swedish low-order streams (Strahler stream order 1-4) indicate a median CH4 concentration of approximately 6.7 µg C L -1corresponding to 560 nMbut 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 µg C L -1 , corresponding to 300 nM) was reported for the largest streams (Wallin et al., 2018).
CH4 produced in freshwater sediments and wetlands is presumably mainly resulting from acetate fermentation (see Sect. 2.3.5), with isotope values in a typical range -65‰ to -50‰ (Whiticar et al., 1986;Quay et al., 1988).However, both CH4 oxidation and outgassing cause a 13 C 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 values in a range -57‰ to -47‰ (Atkins et al., 2017), i.e., values close to, or lower than the atmospheric δ 13 CCH4 (see Sect. 2.3.2).Similarly, measurements in an urbanized river system in Scotland indicate δ 13 CCH4 values in a range -60‰ to -47‰ (Gu et al., 2021).
As a fist approximation, it will be assumed that the riverine CH4 concentration (CH4riv) is 100 nM and that δ 13 CCH4 = -50‰ in rivers entering the Baltic Sea.

Inflows from the North 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 3 -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 fist approximation, it will be assumed that the CH4 concentration is 5 nM and that δ 13 CCH4 = -47‰ in North Sea water entering the Baltic Sea.

Methanogenesis
There are two primary methanogenic pathways for biologically mediated CH4 production -CO2 reduction and acetate fermentation (Reeburgh, 2007): 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 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 µmol m -2 d -1 , which is a calibrated value that produces deep water CH4 observations reasonably well.The impact from the sediment source is further explored in different sensitivity experiments (Sect.4.1).
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) As a first approximation, the sediment CH4 source in the model is assumed to have a δ 13 C-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).

Anaerobic oxidation of CH4 by sulfate (AOM)
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): 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 [SO4 2-] in the Baltic Sea can be approximated as Here, S is the salinity and [SO4 2-]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 day -1 ) is parameterized as a function of CH4, whereas the sulfate concentration is assumed not to be limiting in the water column: ), 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 < 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 a preferential oxidation of 12 C-CH4 compared to the heavier 13 C-CH4, causing a fractionation during the process.The oxidation of 13 C-CH4 is thus computed according to:

Fractionation during CH4 oxidation
Here, αoxi is the fractionation during CH4 oxidation, RCH4 is the 13 C/ 12 C ratio of CH4, and WCH4_O2 is the CH4 oxidation rate (Eq.16).By use of Eq. 16, Eq. 20 can be rewritten as: ) , Observations of fractionation during CH4 oxidation indicate fractionation values in a range ɛ ~ 4-30‰ (Whiticar, 1999).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.

Results
In this section, simulated CH4 concentrations, isotopic compositions, and aerobic and anaerobic oxidation rates are presented for a 'standard' model run (Sect.3.1).Simulated large-scale fluxes and a preliminary CH4 budget are presented in Sect.3.2.

Standard model run
The standard model run was performed over the period 2001-2020 after spin-up (see Sect. 2.2) with parameters as indicated in Table 1.These parameters are mostly calibrated values, where the intension was to reasonably well reproduce existing observations from the Gotland Sea.This simulation will then be used as a basis for the sensitivity experiments presented in Sect.4.1.Simulated contour plots and time series for the period 2001-2020 are presented in Fig. 2-3.Furthermore, monthly mean profiles for years 2014 and 2015 are presented in Fig. 4-5 in order to illustrate seasonal dynamics in surface waters as well as the impact of a major deep water inflow.Figure 2 illustrates the characteristic dynamics of the permanently salinity stratified Gotland Sea.The top of the halocline, which is typically located at around 60 m depth, isolates deeper waters from the atmosphere which means that O2 can only be supplied via deep water inflows of oxic and comparatively high-saline water and through vertical turbulent diffusion.365 Stagnation periods with little or no advective O2 supply to the deep may last for years, and since O2 consumption by degradation processes exceeds the turbulent diffusive flux eventually conditions anoxic prevails.Stagnation periods are also characterized by CH4 accumulation because of a low anaerobic oxidation rate, and the δ 13 C-CH4 in anoxic water is also close to the sediment source because of the marginal influence of anaerobic oxidation processes in the water column.Inflows of new deep water lead to an uplift of the water column above the intrusion depth, which is clearly seen in the simulated O2 and CH4 profiles in 370 February to June of 2015 (Fig. 5, upper panel).Inflows furthermore cause a sharp decline in deep water CH4 concentration (Fig. 2-3), primarily due to water exchange, but additionally because of high aerobic oxidation rates during periods when O2 and CH4 co-occur in the deep water until O2 is again depleted (Fig. 5).In surface waters above the top of the halocline, seasonal changes in temperature and thermal stratification largely influence other parameters (Fig. 4-5; see also Fig. S3-S4, supporting information).The increasing surface water temperature in spring and summer leads to decreasing O2 and CH4 solubility which in addition affects aerobic oxidation rates that depend on O2 and CH4 concentrations (Fig. S3-S4, supporting information; see also Eq. 16).The δ 13 C-CH4 in water above the top of the halocline is thus strongly influenced by the seasonality of temperature stratification, although the amplitude is significantly smaller than the variations at depth where δ 13 C-CH4 mainly depend on transitions between oxic and anoxic conditions.Observations from 2012 indicate CH4 concentrations in a range from ~1000 to 3000 nM in stagnant deep waters of the Baltic Proper (Jakobs et al., 2013), and values below ~150 nM in oxic deep waters in the same area after a major deep-water intrusion 405 in winter 2014-2015 (Schmale et al., 2016;Myllykangas et al., 2017).These values are well reproduced by the model (Fig. 3) using the settings listed in Table 1, which implies that the simulated sediment CH4 source is likely close to the real source, at least in the deep water where AOM rates are apparently very low (<0.1 nM d -1 ; Jakobs et al., 2014).The simulated benthic CH4 release from the seafloor amounts to 50 µmol CH4 m -2 d -1 in the standard model run (Table 1), corresponding to ~0.3 g CH4 m -2 y -1 .This is in the lower range of yearly observations at shallow coastal sites among varying habitats in the Baltic Sea (0.34-0.55 g CH4 m -2 y -1 ; Roth et al., 2023).
Measurements from the central Gotland Sea indicate typical surface water CH4 concentrations in a range 3.5-5 nM, depending on the season (Gülzow et al., 2013), with the highest concentrations observed in winter because of increased gas solubility in cold water.This seasonal cycle is reproduced by the model (Fig. 3).Furthermore, simulated surface water CH4 saturation levels vary between approximately 110% in winter and 150% in summer (Fig. S5), which reproduces observed saturation levels (Gülzow et al., 2013).
Measurements from the central Baltic Sea indicate MOX rates ranging from 0.1 to 4 nM d -1 in the redox zone (Schmale et al., 2012;2016;Jakobs et al., 2014).In the standard model run, the highest oxidation rates (> 3 nM d -1 ; Fig. 5) occur in the deep water after deep water intrusions leading to oxygenation of stagnant water with high CH4 concentrations.In the redox zone, the simulated MOX rates are typically in a range 0.5-3 nM d -1 (Fig. 4-5), which thus matches observed oxidation rates.
Simulated surface water MOX rates are in a range 0.3-0.5 nM d -1 (e.g., Fig. 3), whereas observations, on the other hand, indicate rates close to zero (Jakobs et al., 2014).
Observations indicate a pronounced 13 C-CH4 enrichment in the redox zone.Based on two profiles from 2012, δ 13 C-CH4 increased from values below -70‰ at the bottom of the redox zone (~140 m) to -40‰ at the top of the redox zone (~80 m) in the central Gotland Sea (Jakobs et al., 2014).The δ 13 C-CH4 peak values at intermediate depths coincide with peak oxidation rates (Jakobs et al., 2014) and result from the preferential oxidation of the lighter isotope.In water above the top of the redox zone, observations indicate lower oxidation rates and δ 13 C-CH4 values in a range -60‰ to -40‰ depending on season (Jakobs et al., 2014).In the standard model run, the δ 13 C-CH4 value typically increases from approximately -70‰ at the upper limit for anoxic water (~130 m) to its peak values between -45‰ and -40‰ at approximately 75 m (Fig. 4).The simulated δ 13 C-CH4 in the redox zone thus tends to be less pronounced than what is apparent from the few available observations.Furthermore, a local minimum around 30 m observed by Jakobs et al. (2014) is not reproduced in the model run.

Preliminary CH4 budget
Here, we present preliminary budget calculations based on the standard model run.It is however important to stress that these estimates are heavily dependent on the prescribed benthic CH4 source.As discussed below (Sect.4), different combinations of benthic CH4 release and MOX rates could produce similar CH4 concentrations in the water column.
Total CH4 sources (land load and sediment release) and sinks (outgassing, net export, and pelagic oxidation) were aggregated over the entire Baltic Sea to allow a preliminary assessment of the relative importance of different processes.The CH4 sources were largely dominated by benthic release which amounted to an average 7557 Mmol y -1 over the 2001-2020 period (Table 2).This source was mainly balanced by oxidation in the water column (6598 Mmol y -1 , 87% of the sinks) and to a smaller Sediment release 7557

Net change 9
Figure 6 illustrates simulated monthly fluxes, net accumulation as well as the total amount of CH4 in the entire Baltic Sea.The total CH4 stock amounted to approximately 1800 Mmol y -1 over the ~2010-2014 period, which exceeded the stock before and after that period by a factor 2-3 (Fig. 6).This comparatively large CH4 stock was the result of a large anoxic deep-water volume and thus low oxidation rates (Fig. 2).There was an average net accumulation of 9 Mmol y -1 over the 2001-2020 period (Table 2), but net changes of the total CH4 stock between individual years varied by approximately ± 50 Mmol mo -1 , which largely reflected oxygen dependent changes in CH4 oxidation rates (Fig. 6).

Discussion
This study presents a first quantification of key CH4 fluxes on a Baltic Sea scale.However, there are uncertainties in our estimates, in particular regarding the benthic CH4 source.In the standard model run, benthic release is the dominant CH4 source (Table 2).The sediment source is set as constant over time, at all depths, and in all sub-basins.In the real Baltic Sea, however, large spatial and temporal variations are expected (e.g., Roth et al., 2022).Furthermore, the isotopic composition of the sediment source is set either to -80‰ or -60‰ depending on oxygen conditions in the overlying water.This assumption is a simplified representation.The main uncertainty in our present large-scale estimates is that spatial and temporal variations of the sediment source are not well known.
The simulated CH4 concentrations in anoxic deep waters agree with available observations.The calibrated rate of CH4 release from sediments is for that reason deemed as feasible in anoxic deep waters, since CH4 concentrations are only marginally influenced by oxidation during anoxic conditions (low AOM rates).
It is more challenging to constrain the sediment source in shallower oxic waters, where the source can be largely compensated by MOX in the water column.Coastal systems are also more dynamic and show a larger variety compared to deep anoxic areas.A large CH4 source compensated by high MOX rates could for example yield similar CH4 concentrations as a smaller source combined with lower MOX rates.These two different cases (i.e., large source, high oxidation vs. small source, low oxidation) would produce quite different isotopic patterns that could be used to calibrate the model.However, a complication here is that we generally do not know the isotopic composition of CH4 released from the sediments, with the exception of observational data from a few locations.Justification of the calibrated rates used in the model would require more observational data to fill the knowledge gaps.
The calibrated parameter values used in the computation of MOX rates (Eq.16) differ substantially from other published estimates from lake studies (e.g., Greene et al., 2014;Tan et al., 2015;Bayer et al., 2019).Here, these parameters were calibrated so that the resulting profiles of oxidation rates and isotopic compositionas well as CH4 concentrationsreasonably well reproduce observed profiles from the central Baltic Sea.Results for CH4 concentrations, MOX rates, and isotopic composition are sensitive to O2 profiles, which also means that the calibrated values depend on how well the model reproduces O2 concentrations.
The rate constant for MOX depends on the activity and abundance of methanotrophs, in theory allowing for reduced MOX in spite of favorable conditions in terms of CH4 and O2 concentrations when methanotrophs are not active.The model does not include methanotrophic activity explicitly, and the rate constant for MOX is constant.Perhaps, lower abundance and activity of methanotrophs could be an explanation for the lower rate constant in the present results compared to the results from lakes cited above.
It is furthermore worth to mention here that Schmale et al. (2018) described an unresolved CH4 source in oxic upper waters of the central Baltic Sea, possibly related to zooplankton activity.This source has not been addressed in the present study.

Sensitivity experiments
A series of sensitivity experiments was performed on different parameters used in the modeling of CH4 and its stable isotopes (Table 1).The adjusted parameter values are listed in Table 3. Modeled profiles are then drawn for both winter conditions (February) and summer conditions (August) of 2015 (Fig. S6-S11), which gives an indication of season dependent contrasting conditions in surface waters above the halocline.Methane cycling in the model is largely dominated by benthic release, oxidation in the water column, and outgassing (Table 2; Fig. 6).For that reason, sensitivity experiments on riverine and North Sea CH4 concentrations were not included.Adjusting the potential maximum rate of MOX (vWCH4_O2) by ± 50% (tests 1-2) 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) to lower CH4 compared to 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 to 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 δ 13 C-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 CH4 concentration and 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 (Fig. S7-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 to 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 to 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 are 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.Adjusting the fractionation during CH4 oxidation by ± 4‰ (tests 7-8) has no influence on CH4 oxidation rates and concentrations, but a relatively strong (and predictable) impact on δ 13 C-CH4 values throughout the entire water column (Fig. S9).

Sediment source: CH4 release and isotopic composition
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, respectively.Adjusting the δ 13 C-CH4 value of the sediment source by ± 10‰ during oxic conditions (tests 9-10) has no influence on CH4 oxidation rates and concentrations, but a strong (and predictable) impact on δ 13 C-CH4 profiles (Fig. S10).
In experiments where the rate of CH4 release from the sediments source was adjusted by ± 50‰ during oxic conditions (tests 11-12), 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 concentrationwhich is very similar between the two experiments (not shown)than CH4 concentrations (Fig. S11).

Caveats and outlook
As previously discussed, the main uncertainty in the model simulations lies in our limited understanding of CH4 release from different sediment areas, as well as the isotopic composition of CH4 released into the water column.Both the flux and the isotopic composition depend on the balance between production and oxidation rates in the sediment.A high production could be compensated by high oxidation and thus result in a relatively small CH4 release to the water column in spite of a large production.This would then be evident by a 13 C-CH4 enrichment, i.e., comparatively heavy CH4.Alternatively, a relatively small CH4 production could still result in a substantial release to the water column in a case where the oxidation rate is low, which would then also be evident by CH4 depleted in 13 C-CH4, i.e., comparatively light CH4.
Improved knowledge of properties of CH4 released from sediment to water column in different areas of the Baltic Sea (e.g., the Kattegat and the major gulfsthe Gulf of Bothnia, Gulf of Riga, and Gulf of Finland) would help to improve model parameterizations and thus reduce the main uncertainties of model simulations.This was, however, beyond the scope of the present study because of the missing knowledge concerning both temporal and spatial patterns of the CH4 source.A logical progression at this stage would involve detailed observations combined with modeling studies focused on processes in the sediments, i.e., production and oxidation rates, depending on carbon accumulation rate, oxygen conditions, and the presence of methanotrophs.
A crucial missing link in this study is the formation, transport, and fate of CH4 bubbles.Ebullition has been included in lake models (e.g., Greene et al., 2014;Bayer et al., 2019); however, we do not have experimental data to calibrate and validate the large-scale influence of ebullition in the Baltic Sea.The calibrated benthic CH4 source represents a "bulk" CH4 release, including in theory both the influences of diffusive flux and bubble dissolution on CH4 concentrations in the water column.However, CH4 ebullition might bypass methanotrophy and consequently contribute to higher CH4 emissions, in particular in shallow-water areas (Broman et al., 2020).This indicates that the simulated CH4 outgassing is likely underestimating the real outgassing from the Baltic Sea.Observations of ebullitive fluxes in combination with development of model parameterizations represent important steps to better describe and quantify CH4 emissions from the Baltic Sea.
Roth et al. ( 2023) observed significant CH4 production and release from vegetated oxic shallow-water areas.BALTSEM-CH4 v1.0 does not differentiate between vegetated and unvegetated areas, which means that this CH4 sourceand its contribution to outgassingcould not be addressed here, which consequently represents another gap in our current understanding.Both species distribution models and process-based models for vegetation exist (e.g., Lappalainen et al., 2019;Graiff et al., 2020), but to our knowledge do not include CH4 dynamics.Hence, the inclusion of CH4 in vegetation models could potentially serve as an objective for future scientific projects.
The process parameterizations used in this study to describe large-scale CH4 cycling in the Baltic Sea can also be applied in various other domains.As part of our future plans, we aim to investigate CH4 dynamics in a smaller area where more observations are available and where the CH4 concentration and isotopic composition, as well as properties of end-members (river load, benthic release, and lateral boundary conditions), are better understood.This would further help to constrain process rates in the model.
The calculated average total CH4 emission of 980 Mmol y -1 corresponds to approximately 0.04 g CH4 m -2 y -1 , and constitutes only about 13% of the calibrated sediment source (~0.3 g CH4 m -2 y -1 ).The model includes both shallow-and deep water sediment areas, but the calibrated sediment source is in the lower range of rates reported for a shallow-water coastal area (0.34-0.55 g CH4 m -2 y -1 ; Roth et al., 2023), indicating that the model might not well represent coastal CH4 hotspots.One major knowledge gap at this point is the relative importance of shallow coastal areas compared to the open Baltic Sea in terms of CH4 outgassing.This is an important scientific question that needs to be addressed in future studies.
https://doi.org/10.5194/gmd-2023-211Preprint.Discussion started: 26 March 2024 c Author(s) 2024.CC BY 4.0 License.Benthic CH4 release and the isotopic composition of CH4 produced in the sediments are not well known except for a few specific sites where in-situ measurements have been acquired.This means that the model is, at this point, somewhat poorly constrained.The main objective of this study is to use the model in concert with observed water column CH4 concentrations and isotopic compositions to 1. identify and roughly quantify key CH4 fluxes, 2. set up a preliminary CH4 budget on a Baltic Sea scale, and 3. perform sensitivity experiments on CH4 concentration and isotopic composition depending on transport and transformation processes.
2.3.An initial model run over the period 1970-2000 started with initial profiles for the different state variables based on observations when possible or else calibrated 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).https://doi.org/10.5194/gmd-2023-211Preprint.Discussion started: 26 March 2024 c Author(s) 2024.CC BY 4.0 License.

Figure 1 :
Figure 1: Conceptual sketch illustrating the processes involved in CH4 cycling, including δ 13 CCH4 values of end-members as well as α values of transformation processes (see Sect. 2.3).The benthic release (dashed arrow) is not explicitly modeled, instead a preset calibrated value is used (see Sect. 2.3.5).
. Deep water in the Bornholm basin shows isotope values of approximately -70‰, and deep water in the Arkona basin show isotope values in a range -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 δ 13 C-CH4 values of approximately -80‰ in the Landsort Deep (451 mbss), -70‰ in the Bornholm Deep (87 mbss), and -60‰ in the Little Belt (37 mbss).
https://doi.org/10.5194/gmd-2023-211Preprint.Discussion started: 26 March 2024 c Author(s) 2024.CC BY 4.0 License.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 DIC for each mol of consumed CH4 (Eq.15 and 17, respectively).Observations from the Gotland and Landsort deeps in the Baltic Proper indicate oxidation rates in a range 0.1-4 nM d -1 https://doi.org/10.5194/gmd-2023-211Preprint.Discussion started: 26 March 2024 c Author(s) 2024.CC BY 4.0 License.

Table 1 .
Standard model settings.The values are own estimates/calibrated values (see Sect. 2.3) except where noted.

Table 3 .
Adjusted parameter values and change (%) compared to the standard model run in the various sensitivity experiments.