We investigate the response of relict Arctic submarine permafrost and gas hydrate deposits to warming and make predictions of methane gas flux to the water column using a 2-D multiphase fluid flow model. Exposure of the Arctic shelf during the last glacial cycle formed a thick layer of permafrost, protecting hydrate deposits below. However, talik formation below paleo-river channels creates permeable pathways for gas migration from depth. An estimate of the maximum gas flux at the present time for conditions at the East Siberian Arctic Seas is 0.2047 kg yr−1 m−2, which produces a methane concentration of 142 nM in the overlying water column, consistent with several field observations. For conditions at the North American Beaufort Sea, the maximum gas flux at the present time is 0.1885 kg yr−1 m−2, which produces a methane concentration of 78 nM in the overlying water column. Shallow sediments are charged with residual methane gas after venting events. Sustained submergence into the future should increase gas venting rate roughly exponentially as sediments continue to warm. Studying permafrost-associated gas hydrate reservoirs will allow us to better understand the Arctic's contribution to the global methane budget and global warming.
Permafrost-associated methane hydrate deposits exist at shallow depths within the sediments of the Arctic continental shelves. This icy carbon reservoir is thought to be a relict of cold glacial periods, when sea levels are much lower, and shelf sediments are exposed to freezing air temperatures. During interglacials, rising sea levels flood the shelf, bringing dramatic warming to the permafrost and gas hydrate bearing sediments. Degradation of this shallow-water reservoir has the potential to release large quantities of methane gas directly to the atmosphere (see review by Collett).
Several thermal modeling studies have shown that relict offshore permafrost and gas hydrates should still exist on vast regions of the Arctic shelf of Siberia [e.g., Delisle, 2000; Romanovskii et al., 2005; Nicolsky et al., 2012] and North America [e.g., Judge and Majorowicz, 1992; Taylor et al., 1996a, 1996b] at present day. Because field studies in the Arctic are difficult to conduct, only a few observations have been made which infer or confirm the presence of relict offshore permafrost [Judge et al., 1981; Weaver and Stuart, 1982; Osterkamp et al., 1989; Kassens et al., 2000; Rachold et al., 2007; Brothers et al., 2012] or permafrost-associated gas hydrates [Weaver and Stuart, 1982; Smith and Judge, 1993; Dallimore and Collett, 1995]. The scarcity of observations means the actual extent of relict permafrost-associated gas hydrate deposits on the circum-Arctic shelves remains controversial.
Although relict permafrost-associated gas hydrate deposits likely make up only a small fraction of the global hydrate inventory [Ruppel, 2011], they have received a disproportionate amount of attention recently because of their susceptibility to climate change. This paper is motivated by several recent field studies which report elevated methane levels in Arctic coastal waters. Along the East Siberian Arctic Shelf (ESAS), large gas plumes and seeps are venting methane to the water column, resulting in supersaturated dissolved methane concentrations relative to atmospheric equilibrium [Shakhova et al., 2010a; Sergienko et al., 2012; Shakhova et al., 2013], while vigorous gas plumes are observed along the Canadian Beaufort midshelf and shelf edge [Paull et al., 2011]. At the Alaskan Beaufort shelf, sampled seawater was supersaturated in methane under winter sea ice due to venting from the sediments [Kvenvolden et al., 1993], and areas of high seawater methane concentrations were found nearshore, located near the Colville River Delta [Pohlman et al., 2012]. While these observations are consistent with methane release as a result of decomposing submarine permafrost and gas hydrates, the source of gas cannot easily be distinguished from other possibilities, including the escape of deep thermogenic gas through permeable pathways such as faults, or microbial activity on thawing organic matter within the shelf sediments, clearly documented terrestrial processes [e.g., Walter Anthony et al., 2012]. Regardless of the source of gas, ebullition is of special concern in the Arctic, where shallow and cold waters limit bubble dissolution and oxidation, allowing methane, a potent greenhouse gas, to escape more easily from the shelf sediments directly to the atmosphere [Archer, 2007; Ruppel, 2011; Shakhova et al., 2013].
Permafrost distribution in the Arctic is complex and far from homogeneous. Even in regions of so-called continuous permafrost, unfrozen portions of the sediments, or taliks, are found near anomalous sources of heat in the environment. Taliks can form beneath bodies of water that do not completely freeze in winter, such as large thermokarst lakes and major river channels, or near faults where heat flux is elevated [Walker, 1998; Romanovskii et al., 2000, 2004; Hubberten and Romanovskii, 2003]. Some taliks can extend deep enough to penetrate through the base of the ice-bearing permafrost layer, conceivably making the sediments permeable to fluids where permafrost should otherwise still be largely intact [Delisle, 2000; Hubberten and Romanovskii, 2003; Nicolsky and Shakhova, 2010]. Moreover, complex distributions of salt within the pore fluids, such as brine pockets or layers, or the development of thermokarst features before ocean transgression began, can also locally increase submarine permafrost permeability to fluids and gases [Shakhova et al., 2009a]. As a result, gas escape through taliks has been proposed as an explanation for the observations of elevated nearshore gas venting, where the permafrost layer should otherwise still be stable [Romanovskii et al., 2004; Shakhova and Semiletov, 2007; Shakhova et al., 2009b; Nicolsky and Shakhova, 2010; Shakhova et al., 2010b; Sergienko et al., 2012; Shakhova et al., 2013].
The large spatial variations in bottom water methane concentrations (see Figure 1, modified from Shakhova et al. [2010a]), show that gas venting is localized and may possibly be connected to gas escape through taliks. Because methane concentration tends to be highest near rivers, and was shown to be distinct from riverine methane sources [Shakhova et al., 2009b, 2010b], gas venting through taliks formed by paleo-river channels may provide a possible explanation [Shakhova et al., 2009b; Anisimov et al., 2012; Shakhova and Semiletov, 2012]. As sea level receded during the last glacial period, the great Arctic rivers would have extended their course over the newly exposed ground, as is evidenced today in the bathymetry [Holmes and Creager, 1974]. Therefore, the warming influence of the river bed would have been present over most of the glacial period. Assuming the river did not completely freeze, permafrost would not develop beneath these regions. At present day, the paleo-river beds are submerged, and the taliks beneath them may provide a permeable pathway for methane gas escape.
In this paper, we quantitatively assess the response of submarine permafrost and gas hydrate deposits to warming. We investigate the role of taliks as a pathway for methane gas escape and make predictions of gas flux to the water column as a result of relict permafrost-associated gas hydrate dissociation due to natural climate variations. A desired outcome of this study is to provide a framework for assessing the potential magnitude of methane release that might be attributed to relict permafrost-associated hydrate deposits in regions where the submarine permafrost has been compromised.
2 Numerical Methods
2.1 Numerical Model Formulation
We use a numerical model to evaluate the temperature and salinity fields, fluid and gas flow patterns, and permafrost and gas hydrate evolution within a two-dimensional transect of the shallow Arctic shelf sediments. The model is time dependent and based on the finite volume method.
The temperature field T is solved according to the energy equation,
where ρ is the density, cpis the specific heat, u is the transport velocity, K is the thermal conductivity, and ϕ=ϕi+ϕh is the combined effect of latent heat of ice ϕiand hydrate ϕhformation. The density and specific heat within each computational grid cell are determined by a volume average of components (denoted by an overbar), while the thermal conductivity is obtained via a mixture model,
which defines an effective value K based on the volume fraction S of each component (e.g., rock (Ss=1−φ), pore fluid (Sf=φf), ice (Si=φi), hydrate (Sh=φh), or methane gas (Sg=φg)), where f, i, h, and g indicate the fluid, ice, hydrate, and gas saturation within the pore space, respectively. A steady and spatially uniform geothermal gradient is applied as a boundary condition at the bottom of the domain, and both vertical sides of the domain are insulating.
For numerical stability, the latent heat source is treated as an anomaly in the local specific heat [e.g., Bonacina et al., 1973]. The phase change component in each source term is expanded as
where Si(T) and Sh(T) are prescribed functions of temperature that vary linearly from zero to the maximum allowable value over a narrow 1°C temperature interval around the melting or equilibrium temperature, which is a prescribed function of salinity and pressure following UNESCO . In this form, the latent heat can be treated as an anomaly in specific heat as follows:
where ρis the density, and L is the latent heat, of either ice or hydrate as indicated by the subscript. For hydrate, we determine the equilibrium temperature following the empirical relationship given by de Roo et al.  using the local salinity and pressure.
The salinity field is solved via the advection-diffusion equation
where D is the diffusion coefficient for salt (assumed constant) and Q is a salt source term, which represents the influence of ice or hydrate formation.
A two-phase variant of Darcy's Law for fluid flux, or the transport velocity u, through a porous media with buoyancy [Andler and Brenner, 1988] is given by
where the subscript j indicates the phase (pore water or methane gas). Here P is the nonhydrostatic pressure, and the density perturbation Δρj is defined relative to pure water. The fluid viscosity is μ, and the sediment permeability k(φ) is a function of porosity, based on a modified Kozeny-Carman relation [Mavko and Nur, 1997]. The phase permeability factor kr ranges between 0 and 1, and depends linearly on the phase saturation within the pore space (e.g., f or g). When gas saturation is below 0.10, we set to account for gas immobility at low saturation.
Fluid volume fractions Sjare updated in time by
where Φjrepresents a source of methane gas when hydrate dissociates or a source/sink of fluid when ice or hydrate melts/forms, respectively. Because the mass fraction of methane in seawater in equilibrium with hydrate is much smaller than the mass fraction of gas in hydrate , the gas source term due to hydrate dissociation can be simplified to
The fluid source term is given by
where is the mass fraction of water in hydrate. We assume ρh/ρf≈1 and ρi/ρf≈1, which neglects the small volume change when water changes phase from ice or hydrate.
Pressure P is computed from conservation of mass
where Φjare defined in (9) and (10). We no not consider capillary effects when computing the pressure, which means the pressure within a grid cell is the same for each fluid component within the sediment pore space.
The coupled equations are solved iteratively using a preconditioned general minimum residual method at each time step. The model is run over 130 ka, beginning with the onset of the last glacial cycle and extending 10 ka beyond present day. We assume an initial temperature field that is in equilibrium with marine transgression; thus, permafrost does not exist within the sediments at the start of the initial “spin-up.” All model parameters are listed in Table 1, with further detail provided in the following section.
Table 1. All Model Parameters Used are Listed in the Table Below and are Assumed Constanta
The references listed provided guidance in our choice of parameter values.
A geothermal gradient boundary condition of 25 C km−1was required to recover a present-day geothermal gradient below the permafrost layer matching observations in Weaver and Stuart .
The average gas density is used for typical conditions at 1 km sediment depth.
We model two-dimensional transects oriented parallel to the present-day shoreline at the 20 m isobath. The transects are 6 km long and extend vertically 2 km into the shelf sediments. The numerical model is driven by the boundary conditions at the sediment surface, which depend on the computational transect location (e.g., the North American Beaufort and the ESAS). A sea level curve, based on the models of Peltier  and Kendall et al.  and provided by J. Mitrovica (personal communication, 2013), determines the timing of submergence and exposure of the sediments to seawater or the atmosphere (see Figures 2 and 3). The sea level curves account for the effects of regional isostatic adjustments and self-gravity on the global sea level variations, making each curve site specific. Over the last glacial cycle, the sediments at the 20 m isobath at the North American Beaufort have been exposed to the air for roughly 70 ka, with ocean transgression as recent as ~4 kaBP. At the ESAS, the sediments at the 20 m isobath have been exposed to the air for roughly 105.5 ka, with ocean transgression as recent as ~6 kaBP. At this shallow-water depth, observations show that relict submarine permafrost is still present at the Beaufort Sea and ESAS [Weaver and Stuart, 1982; Brothers et al., 2012; Kassens et al., 2000].
We use the Vostok ice core deuterium data set by Petit et al.  to provide a rough mean annual air temperature reconstruction over the last glacial cycle. We apply the air temperature anomaly in Petit et al.  to the present-day mean annual air temperature at the locations of the computational transect to obtain the top temperature boundary condition when shelf sediments are exposed to the atmosphere (see Figures 2 and 3). The mean annual air temperature for the period from 1987 to 1992 compiled by Zhang et al.  near the Alaskan Beaufort Sea coast averages −12.4°C, while temperatures are slightly colder today along the coast of the ESAS, roughly −14°C [Romanovskii et al., 2005]. The warming influence of a river bed is modeled by applying a localized 1°C surface temperature boundary condition over the river's cross section when the transect is exposed to air. Because the river water temperature is just above freezing, its presence should prevent permafrost from forming under it, as is observed today beneath modern Arctic rivers [Walker, 1998]. We explore several typical Arctic river widths (0.5, 1, 1.5, and 2 km) in this study.
Ocean bottom water temperatures are typically below 0°C in the nearshore Arctic Ocean. For example, in the Alaskan Beaufort, bottom waters range between −0.5°C and −1.7°C, while at the Laptev Sea, temperatures can be as low as −2°C [Osterkamp, 2001]. However, in regions nearby riverine input, bottom water temperatures can be as high as 3°C, as observed during summer near the Lena River delta on the ESAS [Shakhova et al., 2010b]. We apply an ocean bottom water temperature of 0°C as a boundary condition when shelf sediments are submerged, reflecting the assumption that the transect is near a modern river output.
Because direct observations of the lithology, pore fluid salinity, and gas hydrate distribution within nearshore Arctic sediments are scarce, some approximation is necessary when choosing model parameters. We use the available well log data compiled by Collett et al.  at the Alaskan North Slope, Weaver and Stuart  and Sellmann and Chamberlain  at the North American Beaufort Sea, and the overview of observations detailed by Nicolsky et al.  to provide guidance. Offshore well log data indicate that the sediments of the Canadian Beaufort are remarkably fresh between 200 and 2000 m depth, with a salinity of only 0.01 ppt [Weaver and Stuart, 1982]. Drilling and cone penetrometer data beneath the Beaufort Sea near Prudhoe Bay show that the salinity of the shallow sediments (less than 65 m depth) is similar to that of sea water due to infiltration of saline waters into the surface layer of sediments [Sellmann and Chamberlain, 1980]. Measurements of pore water salinity at the ESAS have not been made deeper than 70 m, but the shallow observations indicate that near-surface sediments also have sea water salinity values [Nicolsky et al., 2012]. In the absence of deeper observations, we assume the same salinity for the deep sediments at the ESAS as at the Beaufort (i.e., 0.01 ppt). Additionally, neutron log calculated porosity values reported by Collett et al.  at the Alaskan North Slope are roughly constant with depth in the top 1 km of the sediment column and range between 22% and 48%. Hydrate deposits are found only in discrete sandstone units occurring at 50–100 m intervals and up to 30 m thick. These units are almost completely saturated with methane hydrate (~85%pore volume), but deposits with such high hydrate saturation are likely not common. Although these observations are onshore, they are reasonable values to use given the uncertainties and the long terrestrial history over the last glacial cycle at the locations of the computation transects. Moreover, qualitatively similar hydrate distribution patterns were found in offshore wells at the Canadian Beaufort [Weaver and Stuart, 1982]. We explore a range of initial gas hydrate saturation levels (i.e., 80%, 50%, and 20% pore volume) in 25 m thick horizontal units separated by 75 m vertical intervals within the calculated hydrate stability zone at the last glacial maximum. We assume an average and constant porosity of 35% for both the North American Beaufort and ESAS transects. Due to the absence of hydrate distribution observations at the ESAS, we assume the same initial hydrate distribution at both locations.
3 Model Results
3.1 Continuous Permafrost and Hydrate Extent
Sustained exposure of the shelf sediments to air temperatures below the freezing point forms a thick layer of continuous ice-bearing permafrost (hereafter more simply called “permafrost”) far from the river's thermal influence. Figure 4 presents a 1-D time history of the continuous permafrost layer extent at each transect location. At the last glacial maximum (assumed 18 kaBP), model results predict the base of the permafrost layer at 600 m below the sediment surface along the modeled transect at the North American Beaufort and 700 m at the ESAS. Permafrost extends deeper into the sediments at the ESAS because of the longer duration of exposure to subfreezing air temperatures (~70 ka at the Beaufort versus ~105.5 ka at the ESAS). While observations of the offshore permafrost extent are scarce at the ESAS, several records exist in offshore wells drilled at the Canadian Beaufort Sea [e.g., Weaver and Stuart, 1982; Hitchon et al., 1990; Hu et al., 2013]. Although permafrost varies by location, well records near the 20 m isobath show the submarine permafrost base at 400–780 m depth.
Figure 5 presents a 1-D time history of the sediment temperature for both transect locations in a continuous permafrost region. Rising air temperatures since the onset of the Holocene interglacial warmed the ground, slightly reducing the ice saturation of the permafrost layer near the surface and at the base, but not its overall vertical extent at the time the transect became submerged (~4 and ~6 kaBP at the Beaufort and the ESAS, respectively). Further and more dramatic warming after submergence has caused melting within the permafrost layer. The greatest ice loss has occurred near the surface and at depth. However, temperature and permafrost depth have stayed relatively constant due to the large amount of latent heat, or “thermal inertia,” required to melt the permafrost layer.
Beneath and within this protective permafrost layer, methane hydrate is thermodynamically stable. Figure 6 shows the methane hydrate stability zone in regions of continuous permafrost for both the North American Beaufort and ESAS transect locations. The depth to the base of the methane hydrate stability (MHS) zone far from the river's influence has actually been increasing in recent time at both locations and has not changed since transect submergence at present day. Moreover, the spatial extent of the MHS zone is at its largest at present day. At the last glacial maximum, model results predict hydrate stability to 850 m depth at the Beaufort and 1050 m depth at the ESAS, while the present-day depth extends to 925 m and 1100 m below the seafloor, respectively. The increase in size of the MHS zone, even though the sediment surface is warming, can be explained by the time lag in heat propagation through the sediments and the fact that the permafrost above absorbs much of the heat input from the surface during phase change.
Moreover, model results predict that the continuous permafrost layer and MHS zone should persist well into the future in regions of continuous permafrost. For example, after an additional 10 ka of sustained submergence, the continuous permafrost layer is present down to ~400 m and ~500 m depth (at the Beaufort and the ESAS, respectively; see Figure 4), although at lower ice saturations. The thickness of the MHS zone decreases as permafrost degrades, and the geothermal gradient begins to warm the sediments from below but not until roughly 2 ka into the future at the Beaufort transect location, and longer still at the ESAS.
These results suggest that nearshore submarine permafrost should exist today and well into the future in regimes away from anomalous sources of heat, such as the thermal influence of the river. Based on this numerical study, hydrate deposits should also be stable within and below intact continuous permafrost layers. The fact that the MHS zone actually increased in vertical extent since the glacial maximum, and is not expected to change for several thousands of years after submergence, indicates its resilience. However, permafrost distribution in the field may differ from the continuous permafrost modeling results due to local variations in the salinity field (such as brine pockets or layers) or regions of elevated bottom water temperatures, for example.
3.2 Talik Formation and Methane Gas Venting
Permafrost and the associated methane hydrate deposits within the calculated MHS zone are allowed to evolve within the computational transects over the duration of the last glacial cycle (i.e., spin-up period of roughly 100 ka) and continuing 10 ka into the future, as described in section (2). The warming influence of a modeled paleo-river channel prevents the formation of permafrost beneath it, creating a talik in the otherwise continuous permafrost. Figures 7 and 8 show the permafrost and hydrate structure at the glacial maximum for each paleo-river channel width simulated. The width of the paleo-river channel controls the spatial extent of the talik and whether the talik is open or closed. The surrounding continuous permafrost bulges out slightly beneath the river bed, reducing the talik width near the sediment surface. A paleo-river channel which is 1.0 km wide or smaller fails to form an open talik because of this bulging effect at the ESAS transect location. However, river beds larger than 1.0 km wide do form a pathway from depth that is entirely free from ice or hydrate. At the North American Beaufort transect location, only the smallest river width simulated (0.5 km) failed to create an open talik. The taliks (open or closed) persist beneath the river bed for the entire glacial cycle and do not refreeze upon submergence. In natural settings, the three-dimensional structure may be more complex than what is simulated in our two-dimensional model, as river width is typically not constant along its entire path, and the effects of meander have not been taken into account.
Transect submergence dramatically warms the sediments from above, in addition to the strong warming from below due to geothermal heat flux. Talik width increases, and ice saturation within the pore space decreases as submarine permafrost begins to melt. Warming due to ocean transgression is also felt within the MHS zone at depth but only near the talik edges at first. As hydrates begin to dissociate, methane gas is released into the sediment pore space. Buoyancy drives gas toward the sediment surface according to Darcy's Law, where it vents into the overlying water column. Several snapshots of the permafrost, methane hydrate, and methane gas saturation within the computational transect are shown in Figures 9 and 10 for each river width modeled at present day. Gas charged regions (semitransparent areas highlighted in yellow) exist near the talik edges and are formed from gas which is presently dissociating or from a trail of gas left over from previous venting events. Gas saturation in the highlighted region ranges between 0.09 to 0.11 pore volume. Sediments which have been charged by gas but not currently venting are still vulnerable to later gas venting events. For example, ice scouring which disturbs the seafloor can potentially release this gas, and these old gas migration pathways can help facilitate new rapid release.
Our model does not account for the effects of possible gas traps or sinks, such as the sulfate reduction zone near the sediment surface, or permeability seals to gas such as regions of fine grained sediments, which would limit the amount of gas that can reach the sediment surface. However, gas within the sediment pore space must build up to a minimum of 0.10 saturation before it becomes mobile due to gas relative permeability. This results in a considerable amount of gas left behind in the sediments. Including gas sinks or allowing larger volumes of trapped gas would decrease gas venting, so our predictions provide an upper bound on what is possible given the initial hydrate saturations explored.
3.2.1 Gas Venting History at the ESAS
Figure 11 shows a time history of methane gas venting rate in kilogram per year (on the left axis) at the ESAS transect location since the last glacial maximum to 10 ka in the future. The venting rate is obtained by integrating the flux across the channel, so the total gas flow depends on the downstream length of the channel. Several initial hydrate saturation values (indicated by the line stroke) and river widths (indicated by the line color) are shown. The onset of gas venting depends both on the hydrate saturation within the pore volume at the glacial maximum and the paleo-river (talik) width. In general, larger talik widths and larger gas hydrate deposits will begin venting gas to the sediment surface first. For example, for an initial hydrate saturation of 80% pore volume within the sandy layers (corresponding to 28% by volume within a hydrate layer or 7% by volume within the entire stability zone), venting begins roughly 4 kaBP at the ESAS transect location for the largest river widths considered (2 and 1.5 km wide), 2 ka after the transect becomes submerged. Smaller river widths create thinner taliks, delaying the effects of warming, and hence delaying hydrate dissociation and gas venting. For a 1 km wide river, venting is not predicted until 2 ka BP, which is roughly 4 ka after the transect has been submerged.
Model results also show that small hydrate deposits or small paleo-river channels do not produce observable gas venting at the present day. When the initial hydrate saturation is 20% (corresponding to 1.75% by volume within the entire stability zone), venting is not predicted until 1.5 ka into the future for the largest river width (2 km). A river width of 0.5 km or less fails to create an open talik in the permafrost; therefore, gas venting is only observed once the warming of submergence penetrates the thinned permafrost directly below the river bed. This delays gas venting to the sediment surface until nearly 10 ka after transect submergence (or ~4 ka in the future) for an initial hydrate saturation of 80%. For the smallest hydrate deposits, no gas venting is observed even after 10 ka beyond present day.
As a general trend, gas flux to the sediment surface depends mostly on talik size near the onset of venting. However, as warming penetrates into the continuous permafrost, gas flux accelerates exponentially and shifts its dependence to the initial hydrate inventory instead. After a sufficiently long time, so much submarine permafrost has been compromised that the majority of the transect becomes permeable to gas, and the system loses memory of the original permafrost-talik structure. Widespread venting, no longer associated with the original location or size of the talik, is expected ~7 ka into the future at the ESAS transect location. As shown in Figure 4, this corresponds to an ice saturation level below 50% within the continuous permafrost region. An exception to this trend is observed for the largest river width simulated (2 km). This exception suggests a critical talik width, where taliks larger than 2 km wide would not necessarily cause more gas venting.
On the right axis in Figure 11, the methane gas venting rates in kilogram per year per meter along the paleo-river channel are converted to an equivalent water column methane concentration overlying the venting talik. The water column methane concentration value is useful when comparing model results with measurements taken in the field. The model calculation is based on a constant water depth of 20 m and an average current of 4 cm s−1 along the transect [e.g., Dmitrenko et al., 2010]. For example, at the present time for the ESAS transect location, 33 kg yr−1of methane would mix in a seawater volume of 2.52×107 m3 yr−1above a 2 km wide talik with an initial hydrate saturation value of 50% (solid green line; see inset in Figure 11). Assuming a constant methane flux, complete dissolution into seawater with no preexisting methane, and no methane oxidation in the water column, the resulting methane concentration in the water column overlying the talik would be ~82 nM. Ebullition (gas bubbling) would probably reduce the dissolved concentration, but preexisting dissolved methane would have the opposite effect. We also note that water currents do vary by location, as does the water depth over time; thus, the methane concentration values are only an approximation to aid in the comparison between model results and measurements in the field as they are most often reported. This approximation does not apply to the gas venting rates (on the left axis), as they are a direct quantification of the gas flux from the sediment surface.
The inset in Figure 11 shows part of the same venting plot magnified near the present day. The maximum water column methane concentration that can be expected due to hydrate dissociation through taliks at the ESAS is about 150 nM, given a large talik underlaid with high hydrate saturation values. No venting is expected at the present for taliks less than 1 km in width underlaid by any value of hydrate saturation. Similarly, no venting would be expected at the present for any talik size underlaid by a hydrate saturation of less than 20% pore volume within hydrate layers. Bottom water methane concentrations reported by Shakhova et al. [2010b] during summer range between 2.1 and 298 nM with a mean of 50 nM (also see Figure 1). Methane venting hot spots, where the highest dissolved methane concentrations were measured, tend to be near rivers. Although the source of gas in the ESAS observations remains uncertain, our model suggests that a large portion of the dissolved methane can be explained by gas venting through taliks from decomposing hydrates; however, large taliks (>1 km wide) and large hydrate deposits (>50%pore volume within sandy layers) are required. Additionally, observations indicate bottom water methane concentration tends to increase in the downstream direction of the proposed paleo-river channel. Model results are consistent with this pattern, as sediments in the downstream direction have been submerged longer, causing stronger venting rates.
3.2.2 Gas Venting History at the Beaufort
Figure 12 shows the corresponding time history of methane gas venting rate in kilogram per year per meter along the paleo-river channel (on the left axis) at the Beaufort transect location since the last glacial maximum to 10 ka in the future. On the right axis, the gas venting rates have been converted to an equivalent water column methane concentration overlying the venting talik according to the same method described in the previous section. Gas venting at the North American Beaufort transect location follows the same trends as previously described at the ESAS location. However, because of the warmer air temperatures and shorter duration of exposure, the onset of gas venting occurs sooner after submergence at the Beaufort (1 ka) than at the ESAS (2 ka). For the same reason, the onset of widespread venting which is no longer associated with the original size of the talik is expected much earlier at the Beaufort, ~5 ka into the future. The difference in thermal history results in a more narrow MHS zone which shrinks more quickly at the Beaufort location than at the ESAS (see Figure 6).
The inset in Figure 12 shows a portion of the same venting plot magnified near the present day. The maximum water column methane concentration that can be expected due to hydrate dissociation through taliks is about 80 nM, given a large talik underlaid with high hydrate saturation values. This is nearly half the value expected at the ESAS. No venting is expected at present for talik widths less than 1 km in width underlaid by any value in hydrate saturation. Similarly, no venting would be expected at the present for any talik size underlaid by a hydrate saturation of less than 20% pore volume within hydrate layers. In general, gas venting at the Beaufort is less than at the ESAS because submergence at the Beaufort has been more recent, by roughly 2 ka. However, shifting the inset plot in Figure 11 by 2 ka does not yield a match to the results for the ESAS. If submergence history was the same, gas venting rates at the Beaufort would actually be larger due to the shorter duration of exposure and slightly warmer mean annual air temperature.
Water column methane concentration measurements are few and far between at the Beaufort Sea. Preliminary USGS data from the Alaskan Beaufort have revealed a possible methane hot spot near the Colville Delta [Pohlman et al., 2012]. Older measurements by Kvenvolden et al.  report the bottom water methane concentration at 21 m water depth near the Colville River was 94 nM under winter ice cover. During ice-free conditions at the Canadian Beaufort offshore from the Mackenzie River Delta, Macdonald  measured the largest bottom water methane concentration at 51 nM near the 20 m isobath, and in general, most measurements were between 5 and 27 nM. While the source of methane in these measurements cannot be determined (although they are distinct from the Mackenzie River), they are in range of the predictions made by the model at present day and are consistent with the possibility of gas venting through taliks due to decomposing gas hydrates.
Because of their shallow depth, permafrost-associated methane hydrate deposits along the Arctic continental shelf are much more susceptible to climate change and warming than deep oceanic hydrates. While many previous thermal modeling studies show that regions of relict submarine permafrost should persist today and well into the future, several field observations report elevated dissolved methane levels in the circum-Arctic Ocean. In this study, we have assessed the role of taliks (unfrozen portions within the continuous submarine permafrost) in creating permeable pathways which can facilitate methane gas escape from dissociating hydrate deposits at depth and quantified the expected gas flux to the water column due to natural climate variation. Our model results reconcile and support both seemingly conflicting observations in the literature. Taliks that form beneath presently submerged paleo-river channels provide a pathway for gas flow from depth. Warming during interglacial periods reaches hydrate layers near talik edges first, resulting in methane gas venting to the sediment surface through talik openings. Hydrate deposits further away from the taliks are buffered by the thick layer of continuous permafrost, which absorbs much of the surface warming as latent heat during phase change.
Model results predict the maximum water column methane concentration that can be expected due to hydrate dissociation through taliks is about 80 nM at the Beaufort, or 150 nM at the ESAS, given a large talik underlaid with high hydrate saturation values. Methane solubility in ocean water at 0°C in equilibrium with the atmosphere is roughly 3.5 nM. Bearing this in mind, model results show the present venting rate through large taliks and high initial hydrate saturations is high enough to supersaturate the overlying water column as it flows past the talik, by several orders of magnitude. Methane supersaturated waters likely drive a net flux of methane into the atmosphere.
We stress that the current venting rates predicted by the model, and likely those of the observations, are due solely to the effects of natural climate change, as anthropogenic effects have not been included in this model. Effects of anthropogenic global warming will certainly increase gas venting rates if ocean bottom water temperatures increase but likely will not have immediately observable impacts due to the long response times. Our model results support the idea that permafrost taliks formed by paleo-river channels can facilitate the release of large quantities of methane gas derived from degrading Arctic permafrost-associated gas hydrates at levels similar to those reported in the field. However, the actual inventory of relict permafrost-associated gas hydrate deposits on the circum-Arctic shelves remains controversial due to a lack of observations. Moreover, the source of methane, which has been observed in the field at elevated levels, is not known for certain. While many studies support the idea that the gas is derived from the sediments, a variety of possible methane sources exist other than gas hydrates. Deep thermogenic gas seeps or biogenic activity in the sediments may also be bringing similar amounts of methane to the water column. Future work should focus on including additional talik formation mechanisms, due to faults or thermokarst features, additional methane gas sources, and the effects of anthropogenic warming trends. Continuing studies on permafrost-associated gas hydrate reservoirs will allow us to better understand the Arctic's contribution to the global methane budget and global warming.
This work is partially supported by funding from the Department of Energy (DE-PS26-08NT43260-0). We thank Jerry Mitrovica for kindly providing the site specific relative sea level curves used in this study.