In order to determine the effects of submarine groundwater discharge (SGD) on the
GHSZ we run a 2D advection-diffusion model to steady-state through a range of flow rates and
zones of flow. Flow rates vary from 0.1 m/yr [Deming et al., 1992] to 1.3 m/yr. The thickness of
the flow zones ranging from 600m (approximate maximum thickness of permafrost near shore
[Osterkamp and Payne, 1981]), to 1,600m (approximate top of basement [Houseknecht and Bird,
2011]). We use line 730 (Figure 1) for these models for multiple reasons: (1) line 730 has the
largest discrepancy between the model predicted BSR and the observed BSR (Figure 6), (2) line
730 is located in the eastern part of our study area where the depth to basement is greatest
[Houseknecht and Bird, 2011], and (3) line 730 is located closest to shore (Figure 1). These
circumstances all result in the shortest flow distance, and coldest temperatures, and therefore,
offer the best possible situation for lateral, terrestrially derived, groundwater advection affecting
the GHSZ on the US Beaufort margin.
The initial temperature condition for the 2D advection-diffusion model are imported from
the average steady-state 1977 heat flow model at line 730. Additionally, conductivities are
defined using the average thermal conductivity of 1.1 W/mK as defined in our conductivity
model. To simulate constant SGD we set the landward boundary condition equal to 0 oC
(consistent with the melting temperature of permafrost) from 200 mbsl plus our defined
thickness (up to 1,800 mbsl in total depth). This constant temperature boundary condition is set
30km from shore, consistent with the maximum extent of permafrost in the US Beaufort Sea
[Brothers et al., 2012]. Similarly, the zone of flow is defined laterally for each given flow rate
and the defined thickness for the zone of flow, consistent with the temperature boundary
condition. The seaward side boundary condition is open. The basal boundary condition is a
Neumann heat flow boundary condition as defined by our heat flow map (Figure 5). The top
boundary condition is constant temperature as defined by the 1977 CTD casts. Model resolution
is refined to 12.5 m in the horizontal and 5 m in the vertical to allow for flow rates as high as 1.3
m/yr.
With thermal conductivity, advective rates, and temperatures defined, we run the 2D
finite difference advection-diffusion heat flow model to steady-state. The 2D model assumes a
time-dependent, conductive heat flow regime with constant diffusivity, a constant lateral
advection rate, and no significant in situ generation of heat. It therefore uses the following
equation to solve for temperature changes in time and space:
𝜕𝑇
= ∇ ∙ (𝜅∇𝑇) − ∇ ∙ (𝑣𝑇)
𝜕𝑡
(1)
where T is temperature, t is time, κ is the diffusivity, and v is the velocity. ∇ represents the
gradient and ∇ ∙ is the divergence. To solve this numerically in 2D, we use a finite-difference
technique. We run the model to steady-state for different velocities and vertical zones of flow (as
noted above).
Lastly, we estimate steady-state BSR depth using standard gas-hydrate phase boundary
methods, assuming pure Structure I methane hydrate, hydrostatic pressure, and fresh water pore
fluid [Sloan and Koh, 2008]. To show the effects of lateral groundwater flow on the GHSZ we
note how the BSR depth varies at a depth of 400 mbsl, depending on flow rate and the vertical
extent of the flow (Figure 7).
Model results show that flow rates of ~0.2 m/yr can explain our observed BSR anomaly
only if the vertical extent of the cold water flow is at least 1,600 m thick. Flow rates of ~0.5 m/yr
will also explain the observed BSR depth anomaly, but this also requires a vertical flow zone
~1,100 m thick (Figure 7). Any flow rate <1.3 m/yr in a zone of flow 600 m thick will not
promote hydrate stability. Additionally, flow rates of >0.3 m/yr in a zone of flow 1,600 m thick
and >0.8 m/yr with a zone of flow 1,100 m thick can fully explain the observed hydrate anomaly
as seen in line 730. Currently, however, there is no evidence such significant lateral flow exists.
Additionally, if such flows exist, we would expect to observe very low measured heat flow
values across the region (which we do not). Hydrate formation along the upper feather edge of
the margin is promoted only when the fluid flux is high enough to push the warmer waters
already present under the continental shelf out of the system, leaving only the cool, terrestrially
derived water. If flow is low enough (evident in all cases ≤.1 m/s) advection will actually reduce
hydrate stability instead of promote it. This is because the slower flowing fluids have time to
heat up and transport warmer fluids toward the seafloor.
The cases presented here therefore represent extreme circumstances in which a constant
temperature of 0 oC is continuously present down to great depths (up to 1,800 mbsl) at the
predicted edge of permafrost (30 km from shore [Brothers et al., 2012]). We currently know of
no physical system that is able to produce such an anomaly. Additionally, we assume that the
lateral fluid flow is constant across the entire margin. Even when we employ these extreme
assumptions to increase the depth of hydrate stability along the margin, the model predicts that
flow rates much larger than 0.1 m/yr [Deming et al., 1992] are necessary to explain the observed
GHSZ anomaly.
In sum, these results show that SGD can promote hydrate stability, but only where
groundwater is cold (~0 oC), at significant (>1000 m) depths, and flow is high (>0.2 m/yr). If we
assume the flow rate predicted by Deming et al. [1992] (~0.1 m/yr) is accurate, we are unable to
promote hydrate stability unless our flow zone extends into the basement, or our cold water
boundary condition extends beyond the edge of predicted permafrost [Brothers et al., 2012].
Both situations appear unlikely, however future studies analyzing temperature and groundwater
flow in this region could help further address the role of fluids in promoting or reducing hydrate
stability in this region.
References
Brothers, L. L., P. E. Hart, and C. D. Ruppel (2012), Minimum distribution of subsea ice‐bearing
permafrost on the US Beaufort Sea continental shelf, Geophysical Research Letters, 39(15).
Deming, D., J. H. Sass, A. H. Lachenbruch, and R. F. De Rito (1992), Heat flow and subsurface
temperature as evidence for basin-scale ground-water flow, North Slope of Alaska, Geological
Society of America Bulletin, 104, 528 - 542.
Houseknecht, D. W., and K. J. Bird (2011), Geology and petroleum potential of the rifted margins of the
Canada Basin, Geological Society, London, Memoirs, 35(1), 509-526.
Osterkamp, T., and M. Payne (1981), Estimates of permafrost thickness from well logs in northern
Alaska, Cold Regions Science and Technology, 5(1), 13-27.
Sloan, E. D., and C. A. Koh (2008), Clathrate hydrates of natural gases, 3rd ed., CRC Press, Boca Raton, FL.
Figure Caption
Figure 7. Plot of lateral fluid flow effects on the thickness of the upper slope GHSZ for Line
730. Different colors represent different flow zone thicknesses. The thickness of the observed
GHSZ thickness (300 m) and the diffusive model predicted GHSZ thickness (140 m) are plotted
to emphasize the flow effects.