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 Regions of warm, thin, discontinuous permafrost have been observed to be experiencing rapid changes in lake and pond dynamics in recent decades. Even though surface water and groundwater interactions are thought to play a significant role in heat transport in these regions, the effect of these interactions on permafrost remains largely unquantified. In order to examine the influence of groundwater flow on permafrost dynamics, we modeled the development of a sub-lake talik under permafrost conditions similar to those observed in the southern-central Seward Peninsula region of Alaska using a numerical solution that couples heat transport and groundwater flow, including the effect of water phase changes on soil permeability and latent heat content. A comparison of model simulations, with and without near surface subpermafrost groundwater flow, indicates that stable permafrost thicknesses are 2 to 5 times greater in the absence of groundwater flow. Simulations examining the thermal influence of lakes on underlying permafrost suggest that a through-going talik can develop in a matter of decades and that the incorporation of advective heat transport reduces the time to complete loss of ice beneath the lake by half, relative to heat transport by conduction alone. This work presents the first quantitative assessment of the rates of sub-lake permafrost response to thermal disturbances, such as talik development, in systems with near-surface groundwater flow. The results highlight the importance of coupled thermal and hydrologic processes on discontinuous permafrost dynamics.
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 To examine both the rate of talik development and the role of advective heat transport in thawing warm, thin permafrost we conducted numerical simulations using the Arctic Hydrology model (ARCHY). We first compared stable permafrost thicknesses in the presence and absence of a subpermafrost groundwater flow system. We then conducted simulations to evaluate the time for a sub-lake talik to completely thaw permafrost by only conductive heat transport versus a system with subpermafrost groundwater flow and flow within thawing permafrost. We further compared the influence of vertical water flow through a talik under field conditions where only gravity and density differences drive flow, versus vertical flow driven by a static head equivalent to a constant depth of standing lake water.
 The ARCHY model simulates saturated and unsaturated reactive mass and energy transport in porous, permeable media in one, two, or three dimensions and time. It is a general purpose, highly flexible multi-phase, multi-component flow and transport solver, allowing a variety of boundary conditions and heterogeneity in properties. It is similar to SUTRA-ICE [McKenzie et al., 2007] for saturated flow and ice/water phase changes, and MarsFlo [Painter, 2011] for both saturated and unsaturated flow capability with ice/water phase changes, but ARCHY also has the ability to transport solutes such as salts (which affect melt temperature and brine formation), organics and volatiles, with microbial activity. Properties such as porosity and permeability can vary spatially and even temporally. Thermal conductivity and specific heat are volume weighted averages of the individual conductivities and specific heats of soil grains, water, ice and air, which in turn depend on temperature. Fluid density and viscosity are functions of temperature and solute content. Fluid and matrix compressibility are also included.
 ARCHY is a merger of the previously described and applied models MAGHNUM [Travis et al., 2003; Travis and Schubert, 2005; Palguta et al., 2010; Barnhart et al., 2010] and TRAMP [Travis and Rosenberg, 1997]. ARCHY applies an integrated finite difference algorithm to the governing partial differential equations. Intrinsic permeability is harmonically averaged at interfaces between grid cells. Ice fraction is included in the harmonic averaging. Relative permeabilities are donor-differenced at interfaces. Porosity and permeability can be dependent on fluid pressure. Darcy's law is used as a good approximation for the low Reynolds number (Re < 1) flows typical of soil systems, although a Forchheimer formulation is provided for very high permeability environments. ARCHY assumes that ice melts or freezes over a narrow temperature range. A linear dependence on temperature within this narrow range (typically 0.5 C) allows a simple linear form to the thermal transport difference equation without sacrificing accuracy. An important aspect of freezing and thawing is the difference in density between ice and water, with a resulting volume change. This volume change creates a source/sink for the fluid pressure solution.
 The Yoshikawa and Hinzman  study of disappearing lakes near Council, Alaska on the Seward Peninsula is the most concrete example of permafrost lakes draining due to complete thaw of sub-lake permafrost. We configured our ARCHY simulations based on the data from this study and other relevant sources regarding climatic, geothermal, and hydrological conditions of the Seward Peninsula region. We performed a series of one- and two-dimensional simulations to evaluate the effect of groundwater flow on permafrost thickness and rates of sub-lake talik development. The goal of the one-dimensional simulations was to determine stable permafrost thicknesses given our model parameterizations in the absence of a shallow groundwater flow system. At the top of the model domain we set a constant temperature −2°C based on mean annual air temperatures reported for the region [Yoshikawa and Hinzman, 2003; Fraver, 2003]. At the base of the model we prescribed a constant heat flux of 80 mW/m2 [Williams et al., 2006].
 To model the effect of groundwater flow and talik development we expanded the simulations to two-dimensions. We performed simulations with 200 m wide model domains that were 30 and 60 m deep. The 30 m deep simulations were based on geological cross-sections presented by Yoshikawa and Hinzman  with the upper 19 m of unconsolidated materials representing silty sands, underlain by a 2 m thick gravel zone with high hydraulic permeability, that in turn was underlain by low permeability bedrock (Table 1). The entire model domain was saturated at all times. Ice contents of each layer were equivalent to the porosities of the layers when the materials are in a frozen state. The 60 m deep simulation was run to examine the sensitivity of thaw rates to permafrost thickness, and had an additional 30 m of unconsolidated materials above the high hydraulic permeability zone. Model grid spacing was the finest across the high hydraulic permeability zone and under the lake, where we expected the greatest spatial and temporal gradients in heat and fluid fluxes. Vertically, minimum cell heights were 0.2 m and expanded exponentially to a maximum of ∼2 m at the upper and lower boundaries. Horizontally, the minimum cell width was 0.5 m and cells expanded exponentially to ∼10 m at the lateral boundaries.
k - hydraulic permeability; n - porosity/ice content when frozen; Kt - thermal conductivity of solid matrix; Cp - specific heat capacity of solid matrix; ρs - solid matrix density.
Unconsolidated Material (Silty Sand)
9.87 × 10−13
High Permeability Zone (Gravel)
9.87 × 10−10
9.87 × 10−33
 In both domains, the upper and lower thermal boundary conditions were the same as described above. A pressure gradient of 2000 Pa was applied across the high permeability zone to drive a regional subpermafrost groundwater flow. This value is consistent with the topographic gradient of 0.001 for the relatively flat wetland area near Council, Alaska [Fraver, 2003]. We set the temperature of water entering the high permeability zone to 2°C [Williams, 1970].
 Prior to conducting model runs with lakes, we performed simulations to obtain a stable thickness of permafrost in the presence of subpermafrost groundwater flow. For the 30 m deep model domain we considered the permafrost thickness stable when the temperature field exhibited no changes over 25 years of simulated time. The 60 m deep simulation was considered stable when the mean and maximum temperature variations across the model domain were <0.001 and 0.01°C, respectively, over 10 years. The steady state temperature fields for these conditions were then used as the initial conditions for simulations with lakes. To simulate a lake with a talik, we imposed a constant mean annual temperature of 4°C across the middle 60 m of the top of the model domain based on mean annual lake water temperatures used in prior lake studies ranging from 1.5 to 4.8°C [Burn, 2002; Ling and Zhang, 2003; West and Plug, 2008].
 We conducted three sets of simulations for each stable permafrost thickness. Scenario 1 examined conductive heat transport only, without subpermafrost groundwater flow; for these simulations the model domain was truncated in thickness to match the depth of permafrost from the steady state simulations and a linear temperature profile from 0°C at the base to −2°C at the ground surface was applied as an initial condition. Scenarios 2 and 3 used the full model domains with the subpermafrost groundwater flow. In Scenario 2, only gravity and fluid density gradients drove vertical flow. For Scenario 3 an additional constant pressure, equivalent to 2.5 m of standing water, was applied across the portion of the upper boundary corresponding to the simulated lake.
 Given a constant mean annual surface temperature of −2°C at the upper boundary and a constant heat flux of 80 mW/m2 at the base, the one-dimensional model simulation resulted in a steady state permafrost thickness of 78 m. For this simulation the material and thermal properties of the upper 30 m of the model domain were identical to those listed in Table 1; the domain was increased to 200 m in thickness by adding 170 m with the same properties of the bedrock zone (Table 1) to ensure that it would be thicker than the total depth of permafrost. Varying thermal conductivity (Kt) from 1 to 4 W/m/K and porosity (n) from 0.2 to 0.4 in the uppermost layer resulted in permafrost thicknesses that ranged from 65 (Kt = 1 W/m/K and n = 0.20) to 84 m (Kt = 4 W/m/K and n = 0.20 and n = 0.40).
 In the two-dimensional simulations without a lake, permafrost thicknesses stabilized to 16 and 37 m for the 30 and 60 m deep simulations, respectively. A permafrost thickness of 16 m is close to the low end of the 20 m to 60 m range in permafrost thickness reported by Yoshikawa and Hinzman  for the Council, AK area and very consistent with their geophysical profiles of permafrost around the drained pond study site. At 2 m depth, our modeled temperatures of −1.7°C (30 m deep) and −1.8°C (60 m deep) were colder than the −0.35°C reported by Yoshikawa and Hinzman , but closer to the −1.2°C August temperatures reported for a borehole in Nome, Alaska (Cooperative Arctic Data and Information Service (CADIS)). The 20 m Nome borehole temperature of −1°C was very close to the −0.9°C modeled in our 60 m deep simulation. To test the validity in neglecting a surface organic layer, we performed a two-dimensional simulation with a 0.5 m thick organic layer (Kt = 0.24 W/m/K, n = 0.50, and specific heat (Cp) = 1920 J/kg/K). The addition of this layer resulted in a temperature increase of 0.03°C at the 0.5 m depth, an increase of 0.01°C at 16 m, and a decrease in permafrost thickness of ∼7 cm compared to the simulation without such a layer.
 Flow velocities within the high hydraulic permeability zone were 0.85 and 0.86 m/day for the 30 and 60 m deep simulations, respectively. The temperature of the inflowing groundwater within this zone decreased to 1°C within the first 10 m model cell and then decreased linearly to 0.5°C and 0.9°C at the down-gradient boundary in the 30 m and 60 m deep simulations, respectively.
 When a constant temperature of 4°C was imposed across the middle 60 m of the upper boundary, complete thawing of permafrost beneath this zone occurred most rapidly in the simulations with subpermafrost groundwater flow and an imposed pressure equivalent to 2.5 m of standing water (Scenario 3) (Figure 1 and Table 2). It took 15 years of simulated time for a complete vertical section of the model to reach temperatures >0°C (Figure 1a). Scenario 2 took 3% longer and in Scenario 1 (conductive heat transport only) it took 40% longer (Table 2). For the simulations with 37 m of permafrost, Scenario 3 thawed permafrost most rapidly, taking 85 years (Figure 2a and Table 2). The difference between Scenario 2 and 3 was proportionally (∼4%) similar to the thinner permafrost simulation. Scenario 1 took 40% longer to heat the ground above 0°C beneath the lake.
Table 2. Model Results: Times to >0°C and Complete Ice Loss at Base of Permafrosta
Time to >0°C (Years)
Time to Complete Ice Loss (Years)
Scenario 1 - Conduction only, no subpermafrost groundwater flow; Scenario 2 - Conduction and advection, subpermafrost groundwater flow, vertical pressure from gravity and density only; Scenario 3 - Conduction and advection, subpermafrost groundwater flow, additional vertical pressure gradient from 2.5 m of standing water.
Permafrost Thickness - 16 m
Permafrost Thickness - 37 m
 In the ARCHY model, the phase transition from water to ice occurs across a temperature range, a phenomenon documented in natural materials [Williams and Smith, 1989] and incorporated into prior permafrost modeling studies [Ling and Zhang, 2003; McKenzie et al., 2007; West and Plug, 2008; Painter, 2011]. In our simulations the water-ice transition was allowed to occur over a 0.5°C range (0°C ± 0.25°C). As a result, only ∼50% of the pore-ice within the subsurface matrix had melted when the temperature reached 0°C. The time to completely melt all of the ice contained within the subsurface matrix became a function of the rate that heat was delivered to the progressively thawing matrix (Table 2). This rate of heat flow increased with advective transport. For Scenario 3, it took an additional 2 to 5% longer to melt all of the pore ice after reaching a temperature of 0°C. In the absence of a strong vertical pressure gradient (Scenario 2) there was a 30% (16 m permafrost) to 40% (37 m permafrost) difference in times to complete ice thaw. In Scenario 1, conduction-only, complete loss of ice took 44% longer than the time to cross the 0°C isotherm at the base of the permafrost.
 In the absence of subpermafrost groundwater flow, permafrost thicknesses were up to 5 times greater than the stable thickness with groundwater flow 20 m below the ground surface, and 2 times greater when active groundwater flow was 50 m below the ground surface. In our simulations, permafrost thicknesses were more sensitive to the presence of near surface groundwater flow than to changes in the thermal properties of the upper-most layer in the model. The model proved very sensitive to the heat flux transmitted through the high hydraulic permeability layer. In simulations where this zone was narrower or the flow rate was lower (a reduction in the lateral pressure gradient by one half, for example), cooling from the upper boundary was capable of freezing the water in the high hydraulic permeability layer, at which point the entire model domain froze. An implication of this result is that if climatic warming leads to greater surface and subsurface connectivity and/or warmer groundwater, a substantial reduction in permafrost thicknesses may occur.
 In the presence of a thermal disturbance, such as a talik beneath a lake, permafrost with a shallow subpermafrost groundwater system appears more sensitive to thawing. For permafrost of the same thicknesses, it took ∼40% longer for heat transferred by conduction-only to thaw through permafrost than when subpermafrost groundwater and advection supplied heat to the subsurface. Depending on permafrost thickness, our modeling suggests that through-going sub-lake taliks can develop over the course of a few to several decades in regions of warm, thin permafrost. These results are consistent with observations of lake drainage in response to sub-lake loss of permafrost in recent decades [Yoshikawa and Hinzman, 2003; Hinzman et al., 2005b].
 Finally, the time difference between the ground reaching 0°C and the melting of all of the pore ice highlights the role of advective heat transport in creating hydrological connectivity and thawing permafrost. In the simulations with flow driven by 2.5 m of head on part of the upper boundary, all of the pore ice beneath the lake melted almost twice as fast as in simulations having heat transport by conductive processes only. These differences illustrate the sensitivity of permafrost systems to evolving hydrologic connectivity and subsurface heat transport processes.
 This research was supported by the U.S. Department of Energy through the LANL/LDRD Program. ARCHY model development was supported by the Department of Energy Office of Science, Office of Biological and Environmental Research. Detailed and thoughtful reviews were provided by Guido Grosse and an anonymous reviewer.
 The Editor thanks Guido Grosse and an anonymous reviewer for their assistance in evaluating this paper.