Modeling study of talik freeze-up and permafrost response under drained thaw lakes on the Alaskan Arctic Coastal Plain

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2003jd003886, 2004 Modeling study of talik freeze-up and permafrost response under drained thaw lakes on the Alaskan Arctic Coastal Plain Feng Ling 1 and Tingjun Zhang National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA Received 19 June 2003; revised 22 October 2003; accepted 29 October 2003; published 15 January [1] Numerical simulations were conducted to investigate the long-term impact of thaw lake drainage on the thermal regime of ground under and around drained thaw lakes on the Alaskan Arctic Coastal Plain. The numerical model used in this study is a twodimensional unsteady finite element model for heat transfer with phase change under a cylindrical coordinate system. The initial conditions are the simulated ground thermal regime and talik thickness data at year 3000 under a thaw lake with long-term mean lake bottom temperatures of 1.0, 2.0, and 3.0 C near Barrow, Alaska. The simulated results indicate that lake drainage leads to a rapid freeze-up of talik and a substantial decrease in permafrost temperatures under the former lake bottom. The initial ground temperature conditions have significant influence not only on the talik freeze-up time, but also on the permafrost temperature decrease processes. After thaw lake drainage, taliks with thicknesses of 28, 43, and 53 m under the lake will freeze-up completely by 40, 106, and 157 years, and the corresponding ratios of upward and downward freeze-up depths for the three simulation cases are 1: 8.0, 1: 7.6, and 1: 6.1, respectively. After completion of talik freeze-up, permafrost temperatures still decreased with time and gradually reached a relatively stable value, depending on the initial ground temperature and the distance to the former lake bottom. INDEX TERMS: 1823 Hydrology: Frozen ground; 1863 Hydrology: Snow and ice (1827); 1829 Hydrology: Groundwater hydrology; KEYWORDS: permafrost, talik, thaw lake, Alaska, numerical modeling Citation: Ling, F., and T. Zhang (2004), Modeling study of talik freeze-up and permafrost response under drained thaw lakes on the Alaskan Arctic Coastal Plain, J. Geophys. Res., 109,, doi: /2003jd Introduction [2] One of the most obvious manifestations of the hydrological system at work in the Arctic is the vast number of thaw lakes that occur in tundra regions. On the Alaskan Arctic Coastal Plain, thaw lakes comprise more than 40% of the surface area in some locations [Sellmann et al., 1975a, 1975b], and along the western Arctic coast of Canada, including the Tuktoyaktuk Peninsula and Richards Island, thaw lakes cover about 20% to 40% of the total surface area [Mackay, 1988, 1997; Mackay and Burn, 2002]. The majority of these lakes are thermokarst features that owe their origin to permafrost thawing [Hopkins, 1949; Black and Barksdale, 1949; Sellmann et al., 1975a; Burn and Smith, 1990; Mackay, 1997]. These lakes are thought to migrate slowly, and have little potential for increasing their depth, but are known to drain rapidly [Brewer, 1958b; Lachenbruch et al., 1962; Sellmann et al., 1975a, 1975b; Washburn, 1980; Mackay, 1988, 1997, 1999; Brewer et al., 1 Also at Department of Computer Science, Zhaoqing University, Zhaoqing, Guangdong, China. Copyright 2004 by the American Geophysical Union /04/2003JD ; Mackay and Burn, 2002]. Consequently, they are the primary mechanism of regional hydrological systems and tundra landscape modification [Black and Barksdale, 1949; Sellmann et al., 1975a; Kozlenko and Jeffries, 2000; Burn, 2002]. [3] Natural lake drainage along the western Arctic coast of Canada and the adjoining north coast of Alaska has been an ongoing process for thousands of years due to erosion of drainage channels through the ice-rich permafrost [Mackay, 1988, 1997]. Mackay [1988, 1999] and Mackay and Burn [2002] reported that thaw lakes drained at the rate of about two per year during the 36 years from 1950 to 1986 on the Tuktoyaktuk Peninsula in Canada; some draining partially, and others completely. Brewer et al. [1993] noted that at least 10 lakes drained on a section of the Alaskan Arctic Coastal Plain during the summer of When a thaw lake underlain by a talik drains, the exposed lake bottom is subject to the same cold climate as the surrounding tundra, and periglacial features begin to develop, the soft lake bottom sediments harden from water loss caused by drainage, evaporation, and freeze-thaw consolidation [Mackay, 1997], and new permafrost aggradation from downward freezing of the exposed lake bottom begins even in the first winter following drainage [Hopkins, 1949; Mackay, 1988]. In addition, permafrost 1of9

2 also begins to grow upward from the permafrost surface beneath the talik at a slower rate [Mackay, 1997]. Lake drainage results in permafrost highly variable in age, thickness, distribution, and variation [Mackay, 1997; Mackay and Burn, 2002]. [4] On August 13, 1978, a thaw lake about 600 m long and 350 m width was artificially drained as a first time field experiment on the growth of permafrost [Mackay, 1997]. In the years after lake drainage, direct observation and analysis have obtained data on permafrost aggradation, isotopes in the lake water, vegetation growth, active layer variation, lake bottom uplift, ice wedge cracking, the role of convective heat transfer from pore water expulsion in freezing soil, and the development of aggradational ice in lake bottom sediments [Mackay, 1997; Mackay and Burn, 2002] (C. R. Burn and M. M. Burgess, Illisarvik bibliography, available at illsarvik, 2000). This experiment provides otherwise unavailable insights into the spatial and temporal evolution of the ground thermal regime and talik dynamics, and improves our understanding of the role of thaw lakes as a focus for intense interaction and feedback between the land and the atmosphere in the Arctic. This experiment and the related studies also provide the basis for further studies on the long-term response of the thermal regime of ground under former thaw lakes to lake drainage in the Arctic. [5] A quantitative understanding of the role of thaw lakes in the Arctic hydrological system and landatmosphere interactions and feedbacks is critical to understanding how the global processes affect the Arctic environment, and how the Arctic hydrological processes affect the rest of the Earth. This is particularly important in view of predictions that the effects of global change will be amplified and experienced first in the Arctic [Intergovernmental Panel on Climate Change (IPCC), 1990, 1996]. In a previous paper [Ling and Zhang, 2003], based on studies of permafrost and thaw lakes at Barrow, Alaska, we investigated the long-term influence of shallow thaw lakes on the thermal regime of permafrost and talik development by using a two-dimensional heat transfer model with phase change under a cylindrical coordinate system. In this study, we use the simulated ground thermal regime and talik thickness data at year 3000 under a thaw lake with long-term mean lake bottom temperatures of 1.0, 2.0, and 3.0 C at Barrow as the initial conditions to model the talik freeze-up and permafrost response processes after lake drainage, and investigate the effect of initial ground temperature conditions under drained thaw lakes on the ground response. 2. Model Description [6] Thaw lakes on the Alaskan Arctic Coastal Plain are typically elliptical in shape [Black and Barksdale, 1949; Brewer, 1958b; Sellmann et al., 1975a]. Thus a two-dimensional model under a cylindrical coordinate system was developed and used to simulate the thermal regime of talik and permafrost under thaw lakes. Assuming there is no annular heat flow in the cylindrical coordinate system, the governing equations for the thermal regime of talik and Figure 1. Schematic illustration of analysis domain and boundary conditions for simulations. The upper boundary is set at a depth of 0.5 m below the ground surface on the shore and below the former lake bottom (3.0 m deep below the ground surface) off the shore. permafrost can be written in a unique form [Ling and Zhang, 2003]: 8 >< k ¼ þ ð0 < t < D; 0 < x < X ; 0 < r < RÞ ð1þ 8 >< C f W W C ¼ u C f þ L w r b >: T k f þ k u k f T k f C u T < T e T T e T T T e T > T e T < T e T ½T ðt e TÞŠ T e T T T e k u T > T e where the subscripts f and u indicate the frozen and unfrozen phases, respectively. T is temperature in C, t is time in seconds, r is the radius from the centerline of the lake in m, x is the depth from the ground surface downward in m, C is the volumetric heat capacity in J m 3 C 1, k is the thermal conductivity in W m 1 C 1, D is the simulation time after lake drainage in second, X and R are the total depth and radius of the analysis domain in m, T e is the freezing temperature and is set at 0 C, T is the width of the temperature interval in which the phase change occurs in C and is assumed to be 1.0 C for moist soils with fine solid size [Comini et al., 1974], L w is the mass specific latent heat of water in J kg 1, r b is the dry buck density of soil in kg m 3, W is the total water content percent of soil by mass, and W u is the unfrozen water content percent of soil by mass at the temperature T e T [Lunardini, 1981]. [7] On the basis of a previous study of the long-term influence of shallow thaw lakes on permafrost thermal regime and talik development on the Alaskan Arctic Coastal Plain [Ling and Zhang, 2003], the analysis domain for the present study consists of a drained thaw lake and corresponding area with the dimensions shown in Figure 1. Note that only half of the analysis domain is shown and modeled numerically due to the axial symmetric nature of the problem about the centerline of the lake. The radius and ð2þ ð3þ 2of9

3 depth of the analysis domain are chosen as R = 1000 m and X = 500 m. The radius and water depth of the former thaw lake are R 0 = 400 m and H 0 = 2.5 m. The upper boundary is set at a depth of 0.5 m below the ground surface on the shore and below the former lake bottom off the shore, because the active layer thickness in the Barrow area is near 0.5 m [Brown, 1965; Nakano and Brown, 1972; Zhang et al., 1997; Zhang and Stamnes, 1998; Hinkel et al., 2001; Hinkel and Nelson, 2003]. The lower boundary is set at 500 m below the ground surface, about 100 m below the permafrost base [Brewer, 1958a, 1958b; Lachenbruch and Marshall, 1969; Lachenbruch et al., 1982]. [8] The upper and lower boundary conditions are TðH; r; tþ ¼ T ps ðþ t ð0 < t < D; H ¼ H 0 þ 0:5; 0 < r < R 0 Þ ð4þ Tx ð 0 ; r; tþ ¼ T ps ðþ t ð0 < t < D; x 0 ¼ 0:5; R 0 r < RÞ X; r; t k ð Þ ¼ ð0 < t < D; x ¼ X ; 0 < r < RÞ ð6þ where H and x 0 are positions of upper boundary below the former lake bottom off the shore and below the ground surface on the shore, T ps is the mean temperature at the permafrost surface and T ps = 9.0 C in the Barrow area [Lachenbruch et al., 1962; Lachenbruch and Marshall, 1969]. q is the geothermal heat flux, and q = W m 2 at great depth on the North Slope of Alaska [Lachenbruch et al., 1982; Osterkamp and Gosink, 1991]. [9] The lateral boundary conditions are treated as zero heat flux boundary r; ¼ 0 ð0 < t < D; H 0 þ 0:5 < x < X ; r ¼ 0Þ r; tþ ¼ ð0 < t < D; 0:5 < x < X ; r ¼ RÞ ð8þ [10] Previous investigations of thaw lake age using radiocarbon dating at Barrow, Alaska, indicate that thaw lakes seldom exceed 3500 years in age [Brown, 1965; Carson, 1968]. Thus this study assumes that the modeled thaw lake drained completely 3000 years after its formation. Three initial temperature conditions, IC1, IC2, and IC3 as shown in Figure 2, are used in this study. The ground temperature fields are our simulated ground thermal regimes at year 3000 under a thaw lake with a depth of 2.5 m and a width of 400 m on the Alaskan Arctic Coastal Plain [Ling and Zhang, 2003]. The corresponding long-term mean lake bottom temperatures for the simulations of the three initial conditions are 1.0, 2.0, and 3.0 C, respectively. [11] The governing equations (1) (8) were solved using a finite element method [Huebner, 1975]. A time step of one day was used, with a total simulation period of 2000 years. The spatial step varies from 0.5 m to 25 m along the x axis direction; and from 5 m to 25 m along the r-axis direction. The soil types in the analysis domain and the soil physical and thermal parameters are derived from Ling and Zhang [2003]. The unfrozen water content of each soil type at the Figure 2. Simulated ground thermal regimes at year 3000 after the formation of a 400 m wide and 2.5 m deep thaw lake, with long-term mean annual lake bottom temperatures of (a) 1.0 C; (b) 2.0 C; and (c) 3.0 C, respectively. The ground temperature fields Initial Condition 1 (IC1), Initial Condition 2 (IC2), and Initial Condition 3 (IC3) are initial conditions for this study. end of phase change interval T e T was determined from Anderson and Tice [1972]. 3. Results 3.1. Talik Freeze-Up and Permafrost Response With IC1 [12] The vertical profiles of ground temperature along the lake center at different years (Figure 3) are drawn by using the simulated temperature values from the initial condition IC1 (Figure 2a). After lake drainage, ground temperature below the drained lake bottom decreased gradually with time because the upper boundary condition changed from close to 1.0 C to a mean permafrost surface temperature of 9.0 C. Ground temperature at a depth of 20 m, for instance, decreased from about 0.4 C for year 10 to about 0.5 C for year 30, about 4.0 C for year 100, and about 6.7 C for year 300. The magnitude of ground temperature decrease is greatest at the surface and reduces with depth. About 10 and 30 years after lake drainage, the depth of the talik table (the upper surface of talik) along the lake center 3of9

4 Figure 3. Simulated temperature profiles from initial condition IC1 for the ground along the lake center r =0 m at years 10, 30, 40, 100, 200, and 300 after lake drainage. had decreased from the upper boundary of 3.0 m to 16.4 m and 23.5 m, respectively. Only 40 years after lake drainage, the maximum ground temperature along the lake center had decreased to 0 C. Since permafrost is defined as ground that remains at a temperature of 0 C or below for at least two years [e.g., Osterkamp and Gosink, 1991; Mackay, 1997], by 40 years the 28 m thick talik beneath the drained lake bottom had become permafrost. [13] Previous studies indicate that the time required for the temperature profile of the ground to adjust to a new surface temperature after an instantaneous change, t c, can be estimated by [Lachenbruch et al., 1982; Osterkamp, 1983]: t c ¼ X 2 4D c where X is the depth of ground and D c is the ground thermal diffusivity. Using the soil types and physical properties of soil at Barrow, Alaska [Ling and Zhang, 2003], we calculated the thermal diffusivity to be m 2 year 1. Thus the temperature wave caused by lake drainage could propagate to as deep as 190 m approximately in about 300 years after lake drainage, but the calculated result here in Figure 3 shows that the maximum depth along the lake center affected by the cooling effect of lake drainage was approximately 70 m at year 300. This is because the phase change occurred in the temperature interval from 1.0 to 0 C. During refreezing of the talik and cooling of the permafrost, latent heat was liberated and the frost penetration was strongly delayed. ð9þ [14] Figure 4 shows variations in ground temperature with time at depths of 15, 25, 35, and 60 m along the drained lake center to investigate the long-term response of talik and permafrost to lake drainage. Ground temperatures at depths of 15, 25, 35, and 60 m decreased from 0.5, 0.1, 0.2 and 0.7 C at beginning to 8.5, 8.1, 7.6 and 6.6 C, respectively, at year Theoretically, the decrease in ground temperature would go on indefinitely, but the magnitude will gradually diminish. In order to evaluate the longterm processes in ground temperature decrease after lake drainage, a parameter of the quasi-equilibrium time, defined as the time at which the ground temperature difference between two successive simulation time steps is less than or equal to C, is used. The quasi-equilibrium time for ground at depths of 15, 25, 35, and 60 m along the lake center is 767, 866, 901, and 1026 years, respectively. Figure 4 also shows that the ground temperature at 25 and 35 m increased slightly before it decreased. This is because the relatively high temperature wave propagated from the upper zone of talik can raise ground temperature in the lower zone of talik and permafrost near talik base after lake drainage, but the magnitude and time are very limited, depending on the depths. [15] Figure 5 presents the simulated horizontal profiles of ground temperature from IC1 along x = 25, 50, and 100 m at Figure 4. Variations in ground temperature with time at depths of 15, 25, 35, and 60 m along the lake center after lake drainage. The initial condition used is IC1. Figure 5. Simulated ground temperature profiles along depth (a) x =25m;(b)x = 50 m; and (c) x = 100 m after lake drainage for 50, 200, 400, and 600 years. The initial condition used is IC1. 4of9

5 Figure 6. Simulated ground temperature decreases from initial condition IC1 at (a) year 200; (b) year 400; (c) year 600; and (d) year 1000 after lake drainage. years 50, 200, 400, and 600 after lake drainage. Ground temperature under the bottom of a drained thaw lake decrease with time. By contrast, the ground temperature under the ground surface (400 < r < 1000 in Figure 1) decreases very little after lake drainage, particularly when the horizontal distance to the lake center is greater than 600 m. This is not surprising as lake drainage only changes the upper temperature boundary condition on the former lake bottom from 1.0 C to 9.0 C; the upper boundary condition on the lake shore remains 9.0 C. [16] At a depth of 50 m in Figure 5b, ground temperatures at years 50 and 200 are almost the same at a horizontal distance to the lake center of less than about 160 m, while ground temperatures at a horizontal distance to the lake center of between 160 and 500 m are significantly different, with a maximum difference of 2.6 C. This can be explained as follows: Ground temperature at a certain depth is highest near the lake center and decreases gradually with distance from the lake center to the lake shore (Figure 2a). Ground temperatures within a horizontal distance of about 260 m from the lake center are higher than the defined lowest phase change temperature of 1.0 C at year 50. When the cold temperature waves caused by lake drainage propagated to a depth of 50 m, the thermal decrease was strongly attenuated by the release of latent heat of fusion from the phase change, and downward progress of the freezing front was strongly retarded. While ground temperatures at a horizontal distance from the lake center of between 260 and 500 m at a depth of 50 m, were less than 1.0 C, the heat transfer in permafrost was dominated by conduction since the phase change process had completed and most of the water in the soil had been converted to ice. Thus the rate of ground temperature decrease near the lake shore was greater than that near the lake center. As a result, the ground temperature decrease started from the lake shore at a certain depth, and gradually to the lake center. The ground cooling processes with phase change can also be seen in the ground temperature profiles at a depth of 100 m for years 50 to 200 and 400 (Figure 5c). The ground temperature cooling processes without phase change can be seen in the ground temperature profiles at a depth of 25 m for years 200 to 400 and to 600 (Figure 5a), at a depth of 50 m for years 400 to 600 (Figure 5b), and at a depth of 100 m for years 400 to 600 (Figure 5c). [17] Figure 6 shows the magnitude of simulated ground temperature decreases at years 200, 400, 600, and 1000 from initial condition IC1 after lake drainage. As described above, if phase change is involved, talik and permafrost temperature decreases start near the lake shore at a certain depth, and gradually to the lake center, due to the latent heat release. Consequently, the magnitude of the ground temperature decrease was greatest near the lake shore, and decreased with distance from the lake shore to the lake center in the first several hundred years. For example, the maximum depths at which ground temperature decreased by more than 1.0 C along r = 0 and r = 350 at year 200 are 43 and 95 m (Figure 6a); at year 400 are 77 and 172 m (Figure 6b); and at year 600 are 120 and 206 m (Figure 6c). After the completion of phase change, energy was transferred more rapidly near the lake center than near the lake shore at a certain depth, since the ground temperature gradient along the lake center is higher than along the lake shore. The maximum depth at which the ground temperature decrease is more than 1.0 C along r = 0 and r = 350 at year 1000 is about 260 m (Figure 6d). The isotherms in Figure 6d show that 1000 years after the lake drainage, temperature decreases of more than 0.5 C occur as far as 500 m from the lake center, and more than 280 m below the ground surface Influence of Initial Temperature Conditions [18] Figure 7 compares the simulated ground thermal regimes with initial conditions IC1, IC2, and IC3 at years 35, 100, 150, 200, and 1200 after lake drainage. After lake drainage, talik volumes reduced rapidly and permafrost 5of9

6 Figure 7. Comparison of simulated ground thermal regimes from initial conditions IC1, IC2, and IC3 at years 35, 100, 150, 200, and 1200 after lake drainage. temperatures decreased gradually with time. Although taliks in the initial conditions IC1, IC2, and IC3 have frozen completely within 200 years after lake drainage, the simulated ground thermal regimes from IC1, IC2, and IC3 still have obvious differences in year This indicates that the differences in initial ground temperature have significant influence, not only on the talik freeze-up time, but also on the permafrost temperature decrease after lake drainage. To better investigate the long-term response of the thermal regime of ground with different initial conditions to lake drainage, we calculated the quasi-equilibrium times for ground at different depths under the former lake (Table 1). The quasi-equilibrium time was strongly affected by the initial ground temperature conditions and the depth. [19] The talik downward freezing processes with initial conditions IC1, IC2, and IC3 in the first 40 years after lake drainage are shown in Figure 8 to further reveal the influence of the initial temperature conditions on the talik freeze-up process. The study chooses the period of the first 40 years because the talik in IC1 has frozen completely in 6of9

7 Table 1. The Quasi-Equilibrium Times (year) for Ground at Different Depths With Different Initial Conditions After Lake Drainage Depths Along the Initial Conditions Lake Center, m IC1 IC2 IC the 40th year after lake drainage (Figure 3). As the former lake bottom temperature changed to 9.0 C from 1.0, 2.0, and 3.0 C, respectively, talik thickness decreased downward with time. The talik freeze-up rates were clearly associated with the initial ground temperatures. Forty years after lake drainage, the talik table had deepened from the upper boundary of 3.0 m to as deep as 24.9, 23.9, and 23.0 m for IC1, IC2, and IC3. From the simulated talik thicknesses, freeze-up times, and the maximum downward frozen depths from initial conditions IC1, IC2, and IC3 (Table 2), the downward and upward talik freeze-up rates differ greatly for each case. The ratios of simulated upward and downward freeze-up thicknesses from IC1, IC2, and IC3 are 1: 8.0, 1: 7.6, and 1: 6.1, respectively, because the ground temperature gradient at the talik base (the lower surface of talik) is much smaller than that at the talik table. Furthermore, the talik in the upper zone is also an effective heat source for the ground near the talik base. [20] Figure 9 presents the simulated talik frozen depth increases along lake center for every 20-year period for initial conditions IC1, IC2, and IC3 during the first 100 years after lake drainage. Because of differences in initial temperature conditions, the talik frozen depth increase for IC1 was the greatest and IC3 was the lowest in the first 20-year period after the former lake bottom temperature changed to 9.0 C from 1.0, 2.0, and 3.0 C. Increases in the talik frozen depth will result in decreases in the ground temperature gradient at the talik table; thus the rate of the downward freezing front progress and the talik frozen depth increase will decrease. For this reason, the increase in talik frozen depth for each simulation case was the highest in the first 20-year period, and decreased significantly in the following 20-year periods. The talik frozen depth increases in the second 20-year period for IC1, Table 2. Simulated Talik Thicknesses, Freeze-up Times, and the Maximum Downward Frozen Depth From Different Initial Conditions After Lake Drainage Initial condition IC1 IC2 IC3 Thickness, m Freeze-up time, year Maximum downward frozen depth, m IC2, and IC3 are 4.9, 6.1, and 5.9 m, respectively; only 28.7%, 41.0%, and 42.8% of the talik frozen depth increases in the first 20-year period. For the same reason, the talik depth increase for IC1 was less than the talik depth increase in the second 20-year period, although it was greater than the talik depth increase for IC2 in the first 20-year period. Similarly, the talik frozen depth increase for IC2 was greater than the talik frozen depth increase for IC3 in the first, second, and third 20-year periods, but was less than the talik frozen depth increase for IC3 in the fourth and fifth 20-year periods. [21] Figure 10 shows variations in ground temperature at talik base at different points along the lake center for IC1, IC2, and IC3 over a time period of 2000 years after lake drainage. As described previously, the temperature gradient at the talik base is small during the talik freeze-up period, due to the effective heat source effect of the upper talik temperature. Therefore ground temperatures at the talik base stayed at 0.0 C in the first several years, depending on the depth, and then dropped with time. The calculated results indicate that the quasi-equilibrium times for ground at points (x = 28, r =0) with IC1, (x = 43, r = 0) with IC2, and (x = 53, r = 0) with IC3 are 879, 1210, and 1538 years, respectively. 4. Discussion [22] Natural drainage of thaw lakes significantly disturbs the permafrost thermal regime, lake dominated tundra landscapes, and the regional hydrological system in the Arctic. Although the talik freeze-up process and the permafrost response after thaw lake drainage have now been studied through a numerical modeling approach, the interaction between climate change and thaw lake drainage are still not clear, owing to the complex interactions between climate, permafrost, and hydrology [Marsh and Neumann, 2001]. Rapid lake drainage is usually associated with the erosion of a channel along interconnecting ice wedge systems [Mackay, 1988]. An increase in air temperature Figure 8. Comparison of simulated time series of talik downward freezing processes from initial conditions IC1, IC2, and IC3 in the first 40 years after lake drainage. Figure 9. Simulated talik frozen depth increase along lake center for every 20-year period during the first 100 years from initial conditions IC1, IC2, and IC3. 7of9

8 elliptical shape, the contributions of convective heat transfer and unfrozen water migration in the unfrozen and frozen ground were not included. In order to simulate the talik freeze-up and permafrost temperature decrease processes more accurately, a two-dimensional conductive-convective heat transfer model under a cylindrical coordinate system, with convective heat transfer and unfrozen water migration factors, should be developed. Figure 10. Simulated time series of ground temperature at talik bases from initial conditions IC1, IC2, and IC3 along the lake center after lake drainage. may lead to deepening of the active layer and increased formation of thaw lakes, and warmer air temperatures and increased snowfall may limit ice wedge cracking, thus diminishing lake drainage. However, changes in the lake water balance with an increase in precipitation would result in more cases of lakes overtopping the ice-wedge system, thus increasing the rate of lake drainage [Marsh and Neumann, 2001]. Brewer et al. [1993] described the drainage of ten lakes in the Alaskan Arctic Coastal Plain during the summer of 1989, a warmer and wetter than normal summer based on the weather record. They suggested that the drainage of these lakes was due primarily to the increased precipitation, resulting in higher water levels, and that a warmer than normal summer was not an important factor. Marsh and Neumann [2001] reported the drainage of the Trail Valley Creek lake, about 50 km northwest of Inuvik, Canada, also occurred naturally in August 1989, a summer that was the warmest on record, but with near normal precipitation. Drainage was preceded by a large rain event. Further studies are needed to better investigate the relationship between climate change and lake drainage. [23] This study indicates that the developed taliks with thicknesses of 28, 43, and 53 m will refreeze completely by 40, 106, and 157 years, respectively, after lake drainage. These results, however, are subject to a caveat. Previous studies show that although most saline groundwater may be derived from marine sediments at depth along the western Arctic coast of Canada [Hivon and Sego, 1992], permafrost growth in sands can also result in saline groundwater [Mackay, 1997]. The Illisarvik Lake drainage experiment on the growth of permafrost [Mackay, 1997] indicates that when pore water expulsion and groundwater flow are involved, the rate of permafrost growth has been dependent, to a considerable degree, upon convective heat transfer from groundwater flow. The permafrost growth is fast and cannot be explained by conventional one-dimensional conductive heat transfer model [Mackay, 1997]. Also, because the unfrozen water films attached to the surface of soil particles in frozen soils allow water to move in the same direction as heat flow, from warmer to colder regions [Hoekstra, 1966; Perfect and Williams, 1980], this can play an important role in talik freeze-up and permafrost cooling. The model used here is a two-dimensional heat transfer model with phase change. Although the model was developed under a cylindrical coordinate system to better describe the thaw lake 5. Summary [24] A two-dimensional unsteady finite element model for heat transfer with phase change, under a cylindrical coordinate system was used to simulate the long-term impact of thaw lake drainage on talik freeze-up and permafrost response on the Alaskan Arctic Coastal Plain. Three simulation cases were carried out to investigate the response of ground temperature under the former thaw lake to lake drainage. The influence of initial ground temperature conditions on talik freeze-up and ground temperature decrease processes also were investigated. [25] Shallow thaw lakes are clearly conduits for significant, but inadequately quantified, heat exchange between the atmosphere and the land. Lake drainage strongly decreases the temperature of ground under the former lake. The developed taliks with thicknesses of 28, 43, and 53 m under a thaw lake with lake bottom temperatures of 1.0, 2.0, and 3.0 C for 3000 years will freeze-up completely by 40, 106, and 157 years after lake drainage. The downward talik freeze-up rate is much faster than the upward one. [26] During talik freeze-up and permafrost temperature decrease, the release of the latent heat of fusion caused by phase change acts to retard the penetration of the freezing front from the talik table and the talik base. As a result, talik and permafrost temperature decrease started from the ground near the lake shore and gradually to the lake center at a certain depth. The differences in initial ground temperature have significant influence not only on the talik freezeup time, but also on the permafrost temperature decrease. [27] The rates of downward and upward talik freeze-up can be strongly affected by the convective heat transfer if pore water expulsion and groundwater flow are involved. Also, the unfrozen water in the soil can play an important role in talik freeze-up and permafrost cooling. In order to simulate the talik freeze-up and permafrost response after lake drainage, further studies are required to improve the model to include the process of convective heat transfer and the influence of unfrozen water. In addition, further studies of the relationship between climate change and thaw lake drainage in the Arctic are needed. [28] Acknowledgments. We would like to express our gratitude to Lyne Yohe who kindly edited the manuscript. This research was supported by the U.S. National Science Foundation through the NSF Grant OPP and the NSF Grant OPP to the University of Colorado at Boulder, and the International Arctic Research Center, University of Alaska Fairbanks, under the auspices of the NSF cooperative agreement number OPP Financial support does not constitute an endorsement of the views expressed in this report. References Anderson, D. M., and A. R. Tice (1972), Predicting unfrozen water contents in frozen soils from surface area measurements, Highway Res. Record, 393, of9

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