Numerical simulation of permafrost thermal ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D16, 4511, doi:10.1029/2002JD003014, 2003

Numerical simulation of permafrost thermal regime and talik development under shallow thaw lakes on the Alaskan Arctic Coastal Plain Feng Ling National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA Department of Computer Science and Technology, Zhaoqing University, Guangdong, China

Tingjun Zhang National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado, USA Received 3 October 2002; revised 24 April 2003; accepted 1 May 2003; published 27 August 2003.

[1] Thaw lakes are one of the most obvious manifestations of the hydrological system at

work in the tundra regions of the Alaskan Arctic Coastal Plain, but the extent of the role of thaw lakes in Arctic land-atmosphere interactions and feedback has yet to be fully understood. This study uses a two-dimensional heat transfer model with phase change under a cylindrical coordinate system to simulate the long-term influence of shallow thaw lakes on the thermal regime of permafrost and talik development on the Alaskan Arctic Coastal Plain. On the basis of previous studies of permafrost and thaw lakes at Barrow, Alaska, a series of simulation cases was conducted using different combinations of long-term mean lake bottom temperature and lake depth. The simulated results indicate that shallow thaw lakes are a significant heat source to permafrost and talik. For a thaw lake with a long-term mean lake bottom temperature of greater than 0.0C a talik forms under the thaw lake. The maximum talik thicknesses (vertical distance from the ground surface to the permafrost surface) are 28.0, 43.0, and 53.2 m 3000 years after the formation of a shallow thaw lake with long-term mean lake bottom temperatures of 1.0, 2.0, and 3.0C, respectively. Talik development rate is very high in the first several years after a thaw lake formation and decreases gradually with time. No talik forms below a thaw lake with a long-term mean lake bottom temperature equal to or lower than 0.0C, but the temperature of permafrost below the thaw lake increases with time. Three thousand years after the formation of a thaw lake with a long-term mean lake bottom temperature of greater than or equal to 2.0C, ground temperature increases of more than 0.5C occur as far as 300 m from the lake shore and as deep as about 400 m below the ground surface. It is concluded that variation of long-term mean lake bottom temperature has a significant influence on permafrost thermal regime and talik development. Continued monitoring for thaw lake bottom temperature and ground temperature under INDEX TERMS: 1823 shallow thaw lakes is needed to further improve the simulation. Hydrology: Frozen ground; 1833 Hydrology: Hydroclimatology; 1863 Hydrology: Snow and ice (1827); 1630 Global Change: Impact phenomena; 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; KEYWORDS: thaw lake, talik, permafrost, modeling, Alaskan Arctic Citation: Ling, F., and T. Zhang, Numerical simulation of permafrost thermal regime and talik development under shallow thaw lakes on the Alaskan Arctic Coastal Plain, J. Geophys. Res., 108(D16), 4511, doi:10.1029/2002JD003014, 2003.

1. Introduction [2] Shallow thaw lakes are a major component of the tundra landscape of the Alaskan Arctic Coastal Plain, and cover as much as 40% of the surface area in some location [Sellmann et al., 1975a, 1975b]. The majority of these lakes Copyright 2003 by the American Geophysical Union. 0148-0227/03/2002JD003014

ACL

are thermokarst features that owe their origin to permafrost thawing [Hopkins, 1949; Black and Barksdale, 1949; Sellmann et al., 1975a]. Some lakes are frozen to the bottom each winter because the water depth is less than the maximum lake ice thickness, while others may not freeze completely to the bottom by the end of the winter [Black and Barksdale, 1949; Brewer, 1958a, 1958b; Weeks et al., 1978; Mellor, 1982]. An investigation of lake ice growth during the winter 1991 – 1992 on the North Slope

8-1

ACL

8-2

LING AND ZHANG: TALIK DEVELOPMENT UNDER THAW LAKES

Figure 1. Schematic illustration of analysis domain and boundary conditions for simulations. The upper boundary is set at lake bottom off the shore and at a depth of 0.5 m below the ground surface on the shore. using spaceborne synthetic aperture radar (SAR) data revealed that 60% of the thaw lakes near Barrow, Alaska, froze completely by January, and inland about 100 km south of Barrow, only 25% of the lakes had frozen to the bottom by the end of winter [Jeffries et al., 1996]. Bodies of water that do not freeze to the bottom in winter have a marked effect upon ground temperatures and the local configuration of permafrost. This arises from the fact that the mean annual bottom temperature must be greater than 0.0C, whereas the temperature of the neighboring land surface may be 5.0C or lower [Williams and Smith, 1989]. The presence of a water body thus constitutes a heat source, giving rise to anomalous heat flow and temperature conditions in the ground. Consequently, a perennial thaw layer between the thaw lake bottom and the permafrost surface, termed as talik, forms and increases in thickness over time [Brewer, 1958a, 1958b; Lachenbruch et al., 1962; Johnston and Brown, 1964; Washburn, 1980; Mackay, 1997; Burn, 2002]. [3] Talik development has a significant influence on the physical, chemical, biological, and geomorphological processes occurring in the ground under and around thaw lakes. Taliks cause thaw settlement and permafrost degradation [Johnston and Brown, 1964; Sellmann et al., 1975b], decreasing the ability of the permafrost to support a load and seriously affecting the performance of structures constructed in permafrost regions [Johnston and Brown, 1964; Lunardini, 1996]. Taliks also provide an environment for microbial decomposition of organic sediment under anaerobic conditions. Phelps et al. [1998] report that thaw lakes contribute a significant amount of methane flux to the atmosphere when the lake ice melts in the spring. Zimov et al. [1997] suggest that methane released from Siberian thaw lakes has enhanced the annual cycle of methane at high latitude in recent years, providing a positive feedback to the climatic system. In addition, previous studies show that soils of the Arctic tundra ecosystems contain about 13% of the global soil carbon pool [Post et al., 1982], and tundra ecosystems are changing from a sink to a source of atmospheric carbon dioxide [Oechel et al., 1993, 1995]. Therefore thawing of permafrost around thaw lakes in such

areas can release great amounts of methane into the atmosphere [Michaelson et al., 1996]. [4] Thaw lakes have long been considered a unique feature of the Alaskan Arctic Coastal Plain. The origin, geometry, growth, age, and the impact of thaw lakes have captured the interest of many investigators [Black and Barksdale, 1949; Hopkins, 1949; Brewer, 1958a, 1958b; Carson and Hussey, 1962; Brown, 1965; Carson, 1968; Black, 1969; Sellmann et al., 1975a, 1975b; Mellor, 1982; Jeffries et al., 1996; Kozlenko and Jeffries, 2000]. Lake ice growth, decay, and sensitivity to climate change have also been studied by some researchers by using energy balance models [Heron and Woo, 1994; Liston and Hall, 1995a, 1995b] and numerical heat transfer models with phase change [Bilello, 1980; Ashton, 1983; Jeffries et al., 1999; Zhang and Jefffies, 2000]. These studies have provided the basis for an excellent understanding of thaw lake features and the energy-related processes controlling the regional geomorphology. However, the long-term impact of thaw lakes on permafrost thermal regime and talik development has yet to be quantified, and we can only speculate on the possible influence of climate in the lake-dominated tundra regions of the Arctic. The objective of this study is to use numerical modeling to investigate the long-term influence of shallow thaw lakes on permafrost thermal regime and talik development on the Alaskan Arctic Coastal Plain. On the basis of the results from previous studies of permafrost and thaw lakes at Barrow, Alaska, a series of simulation cases was conducted using different combinations of longterm mean lake bottom temperature and lake depth.

2. Model Description [5] A two-dimensional heat transfer model with phase change was developed and used to investigate the long-term influence of shallow thaw lakes on permafrost thermal regime and talik development. This finite element model is based on a model by Ling et al. [2000a, 2000b] for highway thermal stability analysis in permafrost regions under a rectangular coordinate system. Because thaw lakes

ACL

LING AND ZHANG: TALIK DEVELOPMENT UNDER THAW LAKES Table 1. Physical Properties of Soils Used in This Study Depth, m 0.5 – 5 5 – 50 50 – 400 400 – 500

Dry Bulk Water Content Unfrozen Water by Mass W, Content by Mass Density kg kg1 Wu, kg kg1 rb, kg m3

Soil Type silt silt and clay gravel and sand gravel

1100 1200 1450 1580

56 32 25 22

(1)– (4) for unfrozen and frozen zones can be written in a unique form: C

4.8 4.8 3.8 3.8

@Tu @ @Tu ku @Tu @ @Tu þ ¼ þ ku ku @t @r r @r @x @r @x

@T @ @T k @T @ @T þ ¼ k þ k @t @r @r r @r @x @x

ð1Þ

ð0 < t < D; ð x; rÞ 2 u Þ

where X and R are the depth and radius of the analysis domain in meters. [7] The volumetric heat capacity, C, and the thermal conductivity, k, are [Lunardini, 1981]:

C¼

k¼

8 > > > > < > > > > :

8 > > > > < > > > > :

ð2Þ

0 < t < D; ð x; rÞ 2 f

Equations (1) and (2) are coupled by the following continuous temperature condition (3) and the conservation of energy condition (4) at the moving interface between the frozen and unfrozen phases: Tu ðS ðt Þ; t Þ ¼ Tf ðS ðt Þ; t Þ ¼ Te

kf

@Tf @Tu dS ðt Þ ku ¼L @n @n dt

ð0 < t < DÞ

ð0 < t < DÞ

ð3Þ

ð4Þ

where the subscripts f and u indicate the frozen and unfrozen phases, respectively, T is temperature in C, t is time in seconds, x is the depth from the ground surface downward in meters, r is the radius from the centerline of the lake in meters, C is the volumetric heat capacity in J m3 C1, k is the thermal conductivity in W m1 C1, L is the volumetric latent heat of fusion in J m3, S(t) is the phase front position in meters, n is normal direction of phase front position in meters, D is the total simulation time (lake age) in years, is the analysis domain, and Te is the permafrost freezing temperature in C. [6] Water in the soil will usually not all freeze even at temperature considerably lower than the usual freezing point for pure water, particularly valid for soils with fine solid size. The liberation or absorption of latent heat will be spread over a finite freezing range rather than a fixed temperature [e.g., Anderson et al., 1973; Lunardini, 1981; Osterkamp, 1987]. By using the apparent heat capacity scheme [Bonacina et al., 1973], the governing equations

T < Te T

Cf Cf þ Lw rb

W Wu T

Te T T Te

Cu

kf þ

ð6Þ

T > Te T < Te T

kf ku kf ½T ðTe T Þ T ku

Frozen zone @Tf @Tf kf @Tf @Tf @ @ þ Cf ¼ þ kf kf @t @r r @r @x @r @x

ð5Þ

ð0 < t < D; 0 < x < X ; 0 < r < RÞ

on the Alaskan Arctic Coastal Plain are typically elliptical in shape [Black and Barksdale, 1949; Brewer, 1958b; Sellmann et al., 1975a], the two-dimensional model was developed under a cylindrical coordinate system. Assuming there is no annular heat flow in the cylindrical coordinate system, the governing equation for heat conduction in the lake-permafrost system can be written as follows: Unfrozen zone Cu

8-3

Te T T Te ð7Þ T > Te

where (Te T, Te) is the temperature range in which the phase change occurs, T is the width of the temperature interval in C, Lw is the mass specific latent heat of water in J kg1, rb is the dry buck density of soil in kg m3, W is the total water content percent of soil by mass, and Wu is the unfrozen water content percent of soil by mass at the temperature Te T. In this study, the permafrost freezing temperature Te is set at 0.0oC, and the width of the phase change interval for moist soils with fine solid size is assumed to be 1.0C [Comini et al., 1974]. [8] Previous studies indicate that permafrost thickness in the Barrow area is about 400 m [Brewer, 1958b; Lachenbruch and Marshall, 1969; Lachenbruch et al., 1982], the active layer depth is less than 0.5 m [Brown, 1965; Nakano and Brown, 1972; Zhang et al., 1997; Hinkel et al., 2001], and the mean permafrost surface temperature is approximately 9.0C [Lachenbruch et al., 1962; Lachenbruch and Marshall, 1969]. The geothermal heat flux at great depth on the North Slope of Alaska is a constant of 0.0565 W m2 [Lachenbruch et al., 1982; Osterkamp and Gosink, 1991]. On the basis of these results, the upper boundary of the analysis domain is set at the lake bottom off the shore and at a depth of 0.5 m below the ground surface on the shore, and the lower boundary is set at X = 500 m (Figure 1), 100 m below the permafrost base.

Table 2. Simulation Cases Carried Out in This Study Lake Depth H0, m 1.3 1.5 2.0 2.5

Temperature at Lake Bottom Tlb, C 2.0

1.0

0.0

C1

C2

C3 C4 C6

C5

1.0

2.0

3.0

C7 C9

C8 C10

C11

ACL

8-4


Figure 2. Simulated ground thermal regimes and ground temperature increases for simulation case C4. (a – d) Ground thermal regimes at different years. (e – h) Corresponding differences between the ground temperature at different years and the initial ground temperature.

[9] The upper boundary conditions are

k

T ð0:5; r; t Þ ¼ T ps ðt Þ

ð0 < t < D; x ¼ 0:5; R0 r < RÞ

ð8Þ

T ðH0 ; r; t Þ ¼ Tlb ðt Þ

ð0 < t < D; x ¼ H 0 ; 0 < r < R0 Þ

ð9Þ

where Tps = 9.0C is the mean temperature at the permafrost surface, Tlb is the mean temperature at the lake bottom in C, and H0 is lake depth in meters. The lower boundary condition is the constant heat flux, q = 0.0565 W m2

@T ð X ; r; t Þ ¼q @x

ð0 < t < D; x ¼ X ; 0 < r < RÞ

ð10Þ

The lateral boundary conditions are treated as zero heat flux boundary conditions, i.e., @T ð x; r; t Þ ¼0 @r

ð0 < t < D; H0 < x < X ; r ¼ 0Þ

ð11Þ

@T ð x; r; t Þ ¼0 @r

ð0 < t < D; 0:5 < x < X ; r ¼ RÞ

ð12Þ


ACL

8-5

Figure 3. Ground temperature change with time for points at depths of x = 50, 100, 200, and 300 m along r = 0, 400, and 600 m for simulation case C4. The soil types in the analysis domain and their physical properties were chosen based on the Barrow soil conditions [Lachenbruch et al., 1962; McGaw et al., 1978; Zhang, 1993]. The unfrozen water content of each soil type at 1.0C was determined from Anderson and Tice [1972]. These results are summarized in Table 1. The corresponding thermal parameters of each soil type are determined by using the empirical formulae described by Kersten [1949]. [10] Thaw lake size varies greatly across the Alaskan Arctic [Black and Barksdale, 1949; Brewer, 1958b; Sellmann et al., 1975a]. A study of the classification and geomorphic implications of thaw lakes on the Alaskan Arctic Coastal Plain indicates that the average major axis of these elliptical thaw lakes ranges from 1.21 km to 2.3 km, and the average minor axis is between 0.68 km and 1.1 km [Sellmann et al., 1975a]. In the current cylindrical model, a lake radius R0 = 400 m is used, and the total radius of the analysis domain is set at R = 1000 m (Figure 1). [11] Thaw lake depths fall into two depth classes in the Barrow area: 0.6 –0.9 m and 1.8– 2.7 m [Brewer, 1958b]. These depth ranges are believed to be representative of most thaw lakes on the Alaskan Arctic Coastal Plain [Brewer, 1958b; Sellmann et al., 1975a, 1975b]. Jeffries et al. [1996] investigated the variability of lake depth using spaceborne remote sensing and numerical ice growth modeling. They found that in the vicinity of Barrow, 23% of the lakes are more than 2.2 m deep, 10% of the lakes are between 1.5 m and 2.2 m deep, 60% of the lakes are between 1.4 m and 1.5 m deep, and 7% of the lakes are less than 1.4 m deep. Inland about 100 km south of Barrow, 77% of the lakes are more than 2.2 m deep. On

the basis of these data, this study set lake water depth, H0, at 1.3, 1.5, 2.0, and 2.5 m, respectively. No attempt was made to accommodate either thaw subsidence or basin deepening. [12] Lake bottom temperature is determined by a number of factors, including the thermal characteristics of the water body and the adjacent ground, the size and depth of the lake, the general hydrologic conditions of the lake, the thickness of lake ice and snow cover, and the composition and history of accumulation of bottom sediments [Johnston and Brown, 1964]. Precise relationships between lake depth, lake ice thickness, and mean annual lake bottom temperature are not available [Burn, 2002], but mean bottom temperature is greater than 0C when a thawed zone exists under lakes [Lachenbruch, 1957; Johnston and Brown, 1964; Williams and Smith, 1989]. A study of thaw lakes near Barrow, Alaska, showed that the historical annual maximum lake ice thickness has varied from about 1.33 m to 2.47 m, with a long-term mean maximum ice thickness of 1.91 ± 0.21 m over the past 50 years [Zhang and Jeffries, 2000]. Because thaw lakes with a depth less than 1.33 m freeze to the lake bottom by the end of winter, it is reasonable to assume that the lake bottom temperature is less than 0C. Thaw lakes with depths ranging from 1.3 m to 2.47 m may or may not freeze completely to the lake bottom by the end of winter; it is possible that these lake bottom temperatures are greater than, less than, or equal to 0.0C. For thaw lakes with a depth greater than 2.47 m, there is a high possibility that the lake bottom temperature is greater than 0C. In this study, the long-term mean lake bottom temperature, Tlb, is assumed to vary from 2.0C to 3.0C, with an increment of 1.0C, depending on lake depth.

ACL

8-6


along the x axis direction and from 5 m to 25 m along the r axis direction.

3. Results [15] To simulate the impact of shallow thaw lakes with different lake bottom temperatures on the thermal regime of the ground below a thaw lake, a series of simulation cases was carried out using different combinations of long-term mean lake bottom temperature and lake water depth (Table 2). In this study, the term ‘‘ground’’ refers to both permafrost and talik.

Figure 4. Simulated ground temperature profiles at different years at r = 0 m (lake center) and r = 400 m (lake shore) for simulation case C4. [13] The thaw lake cycle, consisting of repetitive stages of lake formation and drainage, is the primary geomorphic process that modifies the Arctic Coastal Plain. Previous investigations of lake age using radiocarbon dating in the Barrow, Alaska, indicate that thaw lakes seldom exceed 3500 years in age [Brown, 1965; Carson, 1968]. This study uses a total simulation time of D = 3000 years. [14] The governing equations (5) – (7) were solved using a finite element method [Huebner, 1975]. It is initially assumed that permafrost thickness is 400 m and there is no thaw lake over the permafrost. The model was run using a mean permafrost surface temperature of 9.0C and the boundary conditions (10) – (12) until the soil thermal regime reached an equilibrium with the corresponding physical and thermal parameters and boundary conditions. Then, the equilibrium thermal regime was used as the initial condition, a thaw lake with a lake radius R0 = 400 m was assumed to be over the permafrost (Figure 1), and the model was solved using the boundary conditions (8) – (12). A time step of 1 day was used with a total simulation period of 3000 years. The spatial step varies from 0.5 m to 25 m

3.1. Ground Thermal Regime Variation [16] The simulated ground thermal regimes using Tlb = 0.0oC and Tps = 9.0C with H0 = 1.5 m (C4 in Table 2) are presented in Figure 2. Owing to the temperature difference between the lake bottom (0 r < 400 m, Figure 1) and the permafrost surface (400 r 1000 m, Figure 1), ground temperature under the thaw lake (Figures 2a – 2d) and the corresponding ground temperature changes (Figures 2e – 2h) increase significantly over time. The magnitude of the ground temperature increase is greatest at the lake bottom and decreases with depth from the lake bottom to the lower boundary and decreases with distance from the lake center to the lateral boundary. This has been observed in the field investigation [Brewer, 1958b]. Ground temperature under the permafrost surface, however, changes very little. The isotherms in Figure 2h show that 3000 years after the development of a thaw lake over permafrost, temperature increases of more than 0.5C occur at more than 300 m from the lake shore and more than 400 m below the ground surface. [17] Figure 3 shows ground temperature changes with time at different depths at the lake center (r = 0 m), lake shore (r = 400 m), and permafrost surface (r = 600 m) for simulation case C4. After the thaw lake exists for 3000 years, ground temperature increases at depths of 50, 100, 200, and 300 m along lake center are 7.1, 5.8, 3.5, and 1.5C, along the lake shore are 3.0, 2.7, 1.8, and 0.8C, respectively. The magnitude of the temperature increase decreases substantially with depth from the lake bottom to the lower boundary, and with distance from the thaw lake center to the lateral boundary. The increases in ground temperature at depths of 50, 100, 200, and 300 m at r = 600 m are very limited, generally less than or equal to 0.5C during the 3000 years after the thaw lake is established. Owing to the time lag, ground temperature change rates at different points are quite different. For example, ground temperature at the point (x = 50 m, r = 0 m) increases rapidly with time during the first 500 years, then the increase rate decreases substantially (Figure 3a). Ground temperature at the point (x = 300 m, r = 0 m) remains at its initial value in the first 200 years, increases rapidly with time for the next 300 years, and then increases very slowly with time (Figure 3d). [18] Figure 4 shows ground temperature profiles at lake center and lake shore at different years for simulation case C4. The maximum ground temperature increase from year 50 to year 3000 at r = 0 m is about 5.0C (Figure 4a); while at r = 400 m, the increase is 2.5C (Figure 4b). The permafrost temperature profile at r = 400 m is a product


ACL

8-7

Figure 5. Simulated ground thermal regimes and ground temperature increases for simulation cases C1, C2, and C3 at 3000 years. (a– c) Ground thermal regimes under a 1.3-m-deep thaw lake with lake bottom temperatures of 2.0, 1.0, and 0.0C. (d – f ) Corresponding differences between the ground temperature at 3000 years and the initial ground temperature. of both the lake bottom temperature and the exposed tundra temperature. The surface temperature of 9.0C keeps the temperature at point (x = 0 m, r = 400 m) at 9.0C and cools the ambient ground. Ground temperature at 0 < x < 80 m along r = 400 m is affected by both lake bottom temperature and permafrost surface temperature. On the one hand, the heat transported from the lake bottom (Tlb = 0.0C) causes the ground temperature to increase significantly and quickly. On the other hand, the ground temperature is lowered by the permafrost surface temperature (Tps = 9.0C), and so the ground temperature generally remains unchanged. Permafrost temperature at x 80 m along r = 400 m is affected mainly by the lake bottom temperature rather than ground surface temperature; it remains at its original value before heat transported from lake bottom reaches it and gradually increases with time. As a result, the ground temperature profiles look like zigzag curves and progressively reach a new equilibrium with time (Figure 4b). [ 19 ] The simulated ground temperatures and its corresponding changes for simulation cases C1, C2, and C3 (Table 2) at 3000 years are shown in Figure 5. Although

Figure 6. Comparison of simulated ground temperature profiles at 3000 years at r = 0 m for simulation cases C5, C6, C7, and C8.

ACL

8-8


Figure 7. Simulated ground thermal regimes and talik thicknesses under thaw lakes at 500, 1000, 2000, and 3000 years for simulation cases C9, C10, and C11. the spatial range affected by a thaw lake in each case is almost the same (more than 300 m from the lake shore in the horizontal direction and 400 m in the vertical direction), the ground thermal regime and the corresponding ground temperature increases are significantly different due to the different values of long-term mean lake bottom temperatures. For example, for thaw lakes with lake bottom temperatures of 2.0, 1.0, and 0.0C, the ground temperatures at a depth of 100 m along the lake center are 2.0, 1.3, 1.0C, and the corresponding ground temperature increases are 4.7, 5.4, and 5.7C, respectively. The ground temperatures at a depth of 100 m along the lake

shore are 4.5, 4.3, and 4.1C; the corresponding ground temperature increases are 2.2, 2.4, and 2.6C, respectively. Changes in lake bottom temperature have a obvious influence on the temperature of the neighboring ground. [20] The simulated ground temperature profiles at 3000 years at r = 0 m for simulation cases C5, C6, C7, and C8 are presented in Figure 6 to further show the impact of variations in lake bottom temperature on the thermal regime of permafrost under thaw lakes. The ground temperature differences between the different cases decrease with depth from lake bottom to permafrost base.


Figure 8. Comparison of maximum talik thickness variations with time for simulation cases C9, C10, and C11. For example, the ground temperature difference between C8 and C5 at lake bottom is 3.0C, at 60 m deep is 0.7C, and at 200 m deep is only 0.3C. The main effect of changes in lake bottom temperature from 1.0 to 2.0C is evident at depths between lake bottom and approximately 100 m during the 3000 years after the formation of the thaw lake. Below 200 m, the effect of variations in lake bottom temperature on the thermal regime of permafrost is very limited. 3.2. Talik Formation and Development [21] When the long-term mean bottom temperature of a thaw lake is greater than 0.0C, a talik forms, as the simulated results for cases C9, C10, and C11 show in Figure 7. For a thaw lake with a depth of 2.5 m and with a long-term mean lake bottom temperature of 1.0C, the talik thickness at 500, 1000, 2000, and 3000 years reaches 12.4, 17.0, 23.4, and 28.0 m, respectively (Figures 7a – 7d); when the long-term mean lake bottom temperature is 2.0C, the talik thickness at 500, 1000, 2000, and 3000 years reaches 18.5, 26.0, 36.3, and 43.0 m (Figures 7e –

ACL

8-9

7h). When the long-term mean lake bottom temperature is 3.0C, the talik thickness at 500, 1000, 2000, and 3000 years is 23.4, 33.0, 45.5, and 53.2 m, respectively (Figures 7i– 7l). [22] The simulated talik thickness increases with time for simulation cases C9, C10, and C11 during the 3000 years are shown in Figure 8. As the permafrost surface temperature is raised from 9.0C to a long-term mean lake bottom temperature of 1.0, 2.0, and 3.0, talik growth is very high in the first several years after the thaw lake formation, and reduces gradually with time. For example, the increases in talik thickness for C9, C10, and C11 in the first 50 years are 6.0, 7.7, and 8.8 m and in the second 50 years are 1.0, 1.5, and 1.8 m, respectively. One thousand years after formation, talik thickness generally increases linearly with time, with a rate of 3.7, 5.7, 6.7 mm year1 for simulation cases C9, C10, and C11. The average talik development rates over 3000 years for C9, C10, and C11 are 8.6, 13.7, and 17.0 mm year1, respectively. [23] Figure 9 presents the increases in talik thickness for every 500 years for simulation cases C9, C10, and C11 to further illustrate talik development at various long-term mean lake bottom temperature over time. Increases in talik thickness in the sixth 500-year period for C9, C10, and C11 are 2.1, 3.3, and 3.6 m, respectively. This is only 20.9%, 20.6%, and 17.3% of the talik thickness increases in the first 500-year period but 61.7%, 56.4%, and 53.6% of the talik thickness increases in the third 500-year period. The talik thickness differences between various long-term mean lake bottom temperatures also decrease with time. For instance, the talik thickness difference between simulation cases C11 and C10 in the first 500-year period is 4.9 m, in the third 500-year period is 0.9 m, and in the sixth 500-year period is just 0.3 m. The difference of talik thickness between simulation cases C11 and C9 in the first 500-year period

Figure 9. Simulated talik thickness increases for every 500 years for simulation cases C9, C10, and C11.

ACL

8 - 10


is 11.0 m, in the third 500-year period is 3.4 m, and in the sixth 500-year period is just 1.5 m.

4. Summary and Discussions [24] A two-dimensional unsteady finite element model under a cylindrical coordinate system was developed and used to simulate the long-term impact of shallow thaw lakes on permafrost thermal regime and talik development on the Alaskan Arctic Coastal Plain. A series of simulation cases was conducted using different combinations of long-term mean lake bottom temperature and lake depth, based on results from previous studies of permafrost and thaw lakes at Barrow, Alaska. The following are the principal results of this study: [25] 1. Shallow thaw lakes are a significant heat source to permafrost and talik. The influence of shallow thaw lakes on ground temperature is greatest at lake bottom, increases with time and lake bottom temperature, and decreases with depth from the lake bottom to the lower boundary and with distance from the lake center to the lateral boundary. [26] 2. Taliks form under thaw lakes with a long-term mean lake bottom temperature greater than 0.0C. Talik thickness increases with both time and lake bottom temperature. Three thousand years after the formation of shallow thaw lakes with long-term mean lake bottom temperatures of 1.0, 2.0, and 3.0C, the maximum talik thicknesses (vertical distance from the ground surface to the permafrost surface) are 28.0, 43.0, and 53.2 m, respectively. [27] 3. Talik development rates are very high in the first several years after thaw lake formation and decrease gradually with time. The differences in talik development rate at various long-term mean lake bottom temperatures also decrease with time. The average talik development rates below 3000-year old lakes with long-term mean lake bottom temperatures of 1.0, 2.0, and 3.0C are 8.6, 13.7, and 17.0 mm year1, respectively. [28] 4. No talik forms below a thaw lake with a long-term mean lake bottom temperature of less than 0.0C. However, permafrost temperature under a thaw lake increases significantly with time, depending on the mean lake bottom temperature and the distance to lake bottom. Three thousand years after the formation of a thaw lake with lake bottom temperatures of greater than or equal to 2.0C, ground temperature increases of more than 0.5C occur as far as about 300 m from the lake shore and as deep as about 400 m below the ground surface. [29] 5. Variations in long-term mean lake bottom temperature, which is a product of changes in air temperature, snow thickness and properties, lake ice thickness, solar radiation, and water depth, significantly affect permafrost thermal regime and talik development. [30] This study uses a two-dimensional heat transfer model with phase change under a cylindrical coordinate system to simulate a thaw lake where geometry does not change for 3000 years. Certainly, this is an ideal assumption to simplify the modeling study. Actual thaw lakes are typically elliptical in shape and largely unstable, with active erosion at their basin margins [Black and Barksdale, 1949; Brewer, 1958b; Sellmann et al., 1975a]. Lake size and lake depth change with time due to the lake cyclic process of formation, growth, and drainage. In addition, thaw subsi-

dence and basin deepening can occur. These variations may affect permafrost thermal regime and talik development. The development of a three-dimensional model will allow consideration of these processes. [31] There has been little quantitative analysis of the role of thaw lakes on the ground thermal regime, largely due to an almost complete lack of below-lake temperature measurements. A few boreholes have been drilled into the sediments below lakes in permafrost terrain [Johnston and Brown, 1964, 1966], but the data are insufficient for model input and validation. The precise relationships between lake depth, lake ice thickness, and mean annual lake bottom temperature are not available [Burn, 2002]. As an alternative, this study uses a simplified method of case study with variable long-term mean lake bottom temperature. Field measurement data are prerequisite for numerical simulation. In order to better understand the impact of thaw lakes on the thermal regime of permafrost and talik formation, a systematic, comprehensive, and long-term ground-based measurement, including air temperature, snow cover thickness and properties, lake ice thickness, lake water depth and temperature, and ground temperature under thaw lakes, is clearly needed. [32] Acknowledgments. We would like to express our gratitude to the three anonymous reviewers for their constructive and helpful comments. We also thank Lyne Yohe, who kindly edited the manuscript. This work was supported by the US National Science Foundation through the NSF grant OPP-9907541 and the NSF grant OPP-0229766 to the University of Colorado at Boulder; the International Arctic Research Center, University of Alaska Fairbanks, under the auspices of the NSF cooperative agreement OPP-0002239; and the Cooperative Institute for Arctic Research under the US National Oceanic and Atmospheric Administration (NOAA) Cooperative Agreement NA67RJ0147. Financial support does not constitute an endorsement of the views expressed in this report.

References Anderson, D. M., and A. R. Tice, Predicting unfrozen water contents in frozen soils from surface area measurements, Highway Res. Rec., 393, 12 – 18, 1972. Anderson, D. M., A. R. Tice, and H. L. McKim, The unfrozen water and the apparent specific heat capacity of frozen soils, in Proceedings of Second International Conference on Permafrost, pp. 289 – 295, Natl. Acad. of Sci., Washington, D. C., 1973. Ashton, G. D., Predicting lake ice decay, CREEL Spec. Rep. 83 – 19, Cold Reg., Res. and Eng. Lab., Hanover, N. H., 1983. Bilello, M. A., Maximum thickness and subsequent decay of lake, river, and fast sea ice in Canada and Alaska, CRREL Rep. 80-9, Cold Reg. Res. and Eng. Lab., Hanover, N. H., 1980. Black, R. F., Geology, especially geomorphology of northern Alaska, Arctic, 22, 283 – 299, 1969. Black, R. F., and W. L. Barksdale, Oriented lakes of northern Alaska, J. Geol., 57, 105 – 118, 1949. Bonacina, C., G. Comini, and A. Fasano, Numerical solution of phasechange problem, Int. J. Heat Mass Transfer, 16, 1832 – 1852, 1973. Brewer, M. C., Some results of geothermal investigations of permafrost in northern Alaska, Eos Trans. AGU, 39(2), 19 – 26, 1958a. Brewer, M. C., The thermal regime of an Arctic lake, Eos Trans. AGU, 39(2), 278 – 284, 1958b. Brown, J., Radiocarbon dating, Barrow, Alaska, Arctic, 18, 37 – 48, 1965. Burn, C. R., Tundra lakes and permafrost, Richards Island, western Arctic coast, Canada, Can. J. Earth Sci., 39, 1281 – 1298, 2002. Carson, C. E., Radiocarbon dating of lacustrine stands in the arctic Alaska, Arctic, 21, 12 – 26, 1968. Carson, C. E., and K. M. Hussey, The oriented lakes of arctic, Alaska, J. Geol., 70, 417 – 439, 1962. Comini, G., S. D. Guidice, R. W. Lewis, and G. C. Zienkiewicz, Finite element solution of non-linear heat conduction problem with special reference to phase change, Int. J. Numer. Methods Eng., 8, 613 – 624, 1974. Heron, R., and M. Woo, Decay of a high Arctic lake-ice cover: Observations and modelling, J. Glaciol., 40, 283 – 292, 1994.

LING AND ZHANG: TALIK DEVELOPMENT UNDER THAW LAKES Hinkel, K. M., F. Paetzold, F. E. Nelson, and J. G. Bockheim, Patterns of soil temperature and moisture in the active layer and upper permafrost at Barrow, Alaska: 1993 – 1999, Global Planet. Change, 29, 293 – 309, 2001. Hopkins, D. M., Thaw lakes and thaw sinks in the Imuruk lake area, Seward Peninsula, J. Geol., 57, 119 – 131, 1949. Huebner, K. H., The Finite Element Method for Engineers, John Wiley, Hoboken, N. J., 1975. Jeffries, M. O., K. Morris, and G. E. Liston, A method to determine lake depth and water availability on the North Slope of Alaska with spaceborne imaging radar and numerical ice growth modelling, Arctic, 49, 367 – 374, 1996. Jeffries, M. O., T. Zhang, K. Frey, and Kozlenko, Estimating late-winter heat flow to the atmosphere from the lake-dominated Alaskan North Slope, J. Glaciol., 45, 315 – 324, 1999. Johnston, G. H., and R. J. E. Brown, Some observations on permafrost distribution at a lake in the Mackenzie delta, N.W.T., Canada, Arctic, 17, 162 – 175, 1964. Johnston, G. H., and R. J. E. Brown, Occurrence of permafrost at an Arctic lake, Nature, 21(5052), 952 – 953, 1966. Kersten, M. S., Laboratory research for the determination of the thermal properties of soils, final report, Eng. Exp. Stn., Univ. of Minn., Minneapolis, 1949. Kozlenko, N., and M. O. Jeffries, Bathymetric mapping of shallow water in thaw lakes on the North Slope of Alaska with spaceborne imaging radar, Arctic, 53, 306 – 316, 2000. Lachenbruch, A. H., Thermal effects of the ocean on permafrost, Geol. Soc. Am. Bull., 68, 1515 – 1530, 1957. Lachenbruch, A. H., and B. V. Marshall, Heat flow in the Arctic, Arctic, 22, 300 – 311, 1969. Lachenbruch, A. H., M. C. Brewer, G. W. Greene, and B. V. Marshall, Temperatures in permafrost, in Temperature—Its Measurement and Control in Science and Industry, vol. 3, part 1, pp. 791 – 803, Reinhold, New York, 1962. Lachenbruch, A. H., J. H. Sass, B. V. Marshall, and T. H. Moses Jr., Temperatures, heat flow, and the geothermal regime at Prudhoe Bay, Alaska, J. Geophys. Res., 87(B11), 9301 – 9316, 1982. Ling, F., Z. Zeng, and L. Zhang, The effect of construction of revetment in the side of embankment, in Ground Freezing 2000, edited by J.-F. Thimus, pp. 43 – 46, A. A. Balkema, Brookfield, Vt., 2000a. Ling, F., D. Yan, and Z. Qian, Numerical investigation of thermal regime of roadbed under different type of driving surfaces in Huashixia Valley, China, J. Glaciol. Geocryol., 22, Suppl., 118 – 121, 2000b. Liston, G. E., and D. K. Hall, An energy-balance model of lake-ice evolution, J. Glaciol., 41, 373 – 382, 1995a. Liston, G. E., and D. K. Hall, Sensitivity of lake freeze-up and break-up to climate change: A physically based modeling study, Ann. Glaciol., 21, 387 – 393, 1995b. Lunardini, V. J., Heat Transfer in Cold Climates, Van Nostrand Reinhold, New York, 1981. Lunardini, V. J., Climatic warming and the degradation of warm permafrost, Permafrost Periglacial Processes, 7, 311 – 320, 1996. Mackay, J. R., A full-scale field experiment (1978 – 1995) on the growth of permafrost by means of lake drainage, western Arctic coast: A discussion of the method and some results, Can. J. Earth Sci., 34, 17 – 33, 1997. McGaw R. W., S. L. Outcalt, and E. Ng, Thermal properties and regime of wet tundra soils at Barrow, Alaska, in Proceedings of the Third International Conference on Permafrost, pp. 48 – 53, Natl. Res. Counc. of Can., Ottawa, Ont., 1978.

ACL

8 - 11

Mellor, J., Bathymetry of Alaskan Arctic lakes: A key to resource inventory with remote sensing methods, Ph.D. thesis, Inst. of Mar. Sci., Univ. of Alaska, Fairbanks, 1982. Michaelson, G. J., C. L. Ping, and J. M. Kimble, Carbon storage and distribution in tundra soils of Arctic Alaska, U.S.A, Arct. Alp. Res., 28(4), 414 – 424, 1996. Nakano, Y., and J. Brown, Mathematical modeling and validation of the thermal regimes in tundra soils, Barrow, Alaska, Arct. Alp. Res., 4(1), 19 – 38, 1972. Oechel, W. C., S. J. Hastings, G. L. Vourlitis, M. Jenkins, G. Eiechers, and N. Grulke, Recent change of Arctic tundra ecosystems from a net carbon dioxide sink to a source, Nature, 361, 520 – 523, 1993. Oechel, W. C., G. L. Vourlitis, S. J. Hastings, and S. A. Bochkrez, Effects of Arctic CO2 flux over two decades: Effects of climate change at Barrow, Alaska, Ecol. Appl., 5, 846 – 855, 1995. Osterkamp, T. E., Freezing and thawing of soils and permafrost containing unfrozen water or brine, Water Resour. Res., 23(12), 2279 – 2285, 1987. Osterkamp, T. E., and J. P. Gosink, Variations in permafrost thickness in response to changes in paleoclimate, J. Geophys. Res., 96(B3), 4423 – 4434, 1991. Phelps, A. R., K. Peterson, and M. O. Jeffries, Methane efflux from highlatitude lakes during spring ice melt, J. Geophys. Res., 103(D22), 29,029 – 29,036, 1998. Post, W. M., W. R. Bmanuel, P. J. Zinke, and G. Stangenberger, Soil carbon pools and world life zones, Nature, 298, 156 – 159, 1982. Sellmann, P. V., J. Brown, R. I. Lewellen, H. McKim, and C. Merry, The classification and geomorphic implications of thaw lakes on the Arctic Coastal Plain, Alaska, CRREL Res. Rep. 344, Cold Reg. Res. and Eng. Lab., Hanover, N. H., 1975a. Sellmann, P. V., W. F. Weeks, and W. J. Campbell, Use of sidelooking airborne radar to determine lake depth on the Alaskan North Slope, CRREL Spec. Rep. 230, Cold Reg. Res. and Eng. Lab., Hanover, N. H., 1975b. Washburn, A. L., Geocryology: A Survey of Periglacial Processes and Environments, Halsted, New York, 1980. Weeks, W. F., A. G. Fountain, M. L. Bryan, and C. Elachi, Difference in radar returns from ice-covered North Slope lakes, J. Geophys. Res., 83(C8), 4069 – 4073, 1978. Williams, P. J., and M. W. Smith, The Frozen Earth: Fundamentals of Geocryology, Cambridge Univ. Press, New York, 1989. Zhang, T., Climate, seasonal snow cover and permafrost temperatures in Alaska north of the Brooks Range, Ph.D. dissertation, Univ. of Alaska, Fairbanks, 1993. Zhang, T., and M. O. Jeffries, Modeling inter-decadal variations of lake-ice thickness and sensitivity to climatic change in northernmost Alaska, Ann. Glaciol., 31, 339 – 347, 2000. Zhang, T., T. E. Osterkamp, and K. Stamnes, Effect of climate on the active layer and permafrost on the North Slope of Alaska, U.S.A., Permafrost Periglacial Processes, 8, 45 – 47, 1997. Zimov, S. A., Y. V. Voropaev, I. P. Semiletov, S. P. Davidov, S. F. Prosiannikov, F. S. Chapin III, M. C. Chapin, S. Trumbore, and S. Tyler, North Siberian lake: A methane source fueled by Pleistocene carbon, Science, 277, 800 – 802, 1997.

F. Ling and T. Zhang, National Snow and Ice Data Center, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309-0449, USA. ([email protected])