Time-dependent morphology of thaw lakes and taliks in deep and shallow ground ice

Authors


Abstract

[1] The shape and depth of thaw lake basins depends on lake age, on whether the talik (thaw bulb) is at steady state, and on the distribution of ice in the ground. To investigate implications of this broad hypothesis, we use a numerical model of conductive heat transfer, phase change, and thaw subsidence of ice-rich sediment beneath a lake in cross section. For ground thermal properties with lake temperatures and dimensions consistent with measurements, modeled talik depth approximately increases with equation image except in lakes in deep ground ice which deepen more rapidly because of consolidation on thawing. In deep ground ice environments, basins achieve depths of ≈20 m in ≈5 ka. Expanding lakes with disequilibrium taliks have deep basins with broad, 100+ m wide, inclined margins. In shallow ground ice settings (either original epigenetic ice or in permafrost that has reformed in drained basins), lakes are <3 m deep and flat bottomed. Unaffected by preexisting topography and ground ice variations, first-generation lakes in deep ground ice are rounder and grow larger in area than later-generation lakes. These predictions are consistent with GPS, sonar, and remote sensing measurements of bathymetry and plan view shape of first- and later-generation lakes in substrates with deep syngenetic ground ice (Pleistocene loess, northern Seward Peninsula, Alaska) and shallow epigenetic ice (Yukon Arctic coastal plain).

1. Introduction

[2] Lake basins that form by thawing of ice-rich permafrost cover 15–75% of lowland landscapes in the western Canadian Arctic, Siberia, and the Arctic coastal plain and Bering Strait regions of Alaska [Burn, 2002; Tomirdiaro, 1982; Black and Barksdale, 1949; Frohn et al., 2005; Sellman et al., 1975; Hopkins et al., 1955]. Basins of similar size, also hypothesized to form by compaction of sediment upon removal of an ice matrix, have been described from remote sensing images of Mars [Costard and Kargel, 1995]. Thaw lakes expand by subsidence on thawing of ice-rich permafrost beneath and around the lake, causing basin deepening and banks that retreat up to 10 m a-1 (meters per year) [Hopkins, 1949; Hopkins et al., 1955; Tomirdiaro, 1982; Rampton, 1982; Burn and Smith, 1988]. When an expanding lake intersects a topographic low such as a river valley, coastline or other lake basin, the water drains, often catastrophically [Brewer et al., 1993; Mackay, 1981]. The bathymetry and plan view shape of the former lake, and the characteristics of the ice-rich permafrost that reforms in the basin, set the stage for subsequent landscape evolution.

[3] In broad terms, the bathymetry and plan view shape of thaw lakes depends on a number of factors. Because thaw-derived subsidence of an ice-rich substrate principally generates the basin, bathymetry may be affected by the time-dependent depth and shape of the bulb of thawed sediment (called a talik). Bathymetry also may depend on the depth of the ice-rich layer, which can vary between sites depending on depositional history. The ground ice that reforms in a basin after drainage may differ from the prelake ground ice distribution. Often it is shallower hence bathymetry of succeeding generations of lakes may vary over the >103 a timescale of multiple lake cycles. Moreover, the plan view shape and size of a lake may depend on lake generation, because drained basins from earlier thaw lakes create drainage pathways that impose a maximum limit to the expansion of subsequent lakes.

[4] We investigate these controls over lake morphology by combining a numerical model of heat transfer, phase change, and compaction of thawed sediment in the talik, with measurements of bathymetry and plan view shape from differential GPS, sonar, and aerial photographs. Measurements focus on two areas in which thaw lakes occur in substrates formed by distinctly different late Quaternary depositional regimes: The northern Seward Peninsula (NSP) of northwestern Alaska, in which thaw lakes occur in thick aeolian silt rich in syngenetic ice [Hopkins, 1949; Hopkins et al., 1955], and the Yukon Coastal Plain (YCP) of northwestern Canada, where surface sediments are predominantly late Pleistocene glaciofluvial in origin and abundant ground ice is limited to the upper 1–5 m [Rampton, 1982]. This paper (1) reviews existing measurements of lake morphology and talik depths focussing especially on their time-dependent behavior; (2) describes the model and investigates the sensitivity of talik shape and lake bathymetry to time, ground ice depth, and rapid lake expansion; (3) presents measurements of active and recently drained thaw lake bathymetry and plan view shape from the NSP and YCP; and (4) tests predictions for bathymetry and plan view shape, derived from the model, against measurements of natural basins.

2. Thaw Lake Morphology and Taliks

[5] To the best of our knowledge, no systematic survey of thaw lake bathymetry has been undertaken across different regions. Existing measurements and descriptions of thaw lakes fall into broad classes of flat bottomed [Dallimore et al., 2000; Tomirdiaro, 1982; Hopkins, 1949; Burn, 2002; Kozlenko and Jeffries, 2000], bowl shaped [Vardy et al., 1997; Johnston and Brown, 1964], or deep centered with broad but shallow littoral shelves [Burn, 2002; Carson and Hussey, 1962; Schwamborn et al., 2002; Murton, 1996; Kozlenko and Jeffries, 2000]. In Siberia, flat bottomed lakes have been described with depths of 1–4 m [Tomirdiaro, 1982], and in the Seward Peninsula, Alaska, lakes with flat bottoms have depths of 0.3–1.8 m [Hopkins, 1949]. Most descriptions of thaw lakes have focused on lakes with shelves, perhaps because these are readily distinguished in remote sensing images because of the higher albedo of shelves than central pools (e.g., Alaskan Arctic coastal plain [Sellman et al., 1975; Pelletier, 2005], Tuktoyaktuk Coastlands, NWT [Cote and Burn, 2002] and the Lena Delta in Siberia [Schwamborn et al., 2002]). Field measurements from the Tuktoyaktuk Peninsula and Lena Delta, Siberia, respectively, show littoral shelves ranging from 0.1 to 1 km from shore, depending on diameter of the lake, and central pools 10–30 m deep [Burn, 2002; Schwamborn et al., 2002]. Other bathymetric types seem to co-occur with shelved lakes within a region: For example, Lake Illisarvik (350 m by 600 m) has a bowl-shaped basin but many lakes in the region have shelves [Hunter et al., 1981; Burn, 2002].

[6] Beneath thaw lakes, a bulb of thawed sediment forms within the 0°C isotherm which advances downward from the basin of the lake. In general, taliks form where mean annual temperature of the lake bottom is >0°C, and are therefore generally limited to lakes with depth exceeding the thickness of winter ice. Talik depths, measured by borehole drilling, include 32 m on Richards Island [Hunter et al., 1981], 57.8 m in northern Alaska [Brewer et al., 1993] and 73 m in the Mackenzie delta, Canada [Johnston and Brown, 1961].

[7] The time-dependent temperature Θ(x, y, z, t) of ground beneath and around a surface thermal disturbance, S (the bounds of the lake basin) at position x, y, z, is given by

equation image
equation image

The boundary temperatures A and B are of the undisturbed ground surface and lake (S) respectively. For conductive heat transfer, ground temperatures evolve by

equation image

where α is thermal diffusivity. Both A and B vary seasonally but mean annual values can be used for the evolution of taliks over tens of years or more, because seasonal effects on temperature rapidly attenuate with depth. Lachenbruch [1957a, 1957b] presented analytical solutions given geometrically simple shapes for S, which have been used to estimate the depth dependence of steady state temperature beneath the center of round or strip lakes [e.g., Mackay, 1962, Brown et al., 1964, Smith, 1976, Burn, 2002], and a method especially suited to graphical integration [Lachenbruch, 1957a] for irregularly shaped surface disturbances [Smith, 1976]. Temperature at depth Z beneath the center of a circular lake, for example, is

equation image

where Tg is temperature of undisturbed ground (°C), Tw is mean annual bottom temperature of lake water, I is geothermal gradient (m/°C) and RB is mean basin radius [Mackay, 1962]. Talik depth (where TZ = 0°C) depends on lake radius for small lakes, an effect that arises because horizontal temperature gradients are significant beneath small lakes, which decreases the steady state depth of the talik. Because the steady state approximation is appropriate only where a suitable length of time has elapsed, whereas lakes are dynamic, the one-dimensional Stefan equation has been used estimate time to steady state depth beneath thaw lakes [Burn, 2002]. For small lakes (<several hundred meters across), horizontal temperature gradients beneath the lake center cause the Stefan solution to overestimate thaw depth because of the assumption of downward conduction only.

[8] An alternative is to use numerical solutions to the heat conduction equation to investigate time-dependent perturbations in ground temperature and talik shape beneath lakes. Ling and Zhang [2003] use a two-dimensional finite element model to explore temperature profiles in permafrost as a function of lake temperature and time, predicting talik depths of 28 to 53 m beneath a lake of 800 m diameter after 3000 a, depending on water temperature. Zhou and Huang [2004] examine the response of varying air temperature on lake ice and talik development, showing lake ice thickness is closely linked to air temperature, and isotherms beneath a shallow lake (3 m, with lake ice thickness <2 m) migrate downward during the winter. One difficulty with existing dynamic numerical and steady state analytical models is that lake deepening caused by thaw subsidence in the talik is not addressed, even though this changes the boundaries and volume of the heat source, the lake. Also not addressed is radial expansion of the lake by bank retreat, which varies the area of the thermal disturbance thereby potentially creating a disequilibrium talik.

3. Modeled Taliks and Bathymetry

3.1. Model

[9] To investigate the relationships between ground ice, talik configuration, and lake bathymetry, we use a time stepping finite difference model for the two-dimensional (cross-section) version of equation (3), under the assumption of reflective lake symmetry across the modeled vertical plane. Mean annual lake bottom temperature, Tw, is applied at the periphery of a lake. Latent heat is included by effectively reducing thermal diffusivity, α (= k/C), within a phase change envelope because conductivity, k, and heat capacity, C, have temperature dependence [Lunardini, 1981]

equation image
equation image

where W is the ice content and Wu the water content. The temperature at which ground begins to freeze, Te, is assumed to be 0.0°C. The width of the phase change envelope, δT, is assumed to be 1°C in fine grained soils [Comini et al., 1974] as has been used elsewhere in modeling permafrost thawing beneath lakes [Ling and Zhang, 2003]. Subscripts u and f denote frozen and unfrozen states respectively. Lw is the latent heat of water and ρb dry bulk density.

[10] A time-marching Dufort-Frankel scheme is used to solve the parabolic two-dimensional heat equation (L. N. Trefethen, Finite difference and spectral methods for ordinary and partial differential equations, unpublished text, 1996, available at http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html.) using a grid spacing of 0.3 m, and a time step of 5 d. The lake bottom elevation (z of surface thermal disturbance) migrates downward in each time step a distance that is the product of increase in talik depth and mean excess ice content in the new zone of the talik (excess ice is the volumetric ice content that is in excess of the porosity of the substrate were it thawed). In nature, thaw subsidence may be delayed, particularly in fine-grained (clayey) soils in which low hydraulic conductivity impedes drainage of water released by thawing of excess ice. However, where drainage is likely to be slowest (at the bottom of a deep talik) the rate of release of liquid water also is at a minimum because of slow advance of the thaw front. We do not attempt to include a delay in thaw consolidation. Hence our results are likely most pertinent for soils which are not clay rich, and the ages of our modeled bathymetric profiles are minimums.

[11] Parameters are chosen to match measured values for thaw lakes and surrounding substrates. Precise relationships between climate, lake size, lake ice, and mean annual lake bottom temperature (Tw) are not available. However, Burn [2002] reports mean annual lake bottom temperatures of ∼ 3.5 to 4.5°C for lake depths of 4–11 m (temperature increasing with depth) for a thaw lake in NW Canada. Ling and Zhang [2003] use temperatures of 1–3°C in simulations of thawing beneath shallow, <4 m deep, lakes on the Alaskan Arctic coastal plain. We set Tw to 3°C in all simulations to facilitate their comparison, and because this is within the relatively narrow range of available measurements.

[12] Mean annual ground surface temperature is set to −8°C, chosen to approximate the mean annual temperatures of our field sites (−6 and −10°C in NSP and YCP respectively). A geothermal heat flux of 0.055 W m−2, a value measured from deep beneath thaw lake terrain in northern Alaska [Lachenbruch et al., 1982], is applied to the bottom boundary, and an equilibrium temperature profile imposed as an initial condition. Thermal conductivity, k and heat capacity, C, are 1.17 W m−1 K−1 and 4.0 × 108 J kg−1K−1 in the frozen state, and 0.33 W m−1 K−1 and 6.7 × 108 J kg−1K−1 in the unfrozen state, which are within the range of thermal parameters used by Lachenbruch et al. [1988] and Zhou and Huang [2004]. These assume k and C values for soil components summarized by Williams and Smith [1991], with volumetric proportions: 10% organic material, 40% mineral soil and 50% ice.

[13] Our goal is to investigate bathymetry and talik development through time, and the effect on this of variations in ground ice depth. For these purposes, we use two end-member ground ice scenarios in which the icy layer (30% mean excess ice) reaches 300 m deep (deep scenario representing syngenetic ice settings) and 5 m deep (shallow scenario representing epigenetic ice). Ice content and thermal properties of permafrost will of course vary at and between field locations. Because the principal model process is linear diffusion (heat conduction), different values for diffusivity will scale rates of thaw front advance and subsidence in the lake bed but not change fundamental talik and bathymetric shapes. Section 3.3 presents the dependence on thermal diffusivity of the rates of talik and lake deepening.

3.2. Simulations

[14] From an imposed initial lake of depth 2 m and radius 350 m, the talik and lake bottom migrate downward at differing rates (Figure 1). For the shallow ground ice simulation, talik thickness increases to 48 m after 8000 a, but the increase in lake depth is <0.2 m. For the deep ground ice simulation, talik thickness reaches 45 m and lake depth 22 m after 8000 a. Basin morphology follows the shape of the underlying talik, with the talik possessing rounded crescent-shaped margins and a flat central basin. The total thaw settlement in the deep ice simulation is 30%, as expected given the volumetric excess ice content (because the talik's depth is 67 m and its thickness 45 m). Talik thickness in deep ground ice, compared to shallow ground ice, is reduced beneath a thaw lake of equal radius and depth because of thaw-driven subsidence (Figure 2).

Figure 1.

Talik development and lake morphology through time in the model. Top plots show temperature profile to 400 m depth, and bottom plots show lake morphology and temperature profile to 20 m depth. (a) In a deep ground ice environment, thaw-driven subsidence continues throughout the model run, producing a deep lake with inclined margins. (b) In a shallow ground ice environment, lake depth remains shallow (several centimeters increase) and flat. Both models show near-equilibrium conditions after 8000 a. Model parameters include a nonexpanding lake (radius 352 m, initial depth 3 m) in permafrost where compaction of sediments corresponds to 30% excess ice to 5 m depth (shallow ground ice) and 400 m (deep ground ice).

Figure 2.

Modeled lake depth and talik thickness, beneath the lake's center, over 8000 a for small and larger lakes in (left) deep ground ice and (right) shallow ground ice environments.

[15] To investigate the effects of rapid lake expansion on talik shape and bathymetry beneath rapidly expanding lakes, the lake in the deep ground ice simulation (Figure 1b) increased in a step function change at year 8000 from an initial radius of 350 m to 500 m, with initial water depth of 2 m beneath this expanded region. Figure 3 shows talik development and lake bathymetry 3000 a after rapid bank retreat. The talik rapidly expands to the new lake shore by growing rapidly downward beneath the shallow lake terrace. At 200 a after lake expansion, talik thickness beneath the terrace reaches 6 m, and after 1000 a 12.6 m. In comparison, talik thickness beneath the lake center, already near equilibrium position, increases by <2 m over the same 1000 a period. The former lake shore is marked by a “step” in both bathymetry and talik bottom position, both of which diffuse with time following lake expansion. At 3000 a after expansion, an approximately linear slope extends upward at ∼5° from the flat basin of the original lake to the new shoreline. This transient behavior is a simple illustration of the bathymetry and talik shape of an expanding lake with a nonequilibrium talik. Limitations of the simple step function approximation for an expanding lake are considered in the Discussion.

Figure 3.

Evolution of ground temperatures and bathymetry of a modeled lake following an increase in lake radius from 350 to 500 m (the morphology and temperature profile prior to the increase is from a deep ground ice simulation at 8000 a). The transient morphology of expansion is a flat-bottomed basin with inclined margins ramping up to the water line.

3.3. Sensitivity to Parameters

[16] Three substrate scenarios, each differing from the reference parameters (section 3.1) were used to test the sensitivity of talik thickness and lake depth to substrate properties. Each simulation spanned 8000 a (Figure 4). Substrate I, consisting of 20% mineral soil and 80% ground ice, has a talik thickness of 48 m and lake depth of 23.1 m after 8000 a, 8% and 7% higher than reference model results, respectively. Substrate II, consisting of 10% mineral soil, 50% ground ice and 40% organic soil, has talik thickness 40.9 m and lake depth 20.6 m, 6% and 9% less than the reference scenario. Substrate III, consisting of 60% mineral soil and 40% ground ice, has lower thermal diffusivities (1.2 × 10−6 m2 s−1 and 4.1 × 10−7 m2 s−1) than the reference scenario because of reduced ground ice. The lake reaches 18.5 m depth and taliks develop to 37.3 m thickness, 14% and 17% less than the reference scenario. Thaw lakes growing in substrates with high thermal diffusivities (uniform with depth) have rapidly propagating thaw fronts, and develop thicker taliks and deeper basins. The relatively minor changes, <3 m, in lake depth and talik thickness across the different scenarios indicates basin morphology and talik thickness are not highly sensitive to substrate thermal properties over the range used.

Figure 4.

Sensitivity of modeled talik thickness and lake depth to thermal diffusivity. Substrate I is an ice-rich mineral soil (30% more ground ice than the reference scenario); substrate II is ice and organic rich; and substrate III is a mineral soil with small amounts of ground ice (10% less than the reference scenario). Substrates with higher frozen thermal diffusivities develop thicker taliks and deeper lakes beneath nonexpanding thaw lakes of identical dimensions.

4. Measured Basins

[17] We measured lakes and basins on the Yukon Coastal Plain (YCP) and Northern Seward Peninsula (NSP) (Figure 5). Permafrost at the NSP contains deep syngenetic ground ice and at the YCP primarily shallow ground ice where lakes were measured (Appendix A1). Five NSP basins and six YCP basins representing different combinations of lake generation, size, and ground ice type were selected (Table 1 and Appendix A2). Differential GPS and sonar were used to measure the three-dimensional (3-D) bathymetry of basins ≤300 m across (Figure 6) and the representative cross sections of larger basins (Figure 7). In addition to bathymetric measurements from these selected lakes, plan view measurements were collected from lakes and basins in ≈400 km2 areas of the NSP and YCP. These included lake area, ellipticity (E), long-axis orientation, and margin smoothness (S, the ratio of margin perimeter to that of a best fit ellipse) (Appendix A3 and Tables S1 and S2). These measured lakes are in well-developed thermokarst palimpsests in both regions. Radiocarbon dates from basins in palimpsests indicate that the oldest basins formed in the early Holocene or earlier, draining at ≈8–9 ka BP. The superposition of younger drained basins on early Holocene basins indicates complete “thaw lake cycles” have occurred over the Holocene in both regions (Appendix A4). Active slumps, exposed permafrost, and unvegetated bluffs that bound many lakes, indicate modern lakes are expanding in the NSP and YCP.

Figure 5.

Images of thaw lakes at (a) Seward Peninsula, northwestern Alaska (mosaic of U.S. Geological Survey color-IR photos, lines 54 and 55) and (b) Yukon Coastal Plain, Yukon Territory, Canada, with Running River at the bottom right (Landsat7, product ID 065012.0100.020718). In Figure 5a, Kitluk River is left of center, and Espenberg River is at far right. The inset shows the location of field sites.

Figure 6.

Bathymetry of (a) Buck Lake and (b) Doe Lake (both with margins inclined 2°–7°), (c) Rack Lake, (d) Long Lake (with margins inclined ∼5°), and (e) Little John Lake, all from the YCP. Horizontal distances are in meters. Depths are in centimeters.

Figure 7.

Bathymetric cross sections of lakes (a) Olive, (b) Oxford, (c) Peat, (d) Pear, and (e) Claudi. Water levels are marked WL (approximate for drained basins A, B, and D). Water level for Peat Lake is at 0 m. Small-scale irregularities in point elevations are from ±20 cm error in surveys and from tussocks formed since lakes drained.

Table 1. Lakes With Measured Bathymetrya
NamebRegionGround IceGenerationArea, m2Depth, mBathymetry
  • a

    Additional data on these and other lakes in Tables S1 and S2.

  • b

    All names unofficial except for Peat Lake.

PearNSPdeep10.9522broad ramped margins, flat central basin
ClaudiNSPdeep10.213broad ramped margins, no flat central basin
OliveNSPshallow>17.3≈2.0flat bottomed
OxfordNSPshallow>18.4≈2.0flat bottomed
RhondaNSPshallow>10.931.6flat bottomed
BuckYCPshallow10.013.0marginal ramps, flat central basin
DoeYCPshallow>10.012.9marginal ramps, flat central basin
RackYCPshallow>10.042.8marginal ramps, flat central basin
LongYCPshallow>10.032marginal ramps, flat central basin
Little JohnYCPshallow>10.013.2shallow bowl-shaped basin
PeatYCPshallow>13.11.6flat bottomed

5. Results and Discussion

5.1. Relationship Between Lake Age and Depth

[18] Lake depth increases with approximately equation image in permafrost with a deep layer of excess ice. Large diameter basins in icy permafrost are predicted to require ≈5000 a to reach depths of ≈20 m, the typical depth of such basins on the Seward Peninsula (Figures 2 and 4), and slightly longer time for lakes that are less in diameter, <100 m. Given the sensitivity of talik advance to lake bottom temperature [Ling and Zhang, 2003], a 1°C increase in lake bottom temperature (above the 3°C used here), would increase the deepening rate of large lakes to 20 m in ≈3500 a. The volumetric excess ice in permafrost also can influence the deepening rate of a lake, with values greater than the 30% excess ice used here causing greater thaw compaction and hence depth. Conversely, however, talik deepening will slow with greater ice content because latent heat in thawing permafrost increases. Model-based predictions for deepening are based on heat conduction and thaw subsidence only, and so are maximum limiting estimates given the thermal properties and ice content of permafrost used in the simulations (sediment redeposited into the deepest parts of natural basins would reduce depth). The effect of sediment redistribution probably is minor, however, as the timescale for lake deepening in the model is generally consistent with the depths and estimated ages of NSP basins. Lake Claudi, 1000–2000 a old, has a 13 m deep basin. Pear Lake basin and the earliest basins in the NSP palimpsest, >8000 a old, have relief of ≈22 m. The oldest basins persisted ≈5000 a, given an initiation by the deglacial warming that triggered circumarctic thermokarst at 13,000 BP [Walter et al., 2007] and drainage at 8200 BP (Appendix A4).

[19] In comparison, lakes in permafrost with shallow epigenetic ground ice have depths that are independent of lake age because a steady state depth is achieved within 100 a (Figure 7). For example, later-generation lakes on the NSP have areas spanning an order of magnitude (0.93–7.3 km2), but consistent depths of ≈2 m. YCP lakes, all in shallow ground ice, have depths of 1.6–3.2 m independent of size.

5.2. Effects of Lake Expansion on Bathymetric and Talik Shape

[20] In permafrost with deep syngenetic ground ice, lakes that are not expanding radially develop deep basins with relatively narrow marginal ramps, <10 m across (simulations in Figure 1). In contrast, the simulation in which lake size is increased after 8000 a (section 3.2 and Figure 3) illustrates the morphology of taliks and basins for lakes in which radial expansion has exceeded the rate of adjustment of the talik. A broad, inclined talik bottom slopes downward from the lake's margin to its central basin. The width and gradient of the corresponding slope in the basin, which overlies the out-of-equilibrium region of the talik, depends upon the rate of expansion of the lake with respect to the diffusivity of permafrost: Faster expansion will induce broader margin slopes. For small lakes, the margin slopes may meet at the lake center to form a deep v- or bowl-shaped bathymetry. For larger lakes, a flat central basin may form over the region of the talik that has passed beyond the ice-rich permafrost layer or has achieved a steady state depth. Quantitative values for the depth to the flat bottom, the lake diameter, and time taken to reach this morphology will depend on the depth of the ice rich layer, the thermal diffusivity of permafrost, and the expansion rate of the lake. Quantifying this interplay would require a different model, discussed below. However, Lakes Claudi and Pear at the NSP illustrate the bowl-shaped bathymetry and that of a flat central basin surrounded by broad ramps, respectively (Figure 7). Claudi, 100 m across its narrow axis, is bowl shaped. Pear, ≈1000 m across, has marginal ramps 200 m wide that slope at ≈4° into a flat central basin (the basin appears to have domed upward since drainage, because of fluvial erosion and/or inflation by refreezing of permafrost: Appendix A2). Only lakes in deep syngenetic ice have bathymetry that is sensitive to radial expansion; bathymetry is not diagnostic of a lakes radial expansion for lakes in shallow epigenetic ice because a steady state depth is achieved rapidly, in <100 a (Figure 1).

[21] Changes in the radial expansion rate of a lake cause persistent inflection points in the lower boundary of the talik, and consequently in its bathymetry. Hence measurements of talik morphology might be used to infer past lake dynamics. In the model, a step function increase in lake radius causes an inflection point in the talik beneath the initial lake margin (at 300 m) that diffuses slowly, persisting for ≈3000 a after the lake's size increased (Figure 3). The presence of inflection points in taliks may be illustrated by Lake Illisarvik (Richards Island, Northwest Territories), a recently drained basin [Mackay, 1981]. Illisarvik has a pronounced step in its talik, with corresponding inflection points in basin morphology (Figure 8). Illisarvik has been proposed to have a talik that is at equilibrium because the lake has existed for much of the Holocene [Burn, 2002], with the lake interpreted to have initiated at ∼9500 radiocarbon years BP, followed by expansion until 6000 a BP then shrinkage to its predrainage size at ∼2000 a BP [Michel et al., 1989]. The transient response of the talik to lake shrinkage would be a bulbous shape that is deep beneath the current lake margins. However, pronounced inflection points occur in the talik (at ≈20 m depth) and less so in the bathymetry, particularly on the northern half of the lake (Figure 8). The thin, <10 m thick, talik beneath the outermost ≈200 m of the lake might be the result of significant differences in thermal diffusivity of the substrate, that happen to coincide with the position of the steps in the talik, or it might indicate recent radial expansion of the lake.

Figure 8.

Bathymetry (solid line) and talik (dashed line) in a south-north cross section of Lake Illisarvik [Hunter et al., 1981].

[22] The imposition of a step function increase in lake size in our model (section 3.2) is a heuristic device to examine, qualitatively, the transient dynamics and morphology of a talik beneath a rapidly expanding lake. Natural lakes expand by thaw subsidence and mass movement in more or less continuous fashion. It seems reasonable to assume that, in general, radial expansion will be more rapid when summer air temperatures are higher, and the thaw season longer, causing deeper thawing and more frequent failures on subaerial bluffs. Expansion also is likely to be greater where the ice content of permafrost is greatest. Hence we anticipate that thaw lakes in warmer climates and in deep, abundant, excess ice will have taliks with inclined margins (similar to our step function simulation). To investigate the dependence of thaw lake expansion, and talik shape, on climate and ground ice, a model combining heat transfer and thaw subsidence with mass wasting and deposition in the basin would be required.

5.3. Dependence of Lake Area and Shape on Ground Ice and Lake Generation

[23] Thaw lake landscapes with deep syngenetic ice can be dissected by 20+ m deep basins within ≈5000 a (section 5.1). As more first-generation basins initiate and expand, the increasingly dissected landscape has more drainage pathways that impose limits to the maximum diameter of subsequent lakes. The resulting trend to smaller later-generation lakes is present in the NSP where the mean area of first-generation basins is approximately twice that of later-generation basins, but both have broad variability (Figure 9). Conversely, for shallow ground ice environments, first- and later-generation lakes should have similar area because the relief of basins is insignificant, <5 m. YCP lake properties are consistent with this prediction: their depths are <4 m across all lake generations and areas of first- and later-generation lakes are similar (Table S1 and Figure 9).

Figure 9.

Distributions of lake area for first-generation lakes (black bars) and later-generation lakes (white bars) on the (a) NSP and (b) YCP. On the NSP, first-generation basins (black bars) have mean area 4.8 ± 1.2 km2, and later-generation basins (white bars) have mean areas 2.2 ± 2.7 km2. On the YCP, first-generation basins have mean area 0.5 ± 0.5 km2, and later-generation basins have mean area 0.6 ± 0.8 km2. Two outlier NSP basins and two outlier YCP basins, not plotted, are included in means.

[24] The smoothness and circularity of lake margins also can vary between lake generations, depending on ground ice depth (Figure 10). In the NSP, first-generation lakes are more circular than later-generation lakes (EF = 0.52 ± 0.18 vs. EL = 0.62 ± 0.17) and have smoother margin outlines (SF = 1.09 ± 0.04 vs. SL = 1.24 ± 0.20). In the YCP, first- and later-generation lakes have similar ellipticity (EF = 0.70 ± 0.16 vs. EL = 0.78 ± 0.12) and similar border smoothness (SF = 1.18 ± 0.12 vs. SL = 1.22 ± 0.22, where S is the ratio of basin perimeter to a fitted ellipse). In deep, homogeneous substrates where lakes are not influenced by external controls such as wind [e.g., Cote and Burn, 2002, Hinkel et al., 2005] or topographic gradient [Pelletier, 2005], both of which have been hypothesized to generate oriented basins, banks retreat radially from the center of the water body creating a circular lake. In shallow ground ice environments, the low-relief terrain contributes to more frequent coalescence of lakes causing noncircular shapes (higher E) and irregular margin outlines (higher S). Lacking morphologic change over time by the addition of deep basins, the YCP landscape has thaw lake basins for which ellipticity and smoothness are independent of lake generation.

Figure 10.

Smoothness and ellipticity of lakes and basins on (a, c) the NSP (deep ground ice) and (b, d) the YCP (shallow ground ice) versus lake basin area. In the NSP, first-generation basins (solid circles) have smoother borders than later-generation basins (crosses), and ellipticity decreases with lake area. In the YCP, larger lakes have more irregular margin outlines. Ellipticity of YCP lakes is independent of lake area and generation.

[25] The orientation of thaw lakes, where it occurs, is commonly attributed to differential erosion caused by wind-driven water circulation. The long axes of lakes are predicted to be perpendicular to the predominant wind direction [Rex, 1961; Carson and Hussey, 1962; Cote and Burn, 2002; Hinkel et al., 2005]. In the NSP, lakes are only weakly oriented, at 77° off the wind direction. In the YCP, lakes are parallel to the wind direction (Figure 11). These results are based on a relatively small number of basins. The mechanisms for lake orientation are beyond the scope of the two-dimensional cross-section model presented in this paper. However, our observations may be useful to constrain the conditions under which a steady and dominant wind direction will cause a preferred orientation to arise.

Figure 11.

Rose plot of NSP thaw lake orientation and wind direction measurements from Kotzebue, Alaska, and YCP thaw lake orientation and wind direction measured at Shingle Point, Yukon Territory. Thaw lake data are normalized from Tables S1 and S2. YCP wind measurements are from Canadian climate normals (1985–2001), and NSP wind measurements are from the Western Regional Climate Center, 1992–2002.

6. Conclusions

[26] 1. Our model of heat transfer and subsidence generates depths and bathymetric profiles broadly similar to measured thaw lakes on the Northern Seward Peninsula (deep ground ice) and Yukon Coastal Plain (ice-rich layer <10 m). The 20 m deep basins on the Seward Peninsula are predicted to take ≈3000–5000 a to form.

[27] 2. Bathymetry and talik shape can reflect the past 0–3000 a of a lake's history of expansion in deep ground ice environments. Small, actively expanding lakes are deep and have inclined margins from shore to lake center (or bowl shaped) and the underlying taliks are completely enclosed by an ice-rich substrate. As these lakes expand (>300 m diameter) they may develop inclined margins ramping up to the water line and a flat central basin. Lakes in shallow ground ice environments and later-generation lakes in deep ground ice environments, where ground ice has been depleted by the thaw lake cycle, have flat lake bottoms with narrow margin slopes up to the water line, irrespective of the lake's rate of radial expansion.

[28] 3. In the NSP where syngenetic ground ice is deep, later-generation lakes are smaller in area than first-generation lakes. Their expansion is limited by the ∼20 m of relief formed by earlier basins. Unaffected by preexisting topography and ground ice variations that would have been caused by earlier lake basins, first-generation basins are relatively circular. Later-generation lakes tend to coalesce into irregular shapes and drain more often than first-generation lakes. In shallow epigenetic ground ice, basin shape is less sensitive to lake generation because landscape morphology and ground ice depth are not changed as significantly by recurring thaw lake cycles.

Appendix A:: Measurements

A1. Field Sites

[29] The northern Seward Peninsula, Alaska, is a coastal plain along the Chukchi Sea (Figure 5a). At the nearest meteorological station in Kotzebue, 60 km northeast but of similar coastal position, mean annual precipitation is 230 mm, mean annual temperature is −6°C, and the predominant wind direction is from the east (Western Regional Climate Center, Historical climate for western region of the United States, 2005, http://www.wrcc.dri.edu). The depth of permafrost in the Seward Peninsula generally exceeds 90 m [Hopkins, 1949; Hopkins et al., 1955] and the active layer is 0.3–0.6 m thick (shallower in peat than mineral material). The region formed the central part of the Beringian subcontinent during Pleistocene sea level lowstands, with much or all of neighboring Kotzebue Sound subaerially exposed, providing a ready supply of loess transported by glacially charged rivers [Goetcheus and Birks, 2001]. Deposition of aeolian silt on the Seward Peninsula during the late Pleistocene was accompanied by an in-step rise in the permafrost table, leading to deep syngenetic ice in the form of ice wedges, lenses and pore ice forming 60–80% of the substrate by volume [Hopkins and Kidd, 1988; Hopkins et al., 1955], which translates to excess ice of 30–50% [Hopkins, 1949]. Over the Holocene, thermokarst processes have substantially dissected the landscape into extensive, low-relief plains containing thousands of thaw lakes, separated by residual uplands 10–20 m high [Hofle et al., 2000]. Modern thaw lakes cover roughly 20% of the land surface and drained lake basins 80%.

[30] The second study area includes thaw lakes and basins on the Yukon coastal plain near the mouth of the Running River on the Beaufort Sea, inland 2–5 km from Shingle Point (Figure 5b). Mean annual air temperature is −10°C, mean annual precipitation 250 mm, with the most frequent wind direction from 300° (from Environment Canada, Historical climate normals, 2005, http://www.climate.weatheroffice.ec.gc.ca/ for Shingle Point). Permafrost thickness on the coast is at least 300 m [Rampton, 1982], and the active layer is ∼0.3 m. A glacial advance or advances between 130ky and 75ky deposited glacial and glacial-fluvial gravels, sands and silts in eskers, kames and meltwater channels, intermixed with clays, silts and sands from marine transgressions, leaving unconsolidated deposits more than 60 m thick. Estuarine sediments and fine grained colluvium are particularly ice rich, containing excess ice of 10–90% in the form of lenses, veins and wedges, with the highest ice contents in the upper 1.5 to 3 m [Rampton, 1982]. Post glacial alteration of shallow marine and glacially derived morphology has predominantly been by thermokarst activity forming lakes [Rampton, 1982] and localized retrogressive thaw slumps [Lantuit and Pollard, 2005]. Deeper beds of massive ice (some 10s of meters deep and 200% ice content by weight, compared to dry soil) have been reported in permafrost along the western Arctic coast [Mackay, 1971], a region which includes the YCP study area. For example, beds of massive ground ice are exposed along the coast near Sabine Point, ≈35 km NW of Shingle Point [Harry et al., 1988] and further NW at Herschel Island [Pollard, 1990] where they host retrogressive ground ice slumps [Lantuit and Pollard, 2005]. However, these deep beds of massive ice are localized. Only 6% of 4150 shot hole logs along the western Arctic coast showed massive ice [Mackay, 1971], and the shallow depth of thaw lakes and lack of exposed massive ice in exposures along thaw lakes and the Running River indicate extensive massive ice beds are lacking or rare in the YCP locale where we measured lakes.

[31] Ground ice conditions can be highly variable between and within regions. We emphasize that our use of “deep” and “shallow” ground ice conditions (the NSP and YCP model scenarios) is a simplification of this complexity. The two scenarios are end-member conditions of syngenetic ice and epigenetic ice respectively, useful for sensitivity tests of the model.

A2. Lakes and Drained Basins

[32] Claudi Lake is actively expanding as shown by unvegetated margins with mass wasting scars, floating rafts of peat in the lake, and approximately 80 m of bank retreat into Pear Lake basin which drained within the past few hundred years. The basin of Lake Claudi is bowl shaped and 13 m deep (maximum water depth 9 m) from the surrounding uplands. The estimated age of Lake Claudi, 1000–2000 a, is based on its current maximum radius and a sustained bank retreat 0.4 m a−1. This expansion rate is based on its bank retreat distance over the ≈250 since Pear Lake drained.

[33] Pear Lake basin exhibits evidence of active expansion prior to its recent drainage, including steep above-water line bluffs averaging ∼20° and locally exceeding 40° where cut by slump scars. Recent drainage of Pear implies its margin was expanding prior to encountering a topographic low, in this case the Kitluk River valley into which it drained. Figure 7d shows the ∼300 m wide, inclined margins of this lake (∼4°) and the flat lake floor, which is ∼400 m wide. Apparent doming of the basin center likely is a residual effect of the circular drainage channel around the outer edge of the central basin. Some of the doming of the central part of Pear's basin may be because of inflation by refreezing of the talik. Mackay [1997] describes lake bottom uplift of 0.1–0.3 m during the 15 a period following drainage (of Lake Illisarvik), with nearly all occurring within the first 5 a. The doming of Pear is ≈5 m, indicating that apparent ‘doming’ is likely morphology formed by incision during drainage. The depth of incision may be particularly great in Pear basin, compared to most thaw lake basins, because the steep gradient to the Kitluk River (the outlet of the drainage event) allowed significant headward incision into the basin. Lakes Oxford and Olive are expanding lakes in shallow ground ice (these are later-generation lakes on the NSP, and hence in shallower ground ice). Both drained after 1978 and before 1992, given available air photo and satellite images. Lake Rhonda, <1 km from the coast, has an irregular shape in plan view, two round pools and a long bay, with depths of 1.6 ± 0.2 m across the basin.

[34] On the YCP, Peat Lake is a large, later-generation, modern thaw lake with steep, vegetated, unscarred northern banks, >10 m from water level to the uplands, and low southern banks of thawing ice wedge polygons within a drained thaw lake basin (Table S1).

A3. Lake Bathymetry and Shape

[35] We used differential GPS (DGPS) to measure morphology of active lakes and drained basins and to determine horizontal position for sonar surveys. For bathymetric surveys of active lakes, we used a Leica GS20 single frequency (L1) DGPS system to measure positions and a 400 kHz SpeedTech depth sounder with 6° beam angle was used to determine depth at each location. Postprocessing of differential corrections against a Leica 1230 reference receiver rendered a horizontal accuracy of ±0.2 m. Sounder resolution is ±0.1 m for depths from 0.5 to 10 m, a value confirmed by comparison to selected manual depth soundings. Measurements were collected along transects across lakes, with point spacing and number of transects depending on lake size and basin morphology. The number of points was increased for deep and multibasin lakes. Larger lakes were measured in cross section. We lost a 3-D DGPS survey of Lake Claudi as a result of hardware failure, but a manually recorded cross section was retained (shown in Figure 7).

[36] For surveys of recently drained basins, we used a Leica 1230 dual frequency receiver with real-time differential correction against a second similar receiver as reference. Up to three transects per lake were used to produce bathymetric cross sections and plan view maps. Combined vertical and horizontal instrument error is <1 cm, but effective vertical precision for surveys in which the receiver is backpack mounted is ∼0.2 m, determined by comparing pack mounted surveys against a survey in which the receiver was mounted on a vertically levelled survey pole.

[37] To characterize the plan view shape of lakes, basin areas and shapes were measured using DGPS for six active lakes and from black and white air photos of the YCP (National Air Photo Library, 3 and 6 m resolution) and near infrared air photos of the NSP (U.S. Geological Survey mapping photos, lines 54 and 55, 5.6 m resolution). Air photo measurements of lake radius were within 1.2% of DGPS measurements, with no bias to overestimating or underestimating radius detected. Lakes and basins were classified as either first generation or later generation on the basis of overlapping relationships with other basins. First-generation basins are set into Pleistocene uplands, whereas later-generation lakes and basins are enclosed by or intersect larger, older basins (Figure A1). Measured characteristics of basins included perimeter, area, ellipticity, margin smoothness and long-axis orientation. Ellipticity, E, is equation image, where a and b are the semimajor and semiminor axes of an ellipse fitted to the lake outline by minimizing the sum of squared differences between the measured margin and the ellipse. Margin smoothness, S, is the ratio of lake perimeter to that of the fitted ellipse, with perimeter taken to be the summed distances between centroids of edge pixels in the object. Values of S > 1 indicate increasingly irregular lake perimeters.

Figure A1.

Examples of first- and later-generation basins in the Seward Peninsula, Alaska, with a small portion of each basin outlined. Later-generation basins are found within earlier-generation, drained lake basins. Lake A is SP22, B is SP20, and C is SP09 in Table S2.

A4. Constraints on Basin Ages and Bank Retreat Rates

[38] A minimum limiting estimate for the number of years since drainage was obtained for Pear Lake basin on the NSP (Table S2) by accelerator mass spectrometer radiocarbon assays of basal terrestrial peat in cores and excavations from the basin. Pear Lake drained recently (uncalibrated radiocarbon age 150 ± 40 a, [Lab number β-199567]). Adjacent Lake Claudi has expanded 60 m into Pear Lake's basin since Pear drained. This imposes a bank retreat rate of 0.4 m a−1. Although not a precise estimate of the rate of bank retreat, this establishes that the lake is presently expanding and so may possess a disequilibrium talik.

[39] The basin at the lowermost level in the NSP basin palimpsest was selected from superposition of other basins and from the low gradient of the basin's margins. It also has the greatest depth of peat compared to six other basins low in the palimpsest that we cored. Basal peat in this basin was sampled from an exposure of peat and underlying thaw lake deposits, revealed in section along the shoreline of a modern lake which is presently expanding within the old basin. The calibrated calendar age of 8410–8200 a (1 sigma range, β-199569) of this peat sets the minimum time since the lake drained. Given the diameter and depth of the basin (2 km and 25 m respectively), we infer that the lake probably initiated between 12 ka and 10 ka. For the YCP, the oldest dated drained lake basin also is early Holocene: 9250 ± 70 a, from the deepest peat in 3 cores [β-199570] (YCP 21, Table S1).

[40] In summary, dates from YCP and NSP lake palimpsests indicate that the oldest basins formed in the early Holocene or earlier, draining ≈8–9 ka BP. The superposition of younger drained basins on the oldest basins indicates active expansion and complete “thaw lake cycles” have occurred over the Holocene. Modern lakes are expanding at the NSP and YCP.

Acknowledgments

[41] We thank D. W. Gardner, J. C. Gosse, S. G. Sikaneta (Dalhousie University), and B. T. Werner (USCD) for discussions and B. Hallet, B. Murray, and J. Pelletier for constructive reviews. D. W. Gardner assisted in the field. Field work was supported by the Northern Scientific Training Program (to J.J.W.) and the Natural Science and Engineering Research Council of Canada and the Polar Continental Shelf Project (to L.J.P.). The Canadian Foundation for Innovation, IBM Canada, and Leica Geosystems provided equipment.

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