Introduction

Permafrost has attracted tremendous attention from the scientific community and society over the past decades1. Global warming and permafrost degradation are impacting all aspects of polar landscapes, including: infrastructure, vegetation assemblage and ecosystems2, lakes and rivers3, and soil biogeochemical cycles4. Additionally, with the microbial decomposition of large stocks of organic carbon, permafrost degradation is contributing to a positive feedback in the global climate-carbon system5,6. However, the nature and magnitude of these changes are dependent on the vertical distribution of ice in permafrost sediments. Ground ice (particularly excess ice) controls the rate of permafrost degradation due to its high latent heat and the complex nature of potential feedbacks of thawing icy permafrost. For example, the positive feedbacks that develop following differential thaw of icy permafrost and ponding of the melted ice7,8. There is therefore a need to improve our knowledge on the factors influencing the vertical distribution of ground ice in the complex permafrost system in different landscapes to better assess the ongoing environmental changes and geohazard risks9,10.

There are four main types of ground ice in permafrost: pore ice, vein ice, buried surface ice, and intrasedimental ice (which includes segregated ice)11,12. Pore ice refers to the in situ freezing of soil moisture and tends to cement permafrost sediments; vein ice (ice wedges) is associated with frost cracking and is recognizable from polygonal patterned terrain, whereas the burial of surface ice is site-specific and relates mainly to glacial limits. In the absence of direct cryostratigraphic observations, the spatial and vertical distribution of intrasedimental ice is challenging to constrain, even when using remote sensing techniques13. As a result, studies often rely on sediment types to infer the abundance of intrasedimental ice: fine-grained sediments are classified as “frost-susceptible” and are inferred to be ice-rich and prone to geohazards14. For example, the ground ice map of Canada classified large areas as ice-rich permafrost with segregated ice based on surficial sediments and their frost susceptibility15,16 (Fig. 1). A similar map classified ice-free regions of South Victoria Land of Antarctica, including the McMurdo Dry Valleys (MDV), almost entirely as dry permafrost due to the coarse nature of the sediments, hyper-arid climate, and age of the surficial deposits17 (Fig. 1). However, for example, clast-rich tills in the Richardson Mountains/Peel Plateau region in the Northwest Territories18,19, muck deposits in the Klondike region in Yukon20,21, fluvial gravels in the Mackenzie Delta22,23, silty colluvium near Salluit in Nunavik24 and sandy-stony sediments in the MDV25,26,27 often contain ground ice abundance similar to frost-susceptible soils, but were identified as regions with low-medium ice content. This suggests that there are factors other than particle size, sediment age, and climate that can lead to near-surface ice enrichment.

Fig. 1: Ground ice maps of and climate conditions in Arctic Canada and South Victoria Land region of Antarctica.
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a Map of segregation ice abundance of Arctic Canada (data from ref. 16) and location of sampling sites mentioned in the text. b Map of ground ice and permafrost type in South Victoria Land region of Antarctica (data from ref. 17) and location of sampling sites mentioned in the text. c Climate conditions in Arctic Canada and McMurdo Dry Valleys of Antarctica (data from refs. 85,86). d Relation between total dissolved solutes in ground ice within permafrost of different regions of Arctic Canada and McMurdo Dry Valleys of Antarctica.

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In this study, we first review the temperature, salinity, and vertical distribution of intrasedimental ice in Arctic and Antarctic permafrost sediments, including organic-rich soils. Then, we determine the unfrozen water content profiles (SL) for different sediment types and water chemistries using the SOIL8MIN model28. Laboratory measurements and modeling have shown that the pore water (SL > ~0.13) can migrate under thermal and pressure gradients induced by temperature cycles in the permafrost sediments (here referred as rheological forces or REGO); whereas the film water (SL < ~0.13) can move under Van der Walls (VdW) forces (i.e., a pressure gradient within the film of water around soil particles that is dependent on temperature, radius of soil particles and the Hamaker constant)29,30,31,32. The REGO forces are also the ones that produce surface tension cracks and patterned ground, and the VDW forces produce segregation ice and frost heaving. Once SL is determined, we quantify the seasonality in the direction and speed of water migration under REGO and VdW forces in permafrost sediments with the WATEREGO model and, based on the ensemble results, determine the redistribution over time of ground ice in a deep permafrost column28. The model uses 17 ensemble parameters that reflect the modern regional permafrost and environmental conditions, and the final computation represents the average of 18 to 54 realizations. Together, this allows us to determine the effects of REGO or VdW forces on moving the unfrozen water in permafrost sediments with varying temperatures and salinities, and the rate at which ice can accumulate in the near-surface permafrost. Overall, this study provides the framework to develop a quantitative assessment of the vertical distribution of intrasedimental ice in permafrost sediments, a product that would improve environmental and geohazard risk assessments.

Results and Discussion

Arctic and Antarctic permafrost sediments: temperature, salinity, and ground ice

Permafrost is defined as a thermal condition of the ground where the sediments or bedrock remains below 0 °C for two or more consecutive years33. However, when permafrost contains ice, it can be described as the ground that remains frozen for two or more consecutive years34. The thickness of the active layer may equal, but generally exceeds the maximum depth of the 0 °C isotherm due to soil water salinity and the associated freezing point depression34,35. In the Arctic, the active layer is often moist to water-saturated and the boundary between the active layer and underlying permafrost is termed the permafrost table36. However, in the cold hyper-arid regions of Antarctica, the sediments above the ice-bearing permafrost are often dry37,38,39. Similar to the Arctic, the near-surface dry sediments in Antarctica may warm above 0 °C due to solar heating and develop an active layer40,41. If the depth to the icy permafrost exceeds the depth of 0 °C isotherm, that zone is termed dry permafrost with the boundary between the dry and icy permafrost called the ice table42. Therefore, in cold hyper-arid regions, the permafrost table represents the depth of the 0 °C isotherm, and the ice table represents a sublimation unconformity43. The depth of the permafrost table (0 °C isotherm or thaw unconformity) can be estimated from heat conduction equations (such as the Stefan equation)44, whereas the depth of the ice table (sublimation unconformity) can be estimated using the water vapor density gradient between the ground surface and the ice-bearing ground45,46,47,48.

In permafrost regions of the Canadian Arctic, the mean annual air temperature (MAAT) and precipitation display a broad latitudinal gradient with relatively warmer-wetter conditions in low Arctic regions and colder-dryer conditions in the high Arctic; thaw degree-days range from ~2000 in the low Arctic to ~250 in the high Arctic49 (Fig. 1). The mean annual temperatures at the permafrost table range from near 0 °C in discontinuous permafrost to ~–15 °C in the continuous permafrost of the high Arctic50. Knowledge of the chemical composition of ground ice in permafrost sediments is scarce. Studies from the Richardson Mountains to the Inuvik region shows that the melted ground ice has a Ca(Mg)SO4 geochemical facies with solute load averaging 6.8 mg kg−1 soils19,51; conversely, the ground ice within the post-glacial marine limit often contains high NaCl, such as near Salluit in the Nunavik region, and in the coastal region of the Eureka Sound Lowlands24,52,53 (Fig. 1). Permafrost in the Canadian Arctic is relatively young and largely reflects the late Quaternary post-glacial history54,55. The vertical distribution of ground ice in permafrost sediments were initially assessed from shot holes drilled for seismic studies as part of oil and gas exploration in the 1970s56,57. The qualitative distribution of ground ice (presence and thickness) in a variety of surficial deposits from the western Arctic (Richardson Mountains–Peel Plateau region and Richard Island, NWT) and the high Arctic (Fosheim Peninsula, NU) showed that the uppermost 1–2 m was typically ice-rich (Fig. 2). This was later confirmed by measurements of ground ice content from permafrost cores (Fig. 2). The gravimetric water content (GWC) shows significant intra-site variations, but the uppermost section of permafrost at all sites is generally ice-rich (with excess ice) and some sites also display an ice-rich zone at ~4–5 m depth. Perennially frozen peat, and frozen organic material in general, contain a much higher ground ice content than permafrost soils due to its higher porosity (sometimes exceeding 96%vol) and the higher water-absorbing capacity of organics (Fig. 2; Supplementary Data 1). Frozen peat, similar to permafrost soils, also displays zones of higher ice content, typically near the top of the frozen peat and ~2 m depth.

Fig. 2: Vertical distribution of ground ice at hundreds of sites in Arctic Canada and McMurdo Dry Valleys, Antarctica.
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a Ground ice abundance derived from seismic shotholes in western Arctic Canada (low Arctic). b Gravimetric water content from 11 sites in the Richardson Mountains and Inuvik region (low Arctic). c Gravimetric water content from 74 sites in the Fosheim Peninsula region (high Arctic). d Gravimetric water content from 2 sites in Northern Quebec (low Arctic). e Gravimetric water content from 94 sites in the McMurdo Dry Valleys of Antarctica. f Gravimetric water content from 2 sites with organic-rich soils. See Fig. 1 for locations of sites and methods for source of data.

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The MDV are the largest ice-free area of Antarctica and is classified as a cold and hyper-arid desert58 (Fig. 1). In the coastal thaw zone, the MAAT ranges from –15 to –20 °C (~44 thaw degree-days) and precipitation approaches 100 mm snow water equivalent (swe); whereas in the stable upland zone at higher elevation, the MAAT and precipitation decreases to –20 to –25 °C (0 thaw degree-days) and <10 mm swe, respectively59,60. The predominant surficial material is glacial till, usually with sandy to silty matrices, that range in age from Holocene to mid-Miocene61. The absence of vegetation and organic matter, reduced snow cover, and dry near-surface sediments (causing little to no seasonal change in thermal conductivity) ensure that the mean annual temperatures at the top of permafrost approximate the MAATs62,63. Salinity is an important property of sediments in the MDV. Since potential ablation exceeds precipitation, salts that are deposited by precipitation of snow or that are released during weathering of soils slowly accumulate in the sediments64. Salt types include sodium, potassium, and magnesium chlorides, nitrates, sulfates, and carbonates65. It was observed that salt concentrations increase with sediment age, but the colder-drier regions also contain higher salt abundances, reaching up to 1100 g kg−1 sediments26, because of the paucity of liquid water (Fig. 1). This salt load is up to four orders of magnitude higher than in most Arctic permafrost sediments. In the MDV, hundreds of sites from the coastal thaw zone to the stable upland zone were investigated for ground ice content and sediment properties as part of the New Zealand Landcare Research (formerly the Soil Bureau) sampling campaigns in South Victoria Land from the 1960s to 1990s38,66,67,68. The GWC of permafrost in the coastal thaw zone averaged 30.2 ± 40.0% (Fig. 2) and this led to permafrost being classified mostly as dry permafrost or ice-cemented permafrost throughout the MDV17. However, the addition of new sites from various research groups over the past two decades indicate that many sites at higher elevations display a zone of ice-enrichment below the ice table that extends to 1–2 m depth; below that depth, the GWC remains <30% with the exception of discrete ice lenses25,26,27,69,70 (Fig. 2). In the two deep cores from icy permafrost soils (Beacon Valley and Friis Hills), ice-enrichment is also observed at ~5 m26,27. Approximately 70% of the surveyed sites in the stable upland zone (n = 28) have excess ice in the uppermost 2 m below the ice table.

Unfrozen water content and its seasonal migration in permafrost sediments

The in situ development of ice-rich zones in permafrost sediments requires the presence of unfrozen water that migrates to a freezing front71. The unfrozen water content as a function of ground temperatures (SL) was initially determined in salt-free permafrost sediments, and it was shown to be dependent on the specific surface area of sediments72. Later, Rempel et al. expanded the SL function to include soil porosity, dry bulk density, and soil water chemistry73. Here, we use the Rempel-type SL curves (computed from SOIL8MIN model) that encompasses temperature, sediment type, and soil water salinity for four sediment types (Inuvik clay, Chena silt, Lebanon gravel, and Nagare peat; Table 1) and different soil water chemistry (1x and 0.5x sea water, 0.1 molality Ca(Mg)SO4 water and pure water; Table 2) (Fig. 3). For all sediments, the SL at temperatures near 0 °C is determined by the freezing point suppression of the soil water solution (1× seawater = –2.03 °C; 0.5× sea water = –1.01 °C; 0.1 molality Ca(Mg)SO4 = –0.58 °C). Below that temperature, the capacity of clays to hold more water under higher surface tension dominates over the effect of soil water chemistry, even for high salinity waters. However, for low salinity silt to gravel sediments, the SL curve approaches that determined by their specific surface area (i.e., Anderson and Tice SL-type function). But at higher salinity, the SL of these coarser sediments is determined by the soil water chemistry: for example, silt to gravel with brackish to saline waters can have SL near that of clays at equal temperatures. In these coarse sediments with brackish to saline waters, the residual water is precipitating NaCl ·2H2O at its eutectic point of –23 °C, which then substantially reduces SL at lower temperatures due to the incorporation of water in the hydrated salts. Peat appears to have a slightly different behavior in terms of SL curves relative to the other sediments. The intrinsic properties of peat allow it to hold slightly more unfrozen water at temperatures <–2 °C and SL in low salinity peat appears to be kept constant at 0.08 with further cooling. Therefore, SL cannot be simplified by a single curve for each sediment type but instead consists of a range of possible curves that depend on soil water chemistry as well.

Table 1 Values of parameters for the different sediments used in SOIL8MIN model to determine unfrozen water content (SL), a semi‐empirical model that includes the soil properties and the geochemical composition of soil water.
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Table 2 Values of soil water chemistry used in SOIL8MIN model to determine unfrozen water content (SL), a semi-empirical model that includes the soil properties and the geochemical composition of soil water.
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Fig. 3: Unfrozen water content profiles for various sediment types with varying soil water chemistry.
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The SL profiles were computed using SOIL8MIN model28. a Inuvik clay, b Chena silt, c Lebanon gravel and d Nagare peat. The oscillations in the SL curves are due to an instability in the use of the Rempel-type equation to determine the fraction of residual liquid water that would force the ground ice to completely melt, but SOIL8MIN limits the amount of ground ice that can melt based on a heat energy exchange (see eq. 12 in Fisher et al. 2020). The pore water (SL > ~0.13) and film water (SL < ~0.13) domains are illustrated as these determine the dominant process (REGO or VdW, respectively) by which the unfrozen water can migrate.

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Temp/W and NEST are commonly used models to assess thermal and phase changes in permafrost sediments. However, these models do not include the migration of unfrozen water under REGO and VdW forces and its freezing in a permafrost column. Fisher et al. (2020) therefore developed WATEREGO to explore the direction and speed of migration of the residual unfrozen water in >30 m deep permafrost column. The unfrozen water in permafrost sediments can exist as pore (SL > ~0.13) or film water (SL < ~0.13)74. The rate of migration of pore water by REGO forces depends on the permeability of permafrost sediments (with reported values in the 10−11 to 10−15 m2 range)74. When SL is in the film water domain, permeability is reduced by up to 6–7 orders of magnitude and water can move under VdW forces, a pressure gradient within the film of water around sediments particles73. In the Inuvik clay, SL is always >0.13, irrespective of soil salinity (Fig. 3). Conversely, for the Chena silt, Lebanon gravel, and Nagare peat, SL is only > 0.13 when ground temperatures are >–1 °C for low salinity soils and >–7 °C for brackish to saline soil water chemistry (Fig. 3).

Figure 4 shows typical seasonal temperature, stress, and SL variations, the maximum weekly REGO-induced water speeds, and mean annual REGO and VdW-induced water speeds within a 30 m permafrost column of Inuvik clay with Ca(Mg)SO4 water chemistry for mean annual ground surface temperature (MAGST) = –5 °C, amplitude = 5 °C, and thermal diffusivity = 62 m2 yr−1. The SL stays within the pore water domain (SL > 0.13) throughout the full year in the entire 30 m permafrost column (Fig. 4c). The maximum weekly REGO-induced water speeds, moving water upwards, occur near the permafrost table 8 to 23 weeks after the spring equinox (4.2 and 1.8 m yr−1 at 0 and 0.5 m, respectively; Fig. 4d) and the maximum speeds subsequently decrease with depth (reaches 0.0001 m yr−1 at 10 m; Fig. 4e). At each modeled depth, the increase in water speeds lasts 5 to 8 weeks while occurring progressively later in the year at increasing depth. The direction of REGO-induced water movement is entirely upward in the upper few meters, whereas at depths >6 m, there is the beginning of a downward water movement, and at 10 m, the downward and upward water speeds are equal. The VdW-induced weekly water speeds (not shown on Fig. 4) are moving water downward from the ground surface: they reach a maximum speed of 7.58 × 10−5m yr−1 at 0.5 m between weeks 8 and 17 after the spring equinox and are reduced to 2.18 × 10−5 m yr−1 at 2 m. As a result, the net water movement is upward in the upper 10 m whereas it is downward from 10 to 25 m. Considering that mean annual REGO-induced water speeds are 1.5 to 3 orders of magnitude higher than the VdW-induced ones in the top 8 m, for these simulated temperature-stress conditions, the REGO-forces produce most of the water motion in clay soils (Fig. 4f).

Fig. 4: Typical weekly variations in ground temperature, stress, and unfrozen water content, and the REGO-induced water speeds within Inuvik clay permafrost with Ca(Mg)SO4 water chemistry.
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Weekly variations measured from the spring equinox in a ground temperature, b stress deviations in permafrost, c unfrozen water content, d, e maximum water speeds induced by REGO forces in 30 m Inuvik clay permafrost with Ca(Mg)SO4 water chemistry, and f profiles of annual averages water speed from REGO forces and VdW forces up to 30 m depth. Data are presented from the spring equinox. Numerical simulation was performed for mean annual ground surface temperature of −5 °C, amplitude of 5 °C, and thermal diffusivity of 62 m2 yr−1. Table 3 lists values used in the WATEREGO simulation.

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Figure 5 shows typical seasonal temperature, stress, and SL variations and the maximum weekly VdW-induced water speeds and mean annual REGO and VdW-induced water speeds within a 30 m permafrost column of Chena silt with Ca(Mg)SO4 water chemistry for the same conditions as for the Inuvik clay. The SL is in the pore water domain (>0.13) only for 1–2 months in the uppermost 0.5 m (Fig. 5c). Therefore, unlike for the Inuvik clays where the bulk of the water migration is induced by REGO forces, VdW forces dominate water migration in the Chena silts. The maximum weekly VdW-induced forces that move water downwards occur 8 to 17 weeks after the spring equinox (7 × 10−4 and 0.75 × 10−4 m yr−1 at depths of 0.5 and 2 m, respectively; Fig. 5d). Below 2 m, the water speeds are increasingly reduced and occur progressively later in the year (Fig. 5e). The VdW forces move the water downwards from the permafrost table to 8 m depth, and below that depth, water migration is upwards (Fig. 5f). The mean annual VdW-induced water speeds are higher than REGO-forces by a factor of 45–75 in the top 7 m and by a factor of 12–15 from 8 to 25 m depth. The water is moving upward at near-constant speed because of the greatly diminished seasonal temperature amplitude and the gradually warming trend with depth (input of the geothermal temperature gradient of 2 °C 100 m−1). Increasing soil salinity (or the MAGST) would affect these findings for the Chena silt since it would increase the SL at the same temperature and consequently increase the permeability and the water speeds. However, the water speeds would not reach those in the clays because SL would be > 0.13 only at temperatures >–7 °C (Fig. 3). The seasonality in the direction and magnitude of water transport in silty (clayey-silts) sediments, with a net downward flux, has been confirmed from low Arctic regions by tritium measurements75,76.

Fig. 5: Typical weekly variations in ground temperature, stress, and unfrozen water content, and the VdW-induced water speeds within Chena silt permafrost with Ca(Mg)SO4 water chemistry.
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Weekly variation measured from the spring equinox in a ground temperature, b stress deviations in permafrost, c unfrozen water content, d, e maximum water speeds induced by VdW forces in 30 m Chena silt permafrost with Ca(Mg)SO4 water chemistry, and f profiles of annual averages water speed from REGO forces and VdW forces up to 30 m depth. Numerical simulation was performed for mean annual ground surface temperature of –5 °C, amplitude of 5 °C, and thermal diffusivity of 62 m2 yr−1. Table 3 lists values used in the WATEREGO simulation.

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Predicting ground ice content profiles

The combined effects of the REGO and VdW forces on the movement of residual water in permafrost sediments can modify the initial ground ice content profile and, over time, lead to zones of ice-enrichment and zones of ice-depletion. The evolution of ground ice profiles using WATEREGO is compared to the vertical distribution of ground ice at three sites with very different conditions: (1) Peel Plateau/Richardson Mountains, NWT, Canada (MAAT ~–10 °C, clayey-silt till, 0.1 molality Ca(Mg)SO4 chemistry), (2) Friis Hills, upper MDV (MAAT –23 °C, sandy-silt diamict, 0.1× seawater chemistry) and (3) lower Beacon Valley, the upper MDV (MAAT –23 °C, sandy sediments, 0.2× seawater chemistry) (Fig. 6). For each site, the values of the input ensemble parameters were selected to approximate those measured in their respective region and are listed in Table 3. For the ensemble modeling, an initial ground ice profile is produced with downward freezing simulating permafrost aggradation in a water-saturated column of sediments. The initial profile (not shown) shows a high ground ice content in the uppermost 5 m (54%vol), which then gradually decreases to 25%vol at 20 m depth. The seasonal ground temperature cycles then generate stress fields that initiate the migration of the residual unfrozen water at speeds determined by SL and permeability and the REGO and the VdW forces. Due to uncertainties in the e-folding decay of the rate of ice buildup following the freezing of residual water (1/2e to 1/7e; ref. 28,31), the negative depth derivatives of water speeds (dWSREGO/dZ) are used to indicate where ice accumulates by freezing or is removed by melting. But as an example, the depth derivative of water speeds for the Navy Rd clayey silt and Inuvik clay mixture (50:50) were converted to volumetric ice content for comparison with that on the Peel Plateau/Richardson Mountains.

Fig. 6: Comparison of measured and modeled vertical distribution of ground ice in permafrost sediments.
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a Volumetric ice content profile in Richardson Mountains/Peel Plateau region in NWT28 (shown is the median of ground ice volume from 10 permafrost cores and averaged in 0.5 m bin interval) compared with a 50:50 mixture of Chena silt and Inuvik clay type sediment. b Volumetric ice content profile at Friis Hills27 compared with the negative depth derivatives of water speeds (dWSREGO/dZ) of Fujinomori soil type. c Gravimetric ice content profile at Beacon Valley26 compared with the negative depth derivatives of water speeds (dWSREGO/dZ) of Lebanon gravel. The negative depth derivatives of water speeds (dWSREGO/dZ) are used to indicate where ice accumulates by freezing or is removed by melting. Table 3 lists values of all parameters used in the WATEREGO ensemble simulation, in the square brackets are the mean annual ground surface temperature and its amplitude (in K) and the geothermal gradient (in K per 100 m). The colors of the lines in panels b and c correspond to the color of the x-axis titles. Note the change in scale for dWSREGO/dZ in the upper few meters.

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Table 3 Values of input parameters used in ensemble modeling with WATEREGO for Figs. 4–7.
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The measured ground ice profiles at all three sites fit reasonably well with the ones predicted from the ensemble numerical simulations that assumes a homogenous permafrost column and do not account for stratigraphic layering or historical changes in ground temperatures. On the Peel Plateau/Richardson Mountains, both the modeling and measurements indicate ground ice accumulating just below the permafrost table and at 3–5 m, 11–13 m, 17–19 m, and 24–26 m depth intervals (Fig. 6a). At Friis Hills, ground ice accumulates just below the ice table and at ~15–20 m; however, the zone between 5–10 m has a low ice content, as predicted from the modeling (Fig. 6b note the change in scale for dWSREGO/dZ). Finally, in lower Beacon Valley (Fig. 6c), both the modeling and measurements indicate an ice-rich zone just below the ice table with ice content increasing between 5 and 10 m (but remains below that near the ice table; note the change in scale for dWSREGO/dZ). Below 10 m, ice-rich zones develop near 13–15 and 18–20 m. The ensemble modeling results suggest that the rate of ice accumulation in permafrost sediments is dependent on diffusivity, permeability, and SL (and therefore on sediment type, water chemistry, and permafrost temperature). The rate is orders of magnitude faster near the permafrost/ice table than at depth due to the warmer ground temperatures (note SL is an exponential function) and the combined effects of VdW-induced downward and REGO-induced upward water migration. Increasing SL (and hence permeability), either by increasing permafrost temperature or soil water salinity, would increase the rate at which ice can accumulate in the near-surface.

A first-order estimate of the time required to evolve the ground ice profiles at all three sites from the ensemble numerical simulations can be obtained from: −1/(dWSREGO/dZ), which has unit in years; the estimates are reasonable for the three sites. On the Peel Plateau/Richardson Mountains, permafrost aggraded in the clayey-silt tills following glacial retreat during the Late Pleistocene18. For the simulations using the 50:50 mixture of Navy Rd clayey silt and Inuvik clay and 265 K MAGST and Ca(Mg)SO4 soil water, the evolved ground ice profile can be obtained in ~10,000 years, which is within the estimated age of permafrost in the Peel Plateau/Richardson Mountains region; increasing the temperature by 3° would reduce the time to reach the ground ice content profile to ~2000 years. At Friis Hills, the sediments were deposited 15–14 Ma27,77 and the simulations using Fujinori soils and 250 K MAGST and 0.1× sea water soil solution, suggest that the ground ice content profile can be obtained within ~1 Myr. In lower Beacon Valley, no direct ages were obtained on the sediments; Cuozzo et al. estimated the age of the surface sediments to be > 1 Myr based on calculated sublimation rates in the central portion of Beacon Valley48, a region where >8.1 Myr buried glacial ice was discovered78. For the simulations at lower Beacon Valley using Lebanon gravels and 250 K MAGST and 0.2× sea water soil solution, the ice-rich zone in the upper few meters below the ice table can be obtained within hundred thousands of years, but the ground ice profile below that depth can be obtained in ~25 Myr. This is much longer than the estimated age of the surface sediments. Increasing temperatures by 5° warmer (as evidenced from past warm climate intervals) would increase the ice-build up rate by a factor of 2 in the uppermost 10 m. The simulation was performed using gravels, but the sediments contain ~5% clays, and this would increase SL, permeability, and the rate at which the unfrozen water can migrate. Modeling suggests that these clays would become responsible for the bulk of the water motion through REGO forces and ice build-up rate would be 1/20th of full clay sediments or about 1 order of magnitude faster than in gravels only. This approaches the estimated age of the surface sediments, ~1 Myr.

Replacement age of intrasedimental ice in permafrost sediments

The near-surface permafrost sediments are commonly ice-rich with ice contents exceeding that of the deeper permafrost (Figs. 2 and 6). Two scenarios have been advanced to explain this development of ice-rich permafrost. The first is driven by external factors where climate cooling, addition of organic matter, or sedimentation causes the upward aggradation of permafrost and the development of ice lenses if the active layer is moist (i.e., ref. 71). Conversely, at sites where active layer thicknesses have remained stable, it was proposed that VdW forces (internal factors) produce a net downward flux of soil water from the active layer into near-surface permafrost which results in the development of an ice-rich zone in the top of the permafrost. The latter has been shown to occur as well in silts to coarser material from our modeling. However, the rate at which ground ice can accumulate has remained largely unknown. Using WATEREGO, we explored how fast an initial ground ice content profile could evolve over time in the Inuvik clay, Chena silt, and Nagare peat with varying initial soil water chemistry (pure water to 1× seawater). The values for the parameters used to generate the ensembles are listed in Table 3.

The replacement age is calculated as the inverse of the derivative of the net water speed with depth and adjusted by an e-folding function (1/2e to 1/7e) to account for the effect of changing ice content on porosity28. For clays, the replacement age of ice for 0.1 molality Ca(Mg)SO4 chemistry in the uppermost 2.5 m ranges from 1 to 1000 years, but is in the order of 1000 years to 1 Myr for silts (Fig. 7). The Nagare peat has an intermediate replacement age (10–10,000 years) (Fig. 7). For the Inuvik clay, the dominant process in determining the replacement age of ice (for all soil chemistries) is the REGO forces. This is because SL is within the pore water domain (SL > ~0.13) and the permeability is therefore enhanced in relation to SL in the film water domain. For the Chena silt, the VdW forces (which move water at a much slower speed) are dominant for low salinity waters until 0.2× sea water salinity, at which point REGO and VdW processes are of similar importance. At higher salinity, the REGO forces become dominant due to increased SL. Therefore, silts (and gravels) with water chemistry higher than 0.2× sea water can start to have a replacement age of ice in the range of clays with low salinity, and silts with salinity near that of sea water will have a replacement age equal to that of clays with the same salinity. This finding can explain why the permafrost sediments in the cold and hyper-arid stable upland zone of the MDV can have similar vertical ground ice profiles to sites in the warmer-wetter Arctic. Despite the colder temperatures, the sediments in the upper MDV have a salt content 1–4 orders of magnitude higher than along the coastal thaw zone of the MDV or in the Arctic, which results in similar to higher SL in the permafrost sediments. Therefore, the results from our modeling suggest that ground ice content can increase over a relatively short period in clays (10–1000 years in the uppermost 1 m) with low salinity silts taking 1–2 orders of magnitude longer. If the salinity of silts and sands is higher (>0.5× seawater) the rate of accumulation would approach that of clays.

Fig. 7: Replacement age of ground ice in various sediments and soil water chemistries.
figure 7

Table 3 lists values used in the WATEREGO ensemble simulations. The replacement age is calculated as the inverse of the derivative of the net water speed with depth and adjusted by an e-folding function (1/2e to 1/7e) to account for the effect of changing ice content on porosity.

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Re-defining frost susceptibility of sediments

The frost susceptibility of sediments is defined in terms of their frost-heaving and thaw-weakening behavior14. Traditionally, the frost susceptibility of a sediment has been based solely on particle size: with fine-grained sediments having a higher frost susceptibility (i.e., the Andersen-Tice SL functions)79. This is generally correct for Arctic permafrost sediments. However, sediments with increased salinity or that were exposed to sub-aerial conditions for > 100 kyr can become frost-susceptible. For example, the salt-rich sandy permafrost sediments in the upper MDV have been subjected to REGO and VdW forces for 100 s kyr to 15 Myr and the ground ice content in the uppermost 1 m at some sites is as high as in fine-grained sediments in the Arctic regions (Fig. 2). Therefore, given the right conditions (a combination of parameters that affect SL, permeability, and water speeds), all sediment types could be classified as frost-susceptible, it’s just that clays reach that state faster without the need of increased soil water salinity or ground temperatures. This has relevance for mapping the distribution of thaw sensitive permafrost and classification of abundance of intrasedimental ice should consider sediment type and soil water chemistry.

Conclusion

The current ground ice and permafrost geohazard maps rely on the frost susceptibility of surficial sediments. Large areas of these maps under-estimate ground ice abundance. Here we demonstrate the importance of considering the Rempel-type SL (a parameter dependent on sediment type, soil water chemistry, and temperature) when assessing the frost susceptibility of permafrost sediments. With knowledge of sediment type, soil water chemistry, MAGST, and its amplitude, the WATEREGO soil environmental model is able to match reasonably well the vertical distribution of ground ice in Arctic or Antarctic permafrost sediments. As such, the ensemble model could be used to produce a comprehensive estimate of the vertical distribution of intrasedimental ice in permafrost sediments at regional scale and improving geohazard risk assessments. The modeling of the vertical migration of water through sediments can also be used to assess the mobilization and concentration of salts both of which have implication for habitability and microbial activity in permafrost.

Methods

Numerical modeling

Here, we provide the relevant equations to determine the unfrozen water content, the water speeds in permafrost sediments and replace age of ice using WATEREGO. The complete details of the ensemble numerical modeling are presented in ref. 28.

Unfrozen water content

The unfrozen water content profiles (SL) in relation with soil temperature, soil porosity, dry bulk density, and soil water chemistry were determined from:

$${S}_{L}={\left(\frac{{T}_{L}+{Tp}-T}{{\triangle T}_{f}}\right)}^{-\beta }({{{{{\rm{if}}}}}}\; {{{{{\rm{SL}}}}}} \, > \, 1.0\,{{{{{\rm{then}}}}}}\; {{{{{\rm{it}}}}}}\; {{{{{\rm{is}}}}}}\; {{{{{\rm{set}}}}}}\; {{{{{\rm{to}}}}}}1.0)$$
(1)

where SL is the fraction of residual unfrozen water with respect to total volume of water (water and ice), TL is the freezing temperature of the soil water (in K), Tp (in K) is a correction to TL due to dry porosity, T is the temperature of the icy soil (in K), ΔTf is the temperature difference across the freezing fringe in the soil-water system and β is a soil specific empirical constant.

The values for β and ΔTf can be calculated from:

$${\beta }=-{{{{{\rm{B}}}}}},{{{{{\rm{and}}}}}}$$
(2)
$$\Delta {T}_{f}={A}^{B}{\left(\frac{{\rho }_{{ice}}\times f}{{\rho }_{{drysoil}}}\right)}^{-B}$$
(3)

where A and B are fit parameters from Andersland and Ladanyi79, f is soil porosity, ρice is density of the ice (in kg m−3) and ρdrysoil is dry soil density (in kg m−3). The fit parameters can be calculated for any soils by conducting an Atterberg liquid-limit test14,80. Values of parameters used in this study are listed in Table 1.

Water speeds

The speed at which pore water in a coupled soil thermal and pressure gradient (REGO forces) will move can be determined by:

$$w=-\left(\frac{{perm}}{\mu }\right)\frac{{dp}}{{dz}}$$
(4)

where w is the bulk fluid speed (m yr−1) (ref. 81), “perm” is the permeability of the fluid (m2), μ is the dynamic viscosity of the fluid (N m−2 yr+1) and near 0 °C it is 5.6866 10−11 N (m−2 yr−1; ref. 82), p is pressure (Pa), and z is the depth measured (+ downwards).

The permeability of water film (VdW forces) can then be determined from:

$${{perm}}_{{fw}}=\frac{-A}{36* \pi * R}{\left[\rho L\frac{{T}_{L}-T}{{T}_{L}}+\frac{2{\gamma }_{{sl}}}{R}\right]}^{-1}(1-{f}_{d})$$
(5)

where A is the Hamaker constant whose value is specific to the soil type (in J) (ref.83), R is the radius of the soil particle (in m), ρ is the density of water (in kg m−3), L the latent heat of fusion (in J kg−1), TL is the melting temperature of the water (without soil, in K), T is the ambient temperature (in K), γsl is the surface energy of the solid-liquid interface (specific to soil type, in J m−2) and fd is the dry porosity.

Replacement age of intrasedimental ice

The replacement age is calculated as the inverse of the derivative of the net water speed with depth and adjusted by an e-folding function (1/2e to 1/7e) to account for the effect of changing ice content on porosity28. The replacement age (units of time in years) is calculated as:

$$\left|\,{f}_{D}{\left(-\frac{{{dW}}_{s}}{{dZ}}\right)}^{-1}\right|$$
(6)

Since the time can lead to either pure ice or no ice, we use the absolute value.

The changing rate of ice build-up or removal is adjusted by this e-folding function:

$${ave}\left\{\frac{{dWs}}{{dZ}}\right\}=\frac{\tau }{{t}_{m}}{\left(\frac{{dWs}}{{dZ}}\right)}_{o}\left(1-{e}^{\frac{-{t}_{m}}{\tau }}\right)$$
(7)