In the past three decades, an abrupt, pan-Arctic acceleration of ice wedge melting has transformed tundra landscapes, spurring the formation of hummock-like features known as high-centered polygons (HCPs). This rapid geomorphic transition profoundly alters regional hydrology and influences surface emissions of CO₂ and CH₄. In Arctic Alaska, most recent instances of ice wedge degradation have arrested within 15–20 years of inception, stabilizing HCP microtopography. However, feedbacks between ground surface deformation and permafrost stability are incompletely understood, limiting our capacity to predict trajectories of landscape evolution in a still warmer future. Here, we use field data from a site near Prudhoe Bay, Alaska, to develop a modeling-based framework for assessing the strength of positive (i.e., exacerbating) feedbacks on ice wedge degradation, focusing on the importance of heterogeneity in surface drainage and microtopographic conditions. Our simulations suggest that, when troughs are narrow, positive feedbacks on ice wedge melting (associated with thermokarst pool formation) are relatively weak. Positive feedbacks are markedly stronger beneath wide troughs, such as those that form above older, larger ice wedges. Seasonal thaw abruptly accelerates once a talik begins to form beneath wide and deep thermokarst pools. Once a talik initiates, winter severity and snowpack thickness increase in importance as predictors of thaw intensity in summer. Our results indicate that meter-scale heterogeneity in polygonal microtopography potentially exerts strong, nonlinear controls on thermokarst trajectories. These findings are useful for predicting future thermokarst dynamics and for interpreting the results from coarser-resolution land surface models operating at greater spatial and temporal scales.

Key Points

Simulations suggest meter-scale variability in the width of flooded troughs controls the intensity of positive feedbacks on thaw
Positive feedbacks on ice wedge thaw are most intense when soil in the trough fails to freeze completely in winter, initiating a talik
After a thermokarst pool forms in a subsiding trough, mild winters and deep snowpacks may increase in importance as drivers of thaw

1 Introduction

Permafrost-affected soils at high latitudes currently store more carbon than the global atmosphere (Hugelius et al., 2014; Schuur et al., 2008). Projecting what portion of this stock will become mobilized as air temperatures increase is a major source of uncertainty in global climate models (Schuur et al., 2015). On the tundra, one key factor that will influence carbon export from the subsurface is the melting of ground ice bodies known as ice wedges. This process systematically reshapes the overlying microtopography in a way that tends to improve soil aeration (Liljedahl et al., 2016), thereby altering rates of aerobic and anaerobic microbial respiration (Grosse et al., 2011; Lipson et al., 2012; Lara et al., 2015; Wainwright et al., 2015). Ice wedge degradation across the Arctic has accelerated abruptly in the last three decades in response to above-average summer temperatures (Farquharson et al., 2019; Fraser et al., 2018; Jorgenson et al., 2006, 2015; Koch et al., 2018; Liljedahl et al., 2016; Raynolds et al., 2014). However, predicting rates of ice wedge melting in a still warmer future is challenging, as thawing processes are influenced by a complex set of positive and negative feedbacks related to hydrology, geomorphology, and vegetation (Jorgenson et al., 2006, 2015; Kanevskiy et al., 2017). In this study, we develop a modeling-based framework to assess the potency of common microtopographic and hydrological feedbacks on thaw, incorporating field data from a site near Prudhoe Bay, Alaska. Our central goal is to quantify the extent to which fine-scale variability in polygonal microtopography and surface drainage conditions impact the ground thermal regime in the trough, to improve projections of how ice wedge degradation will continue to shape land surface dynamics over the next century.

2 Background

Occupying up to 30% of the upper permafrost volume on the Arctic coastal plain of Alaska (Kanevskiy et al., 2013), ice wedges are large bodies of vertically laminated ground ice which occur just below the active layer or seasonally thawed zone. Their formation occurs over time spans of centuries to tens of millennia, through ice deposition into a network of surficial cracks that open to relieve thermal contraction ground stresses in winter (Lachenbruch, 1962; Leffingwell, 1919). In many landscapes, active ice wedge cracking and growth are reflected in the distinctive microtopography of low-centered polygons (LCPs), characterized by rims of soil up to half a meter in height at the polygon edges (Mackay, 2000). In other landscapes, despite the presence of ice wedges, no polygonal pattern may be visible at the surface (Liljedahl et al., 2016; Mackay, 1990, 1995).

Regardless of whether LCPs are present, any landscape in which ice wedges occur is vulnerable to high-centered polygon (HCP) formation (i.e., thermokarst) when thaw penetrates the upper boundary of the permafrost. This geomorphic transformation begins as the upper several decimeters of wedge ice are eliminated and the overlying ground subsides, accentuating a network of troughs at the polygon boundaries (Jorgenson et al., 2006, 2015). As the troughs subside, soil in the polygon interiors may erode outward, producing a characteristic mounded shape (Abolt et al., 2017). This process has significant climate implications because, relative to LCPs or flat terrain, the soil in HCP centers tends to be well drained, driving enhanced seasonal emissions of CO₂ and reduced emissions of CH₄ (Lara et al., 2015; Lipson et al., 2012; Wainwright et al., 2015). Frequently, as HCPs develop, the subsiding troughs become inundated, and the resulting ponds (or thermokarst pools) may also function as sites of enhanced emissions of both CO₂ and CH₄ (Martin et al., 2018)_.

In the past 30 years, increased air temperatures associated with climate change (Overland et al., 2013; Schuur et al., 2015) have spurred an abrupt acceleration in the onset of ice wedge melting throughout the Arctic (Farquharson et al., 2019; Fraser et al., 2018; Jorgenson et al., 2006, 2015; Liljedahl et al., 2016; Raynolds et al., 2014). Once melting initiates, however, the relationship between summer severity and rates of ice wedge degradation is nonlinear, as thermokarst is influenced by an array of competing feedbacks (Jorgenson et al., 2015; Kanevskiy et al., 2017). At early to intermediate states of thermokarst, for example, the formation of thermokarst pools often coincides with an acceleration in ice wedge degradation, representing a positive feedback. This effect is typically attributed to low albedo of ponded water relative to bare tundra, which increases shortwave energy absorption in the troughs (Murton, 2009; Jorgenson et al., 2010, 2015). It has long been speculated that, unchecked, this positive feedback may culminate in the formation of kilometer-scale thaw lakes, as individual ponds gradually expand and coalesce. In this conceptualization, increases in pond area drive greater energy transfer into the subsurface, which renders ever deeper deposits of ground ice vulnerable to melt, eventually causing subsidence under ice wedge polygon centers (Cabot, 1947; Carson, 1968; Everett, 1980; Raynolds et al., 2014).

Within Arctic Alaska, however, field observations indicate that most recent instances of ice wedge degradation have arrested within 15–20 years of its inception, well before clusters of thermokarst pools join into true thaw lakes (Jorgenson et al., 2006, 2015; Jorgenson & Shur, 2007; Kanevskiy et al., 2017). This stabilization tends to occur due to a fresh accumulation of organic material at the bottom of the trough, which acts as an insulating mat to buffer the ice wedge from elevated summer temperatures. This organic matter may originate through the growth of aquatic vegetation as a degrading trough becomes inundated or as colluvium from outward eroding LCP rims (Jorgenson et al., 2006, 2015; Kanevskiy et al., 2017). In some cases, an additional negative feedback occurs as subsiding (and interconnected) troughs increasingly function as a gutter system for the landscape, reducing or eliminating surface water in former thermokarst pools (Kanevskiy et al., 2017; Liljedahl et al., 2016). In such instances, the insulation provided by the organics which accumulated prior to trough drainage results in an unusually thick zone of frozen soil between the bottom of the active layer and the top of the ice wedge (Kanevskiy et al., 2017). This transition zone near the top of the permafrost is typically divided into two regions: an upper transient layer, which is ice poor, due to interannual variability in thaw penetration; and an underlying intermediate layer, which is rich in ice content due to lens formation as the frozen zone aggrades and therefore helps protect the ice wedge from thaw (Shur et al., 2005).

Most investigations into ice wedge degradation and stabilization to date have relied on intensive, long-term field observations (e.g., Jorgenson et al., 2006, 2015; Raynolds et al., 2014; Kanevskiy et al., 2017) or surveys of historical aerial photography or satellite imagery (e.g., Fraser et al., 2018; Jorgenson et al., 2006; Liljedahl et al., 2016; Raynolds et al., 2014). From the former, a detailed conceptual model has been developed in which thermokarst may follow any of several trajectories, which vary according to how severely an ice wedge melts before it is stabilized by organic matter accumulation or trough drainage. Inspired by this conceptual model, several investigations in the past several years have begun exploring process-rich, physically based computer simulations as a means of capturing ice wedge dynamics at large spatial and temporal scales (Aas et al., 2019; Jan et al., 2018; Nitzbon et al., 2019). To date, these simulations have captured some essential components of thermokarst—such as an initial acceleration of melting as thermokarst pools develop, followed by a gradual deceleration—but in each case, the models have employed a highly simplified representation of polygonal microtopography. These simplifications, which include assuming uniformity in microtopographic attributes such as trough width, have been necessary to maintain computational tractability at spatial scales greater than several polygons. However, no analysis has yet determined how strongly the results may be impacted by incorporating such assumptions.

In this study, we develop a framework for estimating how strongly fine-scale variability in polygonal microtopography influences geomorphic and hydrologic feedbacks on ice wedge degradation, based on intensive numerical simulations of the ground thermal and hydrologic regimes at the scale of an individual polygon. Our experimental design is to estimate the maximum depth of seasonal thaw in the trough (d_thaw), defined as the lowest position of the 0° isotherm if thaw were unimpeded by the presence of an ice wedge, in a diverse set of ice wedge polygons subject to identical meteorological forcing. By comparing d_thaw among sets of polygons representing early and late stages of thermokarst, we estimate how variability in trough width, inundation, and rim height influences positive feedbacks on thaw intensity. Although we do not explicitly simulate transient surface deformation or the accumulation of organic material in the trough during thermokarst, we compare differences in d_thaw among LCPs and HCPs with depths of recent organic material accumulation measured from thermokarst-affected troughs in the field, to derive a first-order approximation of how effectively positive feedbacks on thaw are counteracted by this mechanism. Subsequently, to estimate the capacity for intermediate layers of variable thickness to buffer an ice wedge during increasingly severe summers, we calculate increases to d_thaw as the polygons are subjected to meteorological forcing representing a historically warm summer and a still warmer future. Interpreting the results of our simulations in the context of existing field data, we offer an assessment of how strongly polygon-level geomorphic variability may influence the capacity of positive feedbacks to enhance ice wedge degradation and an appraisal of the durability of restabilized ice wedges in an increasingly warm climate.

3 Methods

3.1 Overview of Numerical Model

Each of our simulations was constructed within version 0.86 of Amanzi-ATS (Coon et al., 2015) (https://github.com/amanzi/ats), an ecohydrology code designed to simulate the ground hydrologic and thermal regimes of variably saturated soils in one, two, or three dimensions. In previous studies, Amanzi-ATS has been applied and validated in diverse permafrost settings (Atchley et al., 2016; Harp et al., 2016; Jafarov et al., 2018; Schuh et al., 2017; Sjöberg et al., 2016), including polygonal terrain, where microtopography was represented employing either simplified 2-D meshes, or an array of 1-D meshes (Abolt et al., 2018; Atchley et al., 2015; Jan et al., 2018). At its core, Amanzi-ATS uses a flexible multiphysics framework to solve simultaneously for conservation of energy and water mass at the surface, in the subsurface, and in the snowpack (Coon et al., 2016). In the present analysis, simulations using three-dimensional, radially symmetric (pie wedge) meshes were forced using meteorological data at daily resolution, which were incorporated into an implicit solution to the surface energy balance. The overview of surface and subsurface physics in Amanzi-ATS presented here summarizes more extensive documentation provided in Atchley et al. (2015) and Painter et al. (2016).

In the subsurface, conservation of water mass is solved using a modified form of the Richards equation:

$urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0001$ (1)

where, on the left-hand side, ϕ represents porosity; the subscripts g, l, and i refer to the gas, liquid, and ice phases within the pore space; ω is the mole fraction of water in a particular phase (mol mol⁻¹); η is the molar density of a particular phase (mol m⁻³); and s is saturation. On the right-hand side, V_l is the three-dimensional Darcy flux in the liquid phase (m s⁻¹), and Q_w captures sources and sinks of water (mol s⁻¹). The flux of liquid water, V_l, in equation 1 is defined using the Buckingham-Darcy law:

$urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0002$ (2)

where k is intrinsic permeability (m²), k_r is relative permeability (a function of liquid saturation), μ is dynamic viscosity (Pa s), p is pressure (Pa), ρ is mass density (kg m⁻³), g is gravitational acceleration (m s⁻²), and $urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0003$ is a unit vector in the vertical direction. In unfrozen conditions, relative permeability and liquid pressure are empirically related to liquid saturation, using the van Genuchten-Mualem parameterization (van Genuchten, 1980). In subfreezing conditions, partitioning of the liquid, solid, and gas phases, and calculations of relative permeability and pressure, are accomplished through a novel extension to this parameterization presented in Karra et al. (2014), designed to account for the effects of cryosuction.

Conservation of energy in the subsurface is represented in the equation

$urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0004$ (3)

where u is the specific internal energy for mass in a particular phase (J mol⁻¹), C_v,soil is the volumetric heat capacity for solid materials in the soil (J m⁻³ K⁻¹), T is temperature (K), h is specific enthalpy (J mol⁻¹), κ_e is the thermal conductivity of the soil (again, a function of liquid and ice saturation), and Q_E accounts for sources and sinks of energy. The term on the left thus represents the time change in energy stored both in the pore space and the soil matrix, while the three terms on the right represent the processes of advection, heat conduction, and external introduction or removal of heat, respectively. The parameterization within Amanzi-ATS of soil thermal conductivity as a function of liquid and ice saturation is omitted here but discussed in Atchley et al. (2015).

The surface energy balance in Amanzi-ATS is calculated either at the surface of a snow pack or pond (if present), or at ground surface for bare tundra. The calculation is

$urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0005$ (4)

where α is surface albedo; $urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0006$ is incoming shortwave radiation; $urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0007$ and $urn:x-wiley:21699003:media:jgrf21157:jgrf21157-math-0008$ are incoming and outgoing longwave radiation, respectively; Q_h is the sensible heat flux; Q_e is the latent heat flux; Q_c is the conductive heat flux, calculated either through the snow pack or ponded water if present, or through the uppermost soil cell if the surface is bare; and T_s is surface temperature (K). All terms in equation 4 have units of W m⁻². Incoming shortwave and longwave radiation are specified in the meteorological forcing data, while outgoing longwave radiation is calculated using the Stefan-Boltzmann law. The sensible and latent heat fluxes are calculated as the products of (1) a turbulent boundary layer conductance coefficient that varies with wind speed and surface roughness and (2) vertical gradients between the surface and the overlying air mass in temperature and vapor pressure, respectively. The albedo of water (0.05) and bare tundra (0.15) used in simulations are constants taken from the literature (in the present study, from Gamon et al., 2012), but the albedo of snow varies with snow age, as estimated through an empirical model that tends to result in increased albedo as the season progresses. As the snowpack ages, snow thermal conductivity and density also increase according to coupled empirical models (Anderson, 1976; Atchley et al., 2015; Ling & Zhang, 2004; Martinec, 1977). Time-variable estimates of snow density are incorporated into calculations of snow depth, to conserve mass.

In response to precipitation, snow and liquid water are allowed to accumulate at the surface; snow mass can be lost through sublimation (estimated through calculations of the latent heat flux) or melting (as snowpack temperature approaches 0 °C), while ponded water mass can be lost through evaporation or infiltration into the subsurface. In two- and three- dimensional simulations, both snow and liquid water can flow across surface topography via a diffusion wave equation, which tends to produce a flat surface over time. As snow or liquid water accumulate at the top of the spatial domain, depth and state variables (such as temperature) are calculated within a single layer of surface cells. Vertical stratification in snow and water temperature is thus ignored, although surface water is partitioned into a frozen layer and an unfrozen layer during freeze and thaw. (We note that this assumption regarding thermal stratification would be limiting within most lakes but is justifiable in the thermokarst pools we model, as observations from North America (Hobbie, 1980) and Siberia (Boike et al., 2013; Wetterich et al., 2008) indicate that shallow (<1 m) ponds in polygonal terrain tend to be well mixed by wind action while in the liquid state). The top-down freezing of surface water in winter is accounted for by calculating a frozen fraction at each time step; the frozen fraction increases as a sigmoidal function from 0 to 1 as water temperature decreases from 0 °C to some fraction of a degree lower, specified by the user. This formulation allows for conservation of energy during freeze and thaw, by accounting for the latent heat of fusion of water during phase change. During freeze-up, snow may accumulate atop a partially frozen pond, even as the water beneath continues to freeze.

3.2 Model Setup and Simulations

3.2.1 Overview of Experimental Design

Each of our simulations consisted of two distinct phases (Figure 1). In the first phase, to isolate the influences of microtopography and surface drainage on thawing processes in the trough, we conducted an ensemble of simulations in which individual polygons of variable rim height, trough depth, trough width, and trough drainage were subjected to identical meteorological conditions. This first phase lasted 19 years, during which simulations were spun up using meteorological data representing mean conditions from the recent past (2000–2015, see section 3.2.3). During the nineteenth summer, d_thaw was extracted from each simulation.

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Schematic illustrating the structure of our simulations. TDD = thaw degree days. (Note: time durations not drawn to scale).

In the second phase of the simulations, we examined how microtopography and surface drainage impact thaw depths in the trough during unusually warm summers. This phase was motivated by the observation that, over the past 30 years, an abrupt acceleration to thermokarst has commonly been documented in the field following a single warmer-than-average summer (such as that of 1989 or 1998), even when temperatures during the years preceding and following were near average (Jorgenson et al., 2006, 2015; Kanevskiy et al., 2017). To quantify the potential for another warm pulse to drive abrupt thermokarst given the current thermal state of the tundra, we simulated an ensemble of extreme years, in each case initializing the simulation after the ground thermal regime had been spun-up as described in the previous paragraph (Figure 1). In a subset of the severe-year simulations, 9 months of weather (January through September) from 1989 were used. The thaw degree day index (TDD), or time integral of air temperatures above freezing, for this year was 1183 °C days. In three additional subsets, the same weather data were used, with manipulations applied to air temperature in summer, producing synthetic years in which TDD equaled 1300, 1400, and 1500. In each case, d_thaw was extracted during the warm summer.

By following this experimental design, we aimed to quantify the intensity of geomorphic and hydrologic feedbacks on thermokarst without explicitly simulating ice wedge degradation and surface deformation, which remains a challenge to couple into hydrothermal numerical simulators. Notably, because we did not aim to simulate deformation, and because the placement of an ice wedge could strongly influence thaw in the trough via latent heat effects, our meshes did not explicitly represent ice wedges. Therefore, we treated the variable d_thaw as a proxy for thaw intensity in the trough, which approximated the depth of soil atop an ice wedge necessary to buffer it from thaw, rather than a true estimate of active layer thickness (this difference is discussed in more detail in supporting information Text S1). At the end of the first phase of simulations, we interpreted differences in d_thaw among ensemble members as a proxy for how strongly factors such as the development (or elimination) of a thermokarst pool exert feedback on thaw in the trough. At the end of the second phase of simulations, we interpreted increases in d_thaw relative to the end of spin-up as a rough proxy for how thick the transition layer must be in normal years to buffer an ice wedge during warm summers. These interpretations relied on a set of simplifying assumptions about the structure of the soil column, discussed in sections 5.2 and 5.3.

3.2.2 Mesh Design, Initial Condition, and Boundary Conditions

Our meshes were constructed with a three-dimensional pie wedge shape, representing an idealized, radially symmetric polygon (Figure 2). In each instance, mineral soil extending to a bottom boundary at 50 m depth was overlain by a 30 cm mantle of peat-rich soil, as observed at a site near Prudhoe Bay, Alaska (Abolt et al., 2018). This site was proximal to, but outside of, a drained thaw lake basin and was characterized by epigenetic ice wedges (i.e., ice wedges which have developed beneath a stable land surface, rather than one which is aggrading or eroding). Soil hydraulic and thermal parameters (Table S1) were identical to those used by Abolt et al. (2018), which were derived from laboratory analysis of cores taken from an LCP at the site. This general parameterization for soil stratigraphy and subsurface physical properties was held constant throughout our sensitivity analysis. In constructing our ensemble, we did not explore how feedbacks on ice wedge thaw vary among different soil types but aimed to develop process-based understanding of thermokarst within a single landscape.

The initial condition for each simulation was an isothermal column of frozen soil, saturated with ice to within 5 cm of the ground surface. Following the method described by Atchley et al. (2015), this condition was obtained by first generating a water table near the surface in unfrozen conditions. The entire domain was then frozen from below, by specifying a constant temperature of −6 °C at the bottom boundary. This lower boundary condition was taken from borehole observations near Prudhoe Bay by Romanovsky et al. (2009), and was maintained throughout the duration of each simulation. Hydrologic and thermal boundary conditions along the radial boundaries of the pie wedge domain were Neumann zero flux, allowing the model to represent a complete, radially symmetric ice wedge polygon, and the hydrologic boundary condition on the outer face (i.e., in the middle of the trough, or along the transparent blue plane in Figures 2a and 2b) was either Neumann zero flux, or a seepage face, as described below.

The parameter space for our sensitivity analysis included trough depths (relative to the center) of 5, 25, 45, 65, and 85 cm; trough widths of 1 and 3 m; and rim heights 30, 10, or 0 cm taller than the center of the polygon. These microtopographic conditions were intended to capture a diversity of polygon morphologies affected to various degrees by thermokarst, including flat terrain, nondegraded LCPs, intermediate polygons, and heavily degraded HCPs. For each mictopographic condition represented, one simulation was executed applying a Neuman zero-flux boundary condition along the outer vertical boundary within the trough, which ensured poor surface drainage and tended to result in the formation of a thermokarst pool (Figure S1). In instances with a trough depth of 65 or 85 cm, a second simulation was also executed, in which a seepage face was applied to the trough, preventing more than 5 cm of ponded water from accumulating. This latter treatment was intended to represent field conditions in which a network of deep, interconnected troughs has become well drained (e.g., Kanevskiy et al., 2017; Liljedahl et al., 2016).

3.2.3 Meteorological Forcing Data

Meteorological data were extracted or derived from the output of the Noah Land Surface Model, a component of NASA's Global Land Data Assimilation System, which simulates global meteorological conditions at a spatial resolution of 0.25° and a temporal resolution of 3 hr (Rodell et al., 2004). Output was extracted from the pixel centered at 148.875°W, 69.875°N, the same location used previously to validate the soil parameters summarized in Table S1 in a polygon-scale numerical model of thermal hydrology (Abolt et al., 2018). Variables used to force simulations in Amanzi-ATS included air temperature, relative humidity, wind speed, incoming shortwave radiation, incoming longwave radiation, rainfall rate, and snowfall rate.

During the first phase of simulations (spin-up), a “baseline” year of data was cyclically applied, representative of recent meteorological conditions near Prudhoe Bay. To construct this baseline year, data were downloaded from 2000–2015, and mean day-of-year values for each variable were calculated. The thaw degree day index of this synthetic year was 873 °C days. In the second phase of simulations, daily data from January through the end of September, 1989 (TDD = 1188 °C days) were used to represent a historically warm and wet year, known to have triggered extensive landscape-scale ice wedge degradation in Arctic Alaska (Jorgenson et al., 2006, 2015). These data represented one of the four “pulse years” depicted in Figure 1. In the remaining three instances of pulse years, the same meteorological data were used, but with manipulations applied to air temperature. During each day of the year with a mean air temperature above 0 °C, air temperature was multiplied by a constant to attain a higher TDD index. This procedure was used to generate years in which TDD was equal to 1300, 1400, and 1500 °C days. During the 133 days in which air temperature was above freezing, the synthetic pulse years represented mean departures of 3.2, 4.0, and 4.7 °C from baseline (2000–2015) conditions, respectively. Although these warm years were meant to represent short-duration events which could occur at present or in the near future, we compared them for reference with ensemble-averaged results from the fifth phase of the Coupled Model Intercomparison Project. Under a business-as-usual scenario (RCP8.5), mean summer air temperatures in the Arctic might increase 3.2–4.7 °C relative to 2000–2015 between 2080 and 2100. These same conditions are unlikely to become typical before 2100 in a reduced-emissions (RCP4.5) scenario (Overland et al., 2013).

3.2.4 Processing of Model Output

The key variable extracted from each simulation, d_thaw, was estimated by calculating the maximum seasonal depth of the 0° isotherm in the center of a trough (or the outermost column of cells in a mesh), using linear interpolation between cell centroids. Other variables extracted from simulations included subsurface temperature (at all cells), snow and surface water depth (at all surface cells), and each component of the surface energy balance (at all surface cells). Finally, to gain a detailed understanding of the thermal budget in the trough, we extracted all energy inputs via conduction or advection into the trough subsurface from each day of the simulations. This time series was monitored in two components: the vertical heat flux (i.e., across the soil-water or soil-air interface at the trough surface), and the subsurface, laterally oriented, conducted, and advected heat flux (i.e., across the yellow plane indicated in Figures 2a and 2b).

4 Results

4.1 Phase 1: Simulations of Average Meteorological Conditions

At the end of the first phase of simulations, d_thaw showed decimeter-scale variability among the microtopographic and hydrologic conditions represented (Figures 3a and 3b). As expected, one of the most prominent trends in the results was that d_thaw increased with trough depth, so long as the trough was poorly drained. This result clearly indicates that the formation of a thermokarst pool enhanced thaw in polygonal troughs, replicating decades of field observations. In all cases, if a trough was deep but well drained, increases to d_thaw relative to nondegraded conditions disappeared, indicating that the elimination of surface water had completely neutralized positive feedbacks on thaw. Notably, trough width had a very strong effect on thaw intensity. Beneath troughs that were 3 m wide, the increases to d_thaw as a thermokarst pool developed were 2 to 3 times greater than simulations in which the troughs were only 1 m wide. In all cases in which d_thaw exceeded 1 m by the end of spin-up, the soil in the trough failed to freeze completely, indicating that a talik had initiated. In all simulations with thermokarst pools, surface water froze completely by the end of winter, but the culmination of freeze-up was latest (typically occurring in mid-March or later) in simulations that ended up with taliks. The development of taliks was more common beneath wide troughs than narrow ones.

Relative to the importance of trough width, depth, and drainage, the influence of rim height on d_thaw was modest. Nonetheless, two trends related to rim height were evident. First, among simulations of narrow troughs, thaw was systematically weaker in HCPs (rimless polygons) relative to LCPs (Figure 3a). This unexpected result suggests that, considered as an independent variable, the loss of rims during thermokarst may weakly impede thawing processes above an ice wedge. However, this factor was weak in comparison with positive feedbacks on thaw associated with the development of deep, inundated troughs. Second, when troughs were wide, deep, and poorly drained, differences in rim height caused decimeter-scale variability in d_thaw (Figure 3b). However, the effect was nonmonotonic with respect to rim height, as the presence of both tall rims (rim height = 30 cm) or no rims at all reduced d_thaw relative to simulations with moderate-sized rims (rim height = 10 cm). This result suggests that the net impact of rims adjacent to wide thermokarst pools is difficult to predict, and likely depends on site-specific conditions (see section 5.2)

4.2 Phase 2: Simulations of “Pulse” Years

In the second phase of simulations, trough width and inundation strongly influenced increases to d_thaw as runs were driven using 3 months (January–September) of weather data representing an historically warm year (1989) or a hypothetically warmer future. Among simulations with narrow troughs, the responses to these conditions were relatively uniform (Figure 3a). During a historically warm year (TDD = 1188, an average increase of 2.4 °C from baseline conditions), d_thaw increased ~15–20 cm relative to the end of spin-up. This indicates the potential to initiate thermokarst in ice wedges that (during average years) are buffered by thin intermediate layers (see section 5.3 for a more detailed discussion). In a more extreme year (TDD = 1500, an average increase of 4.7 °C), increases to d_thaw were slightly less than twice as severe. The uniformity of these results suggests that, in ice wedge polygons with narrow troughs, thaw intensity in the trough is a relatively consistent function of TDD.

Among simulations with wide troughs, in contrast, pulse year increases to d_thaw were strongly influenced by the presence or absence of a thermokarst pool (Figure 3d). In simulations without a thermokarst pool, increases to d_thaw were comparable to simulations with narrow troughs. But notably, among simulations with deep, inundated troughs, changes in thaw intensity were relatively modest, or even negative in some cases. This unexpected result suggests that, relative to narrow or well-drained troughs, thaw intensity beneath wide thermokarst pools shows increased sensitivity to factors besides TDD. In this particular subset of simulations, increases to d_thaw were dampened by colder than average conditions during the first several months of the pulse years, despite that these same meteorological conditions did not impact the results beneath narrower or better drained troughs (see section 5.3).

5 Discussion

5.1 How Trough Width Influences the Strength of Positive Feedbacks

One of the more surprising results of our analysis was the pronounced degree to which trough width influenced positive feedbacks on thaw. This outcome was a consequence of the physical processes that enhance thaw in sediments submerged beneath surface water. To our knowledge, these physics have been investigated extensively beneath larger lakes and ponds (e.g., Burn, 2002, Ling, 2003; Langer et al., 2011, 2016; Westermann et al., 2016) but have not been analyzed rigorously on spatial scales typical of a flooded polygonal trough. Fundamentally, we found that enhanced thaw beneath thermokarst pools was driven by a contrast between efficient downward transfer of energy in summer, and inefficient release of energy back to the atmosphere in winter (Figure 4). In summer, thermal energy was transferred efficiently into the sediments beneath a pool due to low albedo and the thermally unstratified state of the ponded water. During winter, in contrast, upward heat transfer was impeded for much of the season, as temperatures at the top of the soil column could not drop below 0 °C until the surface water completely froze. The process of a pool freezing in winter was much slower than melt in summer, due to the accumulation of insulating snow cover as soon as the ponded water surface froze. Consequently, although each thermokarst pool we simulated froze to the bottom by the end of the winter, the sediments beneath a flooded trough remained warmer than those beneath a drained one, resulting in more efficient thaw the following summer (Figures 4e and 4f).

In this context, the strong impact of trough width on thaw intensity stemmed from the importance of lateral heat transfer as a cooling mechanism in the sediments beneath a pool. Because relatively warm temperatures persisted through much of winter beneath a flooded trough, laterally oriented temperature gradients tended to develop in the subsurface, driving heat transfer toward the colder polygon interior (e.g., Figure 4b). Considered alongside vertical heat losses, this laterally oriented flux often accounted for >40% of cooling in the sediments of the trough (Figure S2). Because a significant proportion of heat loss in the soil above the ice wedge occurred laterally toward the polygon center, rather than vertically through the trough, freeze-up was less efficient beneath wide troughs, relative to narrow ones. This resulted in warmer ground temperatures at the end of winter, which primed the subsurface for deeper thaw in summer.

In some cases, a portion of the trough subsurface remained partially unfrozen at the end of winter, even though the surface water above froze to the bottom (e.g., Figure 4f). This initiation of a talik was more common beneath wide troughs than narrow ones, and significantly accelerated thawing processes in summer. Among our estimates of d_thaw at the end of spin-up, the five largest values were all associated with talik formation (Figure 3). Here we note that, although our simulations were spun-up using historic data from the recent past, it is difficult to verify whether the formation of taliks is presently common beneath deep thermokarst pools. To our knowledge, few observations of the ground thermal regime beneath ponds >30 cm in depth have been published, but from the records available, complete freeze-up was observed in the last 10 years beneath a ~90 cm pond in the Lena River Delta, Siberia (Langer et al., 2011) and beneath a ~60 cm pond at Prudhoe Bay, Alaska (Jorgenson et al., 2015). This difference from our results may possibly be explained by the fact that our meteorological data was extracted from a site farther south than either of the locations mentioned above, which may reduce the negative temperature gradient at the top of the permafrost. Regardless, our analysis suggests that as the climate warms, positive feedbacks on thaw will strengthen as taliks form beneath ponded water, and this feedback will be strongest beneath the widest troughs.

The high sensitivity of positive feedbacks to trough width suggests that areas of the tundra with wide ice wedges may be especially vulnerable to rapid and severe thermokarst. This condition might be expected in areas with old permafrost, but is also influenced by factors including soil type and precipitation (French, 2017; Lachenbruch, 1966). To help contextualize the increased vulnerability of thaw beneath wide troughs relative to narrow ones, we compared variability in d_thaw with observations of soil accumulation in degraded troughs. Quantifying the latter, recent field work near Prudhoe Bay and Utqiaġvik, Alaska indicates that ~20–40 cm of organic material commonly accumulates at the bottom of troughs within several decades of the onset of ice wedge degradation, often through the growth of aquatic moss (Jorgenson et al., 2015, 2006; Kanevskiy et al., 2017). In comparison, our simulations suggest that, when trough width is limited to 1 m, the presence of a deep (85 cm) thermokarst pool only accounts for a 5–15 cm increase in d_thaw, relative to an undegraded trough (Figure 3b). This disparity suggests that, within narrow troughs, negative feedbacks on thermokarst may strongly prevail over positive feedbacks, restabilizing the ice wedge within several decades—an interpretation which is bolstered by the fact that differences in d_thaw among our simulations are confined to the mineral layers of soil, which provide weaker insulation than the organics that typically accumulate in degrading troughs. This prediction aligns well with recent observations of ice wedges buffered by unusually thick intermediate layers beneath degraded troughs in northern Alaska, indicating that negative feedbacks associated with soil accumulation have strongly outbalanced positive feedbacks on thaw since the onset of thermokarst (Jorgenson et al., 2015; Kanevskiy et al., 2017).

Beneath wide troughs, however, our model predicts that increases to d_thaw caused by the formation of a thermokarst pool are several times greater—as much as ~50 cm (Figure 3b). Even when accounting for differences in the thermal insulation provided by mineral soils and organic material, it is ambiguous whether typical thicknesses of organic accumulation observed in the field could neutralize this positive feedback. These results suggest that, so long as ponded conditions exist in troughs, ice wedge melting likely persists over longer time spans beneath wide troughs relative to narrow ones. Additionally, if a degrading ice wedge beneath a wide trough restabilizes due to soil accumulation, it may require longer time spans to develop a thick intermediate layer, increasing its vulnerability to a reactivation of thermokarst in the future. The heightened potential for ice wedge thaw beneath wide troughs implies that the severity of future thermokarst may vary significantly within a single landscape as the climate continues to warm. Accounting for the occurrence of wide or narrow ice wedges at a site may be critical to forecasting the potential for surface deformation.

5.2 The Influence of Rim Height on Thaw Intensity

Unlike trough width, rim height influenced thaw intensity in the trough negatively in some cases and positively in others. This mixed response was related to the seasonal dynamics of subsurface energy transfer between the rims and the trough (Figure 5a). In winter and spring, lateral energy transfer was oriented outward from the relatively warm trough toward the colder polygon interior, as described in the previous section. This lateral flux increased in magnitude with rim height, since taller rims accumulated less snowpack, and therefore became colder in winter. The capacity of rims to enhance subsurface cooling in winter through this mechanism has been well documented in previous studies (e.g., Abolt et al., 2018; Cable, 2016; Christiansen, 2005; Morse & Burn, 2014), but these investigations have either not focused on, or not detected, a meaningful relationship between the presence of rims and thaw intensity in the summer. Our analysis suggests that preferential cooling through the rims meaningfully impacts subsequent thaw only under special conditions not explored in previous work—that is, beneath wide and deep thermokarst pools, where a talik has initiated (Figure 3b, trough depths of 65–85 cm). In these scenarios, the enhanced cooling provided by tall rims (i.e., rim height = 30 cm) reduced the thickness of the talik relative to simulations with moderate rims (height = 10 cm), resulting in weaker thaw in the summer. This result suggests that, if tall rims are preserved as the trough degrades during thermokarst, their presence may enhance the resilience of the ice wedge. However, while this effect may be significant, it is not particularly robust, relative to other environmental factors evaluated here. For example, we found that the complete absence of rims adjacent to a wide thermokarst pool also suppressed thaw in the trough, relative to simulations with moderate-sized rims. This latter result was due to the fact that the walls of the trough in our HCP meshes sloped more gently than in the LCP meshes, which dispersed surface water over a wider area, resulting in a somewhat shallower pool and weaker talik formation (Figure S1). Although thaw in the HCP was therefore suppressed by a different mechanism than in the LCP with tall rims, the nonuniform relationship of d_thaw to rim height suggests that, once a talik initiates, thaw intensity in the trough becomes increasingly volatile. After a talik forms beneath a wide trough, thaw may show heightened sensitivity to factors such as winter climate and summer rainfall, which control depths of inundation and the extent of seasonal freeze-up above the ice wedge.

Besides the case of wide, inundated troughs, rim height also influenced thaw intensity in polygons with narrow troughs, where d_thaw was weakly but systematically smaller in HCPs relative to LCPs (solid lines in Figure 3a). This effect was driven by a reversal of the conductive energy flux between the polygon interior and the trough, which occurred in summer and only in LCPs. From the middle of June to September, heat conduction in LCPs was oriented away from the rims, which were slightly warmer than the rest of the polygon, toward the trough (Figure 5a). Elevated ground temperatures in the rims were associated with relatively low soil moisture content, which reduced the soil heat capacity and weakened evaporative cooling. This flux of energy outward from the rims tended to be much weaker than the reverse flux in winter; however, in some cases, it accounted for >10% of total annual thermal energy inputs into the trough (Figure 5b). Therefore, the absence of rims in HCPs was associated with a slight reduction in d_thaw, on the order of ~5 cm. This result suggests that, among polygons with narrow troughs, the destruction of rims may constitute a negative feedback on thermokarst, helping somewhat to stabilize the ice wedge (Figure S3). Because the effect was driven solely by a weak, lateral energy flux at the edges of the trough, it had no meaningful impact on d_thaw beneath wider troughs.

5.3 How Microtopography Influences Seasonal Thaw in “Pulse” Years

The most important factor influencing changes to seasonal thaw during pulse years was whether a trough was both wide (width = 3 m) and deeply inundated (trough depth > 65 cm), or whether it was not (Figures 3c and 3d). In the latter category, which included most simulations, we simulated a more or less uniform increase to d_thaw of 15–20 cm relative to the end of spin-up when using forcing data from 1989. Physically, this result suggests that, given the current thermal state of the permafrost, a summer approaching 1989 in severity might result in ice wedge degradation in troughs with intermediate layers as thick as ~15–20 cm; however, we note that this figure is likely an overestimate, as the intermediate layer in the field is commonly characterized by volumetric ice content up to 30% in excess of porosity (Shur et al., 2005), which is not represented in our model. Despite this distinction, we conclude that a summer similar in temperature to 1989 (TDD = 1188 °C days) would still have strong potential to effect widespread thermokarst today, as recent surveys indicate that the intermediate layer above most ice wedges in northern Alaska is well below 10 cm in thickness, with the exception of degraded wedges in a state of advanced stabilization (Jorgenson et al., 2015; Kanevskiy et al., 2017).

Among the same subset of microtopographic and hydrologic conditions, our model predicted increases to d_thaw of ~30 cm in a hypothetical pulse year in which TDD = 1500 °C days, representing the most severe summer in our ensemble. This increase to d_thaw is similar in scale to the typical thickness of the intermediate layer above previously degraded ice wedges at a state of advanced stabilization, which varies from ~15–30 cm, as observed recently on the Alaska North Slope (Jorgenson et al., 2015; Kanevskiy et al., 2017). Here we note again that our analysis likely overestimates the expected real increases to seasonal thaw in deep troughs—not only because of increased ice content in the intermediate layer, but also because the troughs above restabilized ice wedges tend to be mantled especially thickly with organic material, which impedes active layer development (Jorgenson et al., 2015). In consideration of these factors, it is ambiguous whether a summer in which TDD = 1500 °C days would manage to drive ice wedge degradation in restabilized HCP troughs. Nonetheless, we conclude that ice wedges at advanced stabilization could withstand a “pulse” year significantly more severe than ice wedges unaffected by thermokarst, and significantly more severe than the historic year of 1989.

In stark contrast to these results, beneath troughs that were both wide and deeply flooded, we found that increases to d_thaw in a summer resembling 1989 relative to the end of spin-up were small to nonexistent, and remained modest even as TDD approached 1500 °C days (solid lines in Figure 3d, representing trough depths of 85 cm). This outcome was a direct result of below-average snowfall during the first four months of our forcing data from 1989 (as well as during the hypothetical warmer years, which used the same precipitation data). Although d_thaw among most ensemble members was relatively insensitive to this factor, weaker snowfall became important in simulations in which a talik had developed by the end of spin-up, as the diminished snowpack enhanced freeze-back in winter, thereby reducing the thermal offset between ground and air temperatures. These conditions inhibited thaw during the subsequent summer (Figure 6). This finding implies that, as a talik forms beneath wide thermokarst pools, the sensitivity of the trough thermal regime to winter conditions heightens. As thermokarst progresses to ever greater degrees across the Arctic, accounting for this shift may ultimately be crucial to forecasting the extent of surface deformation, as observations from the Alaska North Slope suggest that recent trends in winter severity and snowfall may be even more pronounced than in summer thaw degree days (Figure 7).

6 Summary

Our analysis built on current conceptual models of ice wedge melting and stabilization by quantifying the influence of fine-scale microtopographic heterogeneity on feedbacks influencing thermokarst. In summary, we found that

Wider troughs experience stronger positive feedbacks on thermokarst than narrow ones. Increases to thaw intensity associated with the formation of a thermokarst pool are much (up to several times) more potent beneath wide troughs, due to a diminished capacity for laterally oriented heat conduction to cool the active layer in winter.
Seasonal thaw atop an ice wedge intensifies abruptly once a talik initiates in the sediments of the trough. The formation of taliks is more likely to occur in wide troughs than in narrow ones.
In narrow troughs, the destruction of rims in adjacent polygons may constitute a weak negative feedback on thermokarst by eliminating heat conduction from the rims toward the trough in summer. In wider troughs, the impact of rims is more nuanced.
Organic material accumulation at the bottom of troughs is likely to provide a robust negative feedback on ice wedge degradation in terrain with narrow troughs, stabilizing the land surface. Organic material accumulation may not fully offset positive feedbacks beneath wide troughs once a talik begins to form.
After a talik forms beneath wide troughs, seasonal thaw shows heightened sensitivity to factors that control the intensity of freeze-back in the active layer, such as winter air temperatures and snowfall.

These conclusions will ultimately help improve landscape-scale projections of surface deformation in polygonal terrain, by demonstrating the capacity for meter- to submeter-scale microtopographic attributes to influence trajectories of permafrost degradation.

Acknowledgements

We are grateful for the support provided for this research, which included the Next Generation Ecosystem Experiments Arctic (NGEE-Arctic) project (DOE ERKP757), funded by the Office of Biological and Environmental Research in the U.S. Department of Energy Office of Science, and the NASA Earth and Space Science Fellowship program, for an award to Charles J. Abolt (80NSSC17K0376). We acknowledge the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the results reported within this paper. The authors declare no conflicts of interest. Data and code for reproducing the simulations described in this manuscript are available at https://doi.org/10.5440/1561091 (Abolt et al., 2019).

Supporting Information

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Citing Literature

Volume125, Issue3

March 2020

e2019JF005349

Feedbacks Between Surface Deformation and Permafrost Degradation in Ice Wedge Polygons, Arctic Coastal Plain, Alaska

Abstract

Key Points

1 Introduction

2 Background