Permafrost ice lens: thaw, settlement and thermokarst

An 8 m x 10 m block of Arctic ground, cut open. Warm summers push the thaw front down; when it reaches the ice-rich lens the ground collapses and a pond forms.

Experiments

Climate and ground

When a pond forms, water absorbs more summer heat and the ground warms faster.

Time

Live numbers

Ground temperature profile

line: now · band: this year's min/max · blue strip: ice lens · dashed: 0 °C

Active layer and settlement through the years

━ maximum thaw depth (m) · ━ subsidence (m)

Independent numerical checks

The science

Heat flows by conduction through the layers: C dT/dt = d/dz (k dT/dz). Ice melting at 0 °C absorbs latent heat L = 334 MJ per m³ of ice, which is why the thaw front moves so slowly in wet or ice-rich ground. The model uses the enthalpy method: each 10 cm cell stores enthalpy H; T = 0 °C while 0 < H < θ L, where θ is the ice volume fraction.

Stefan's formula for the maximum thaw depth: X = sqrt(2 k I / L), with I the thawing degree-seconds at the surface. It ignores heat capacity, so it slightly over-predicts.
Snow insulates: a thick snow cover keeps the ground warmer in winter (we reduce the winter surface temperature offset by up to 80 %).
Settlement: when a cell with excess ice thaws, the meltwater drains and the cell loses a fraction of its volume (60 % for the ice lens, 4 % for silt). The cutaway is drawn with these thinned cells, and the polygon troughs (ice wedges) sink faster than the centres.
Talik: if the ground below the active layer no longer refreezes in winter it forms an unfrozen layer (talik), and permafrost starts to disappear from the top.

Simplifications (honest list): one-dimensional vertical conduction; sharp freezing at exactly 0 °C (real soils keep unfrozen water below 0 °C); constant conductivities per layer and frozen/thawed state; the surface temperature is the air temperature times a factor (0.85 in summer, 1.15 with a pond) in summer and reduced by snow in winter; the seasonal cycle is a cosine plus a random yearly anomaly of ±1.5 K; subsidence is computed but the thermal grid is not deformed; ponds and lateral heat flow are a display rule, not hydrology; no methane or carbon release is modelled. The illustrated numbers are not a forecast for any real site.

3D diorama modelled in Blender (tundra surface, strata walls, thermistor string, weather station) with baked textures; the cut face is drawn live from the simulated ground; Three.js r160.