Permafrost Thaw (2D) — Stefan Equation Active Layer Simulator

Climate

Mean annual air temp (Ta) -8.0°C

Summer peak temp (Ts) 10.0°C

Soil Properties

Thermal conductivity (k) 1.5 W/m·K

Latent heat (λ) 300 MJ/m³

Permafrost table depth 20 m

Playback

Years per second 0.10

Live Readout

Day of year

Air temperature

0.0°C

Thaw depth (Z)

0.00 m

Max thaw this year

0.00 m

Degree-days thaw

Active layer

How it works

Air temperature follows a sinusoidal annual cycle peaking in midsummer. Whenever it rises above 0°C the excess accumulates as the degree-day thawing index DDT, and the depth the thaw front has reached follows the Stefan equation:

T_air(day) = Ta + (Ts−Ta)·max(0, sin(π·(day−80)/200))
DDT(day)   = Σ T_air(d) for d < day where T_air(d) > 0
Z(day)     = √( 2·k·DDT·86400 / λ ),  capped at the permafrost table

Because Z scales with the square root of accumulated warmth, doubling a summer's degree-days only deepens the thaw front by about 41%, not 100% — the soil column view on the right shows this directly as the thawed (warm) band above the permanently frozen ground growing and shrinking through the year.

Soil column — vertical cross-section: brown = thawed active layer, blue = still-frozen ground, the dashed line marks the permafrost table.
Annual graph — air temperature (orange) and thaw depth (brown) traced across all 365 days; drag on it to scrub to any day.
Thermal conductivity / latent heat — higher k thaws faster for the same warmth; higher λ (more ice-rich soil) resists thawing and keeps Z shallower.

Thawed active layer Frozen ground Air temperature