Permafrost thaw shows how warming ground releases greenhouse gases and reshapes the landscape. Watch the active layer deepen year by year, following the square-root growth of the Stefan equation, while methane bubbles escape from thawing organic soil and ice-rich patches sink into thermokarst ponds.
The simplified Stefan equation links thaw depth to the square root of accumulated warm degree-days, plus the permafrost carbon feedback loop and thermokarst ground collapse from melting ground ice.
Raise the warming offset to add more warm degree-days each year, increase soil organic/ice content to intensify methane release and subsidence, and use fast-forward to watch many simulated years pass quickly.
Some Arctic soils are frozen up to a kilometre deep and have held their carbon in cold storage since the last ice age — thaw can release that carbon into the atmosphere within a single human lifetime.
This canvas-based simulation models a cross-section of Arctic and subarctic ground: a thin organic mat, a seasonally-thawing "active layer", and permanently frozen permafrost beneath, threaded with ice lenses and wedges. Each simulated year cycles through a seasonal temperature curve set by your chosen mean warming offset; whenever the modelled temperature rises above 0°C, the day contributes to a running total of degree-days. The active-layer depth is then computed from a simplified Stefan equation, depth ∝ √(cumulative degree-days), so the boundary between thawed and frozen ground visibly deepens over time, growing fast at first and slowing as the thickening thawed layer insulates the ground below.
As the active layer deepens, organic-rich soil decomposes and releases bubbles of methane that rise and pop at the surface — a visualization of the real permafrost carbon feedback, in which thawing releases greenhouse gases that drive further warming. Where the soil's ice content is high, melting ice leaves voids that the ground collapses into, producing thermokarst subsidence and, in the worst-affected patches, small meltwater ponds. The live readout tracks active-layer depth, cumulative degree-days, elapsed simulated years, illustrative cumulative methane released, and total ground subsidence, so you can see how warming offset, soil composition and elapsed time interact.
What does this simulation show?
It shows a cross-section of tundra ground thawing over simulated years: the active layer (the seasonally thawed soil above permafrost) deepens according to a simplified Stefan equation, methane bubbles rise from thawing organic soil, and ice-rich ground subsides as thermokarst forms.
What is the Stefan equation?
It is a classic approximation used in permafrost engineering stating that thaw depth grows proportionally to the square root of cumulative degree-days above freezing. The simulation implements a simplified version of it so the active layer visibly deepens fastest early in the warm season and slows as it thickens.
What is the "active layer"?
The active layer is the top layer of ground in permafrost regions that thaws each summer and refreezes each winter. Below it lies permafrost, ground that has stayed at or below 0°C for at least two consecutive years, sometimes for millennia.
Thermokarst is ground subsidence and collapse caused by the melting of ground ice. When ice-rich permafrost thaws, the ice's volume converts to water that drains or evaporates away, leaving voids that the overlying soil sinks into — sometimes forming ponds, sinkholes or uneven "drunken forest" terrain.
Permafrost soils store huge amounts of organic carbon built up over thousands of years because cold temperatures prevented full decomposition. When permafrost thaws, microbes break down that organic matter and release carbon dioxide and methane, both greenhouse gases, which contribute to further warming and further thaw — a self-reinforcing feedback loop.
Methane produced in waterlogged, oxygen-poor thawed soil traps substantially more heat per molecule than carbon dioxide over a couple of decades, even though it breaks down faster in the atmosphere. Wetter thermokarst terrain tends to favour more methane-producing (anaerobic) decomposition, which is why the simulation ties bubble release to both thaw depth and soil organic content.
The warming offset raises the modelled mean annual air temperature, increasing how much of the seasonal cycle sits above freezing and how many degree-days accumulate each year. Soil organic/ice content scales both methane release per metre of thaw and subsidence per metre of ice lost. Fast-forward sets how many simulated years pass per second of real time so you can observe decades of change quickly. Reset restores the ground cross-section and all readouts to their starting values.
The Stefan-equation relationship, the seasonal degree-day accumulation, and the qualitative behaviour of methane release and thermokarst subsidence are grounded in real permafrost science. It is a simplified, illustrative model rather than a full coupled thermal-hydrological simulation, so exact depths, methane units and subsidence amounts are for demonstration rather than site-specific prediction.