Both fronts obey the Stefan solution for a phase-change boundary driven by cumulative surface degree-days:
X = sqrt( 2 k |I| / (L ρw θw) )
I = ∫ T_surface dt (surface degree-seconds
since the phase reversed)
where k is soil thermal conductivity, L = 334,000 J/kg is the latent heat of fusion, ρw = 1000 kg/m³, and θw is volumetric water content. Summer thawing integrates air temperature directly at the surface. Winter freezing is different: snow is an excellent insulator, so the true ground-surface temperature is damped from the air temperature by an n-factor,
T_surface = T_air · n_f(snow), n_f = 1 / (1 + 0.045 · snow_cm)
Deep snow drives n_f toward zero, decoupling the ground from a cold winter sky. If the surface freeze front, integrating this damped temperature, fails to reach the depth the thaw front reached that same summer before winter's cold returns, a layer of unfrozen, unfrozen-since-summer ground is left sandwiched between the new surface ice and the permafrost table below — a talik. Real Arctic monitoring networks (e.g. the Alaska Circumpolar Active Layer Monitoring program) track exactly this seasonal mismatch, because a persistent talik is an early sign of permafrost degradation: it lets liquid water and biological activity continue through the winter, deep in ground that used to freeze solid every year.
- Mean annual air temperature — sets the depth of winter cold and the strength of summer thaw around a fixed ±16 °C seasonal swing.
- Peak winter snow depth — the insulating blanket; thicker snow suppresses the winter n-factor and can trap a talik even at fairly cold mean temperatures.
- Soil water content — more pore ice means more latent heat to remove or supply, so both fronts move more slowly through wetter soil.