This 2D cross-section follows a column of tundra soil through repeated summer thaw and winter freeze-back cycles. A Stefan-equation model drives the thaw front down as the square root of accumulated thawing degree-days above 0°C, and a matching freezing front grows down from the surface each winter; when the freeze-back falls short of that summer's thaw depth, a pocket of unfrozen ground survives the winter and the permafrost table permanently deepens. Dial up the mean annual temperature or add extra warming to push the system toward that outcome, adjust the soil's organic content to see how peat both insulates against thaw and multiplies the methane released once it does thaw, and watch the active layer depth, permafrost table depth and live methane release rate respond in real time.