Rosetta observations of 67P/Churyumov-Gerasimenko (67P) reveal that most changes occur in the fallback-generated smooth terrains, vast deposits of granular material blanketing the comets northern hemisphere. These changes express themselves both morphologically and spectrally across the nucleus, yet we lack a model that describes their formation and evolution. Here we present a self-consistent model that thoroughly explains the activity and mass loss from Hapis smooth terrains. Our model predicts the removal of dust via re-radiated solar insolation localized within depression scarps that are substantially more ice-rich than previously expected. We couple our model with numerous Rosetta observations to thoroughly capture the seasonal erosion of Hapis smooth terrains, where local scarp retreat gradually removes the uppermost dusty mantle. As sublimation-regolith interactions occur on rocky planets, comets, icy moons and KBOs, our coupled model and observations provide a foundation for future understanding of the myriad of sublimation-carved worlds.