A review of phase-transition representation in permafrost land surface models: Mechanisms, algorithms, and impacts

Permafrost is a critical component of the Earth system, influencing climate through large carbon stocks and control of land–atmosphere energy and water exchanges. Reliable prediction of permafrost change under warming depends strongly on how Land Surface Models represent the water-ice phase transition, the key process distinguishing frozen from unfrozen soils. This review synthesizes recent advances and challenges in representing phase transition in permafrost LSMs, focusing on physical mechanisms, numerical algorithms, and potential impacts. We show that the widely used Clapeyron-SWCC framework provides an efficient large-scale parameterization but relies on idealized assumptions, including local thermodynamic equilibrium, a single-path SWCC, and invariant soil structure. These assumptions limit representation of drying–wetting and freeze–thaw hysteresis, solute effects, pore-ice-induced changes in hydraulic properties, non-equilibrium phase transition, and thermo-hydro-mechanical feedbacks. Numerical treatment further affects model performance: the strong nonlinearity of phase transition poses challenges for stability and energy conservation, whereas enthalpy-based formulations offer potential advantages but require robust and efficient nonlinear solvers. We also highlight that pore- or column-scale phase-transition relationships cannot be directly transferred to grid-scale LSMs without losing subgrid heterogeneity and nonlinear thresholds. These biases can be amplified through hydrothermal coupling, increasing uncertainty in permafrost carbon–climate feedbacks and land–atmosphere interactions. Future progress requires physically consistent water-potential parameterizations, expanded soil freezing characteristic curve databases, simplified non-equilibrium and structural-feedback parameterizations, improved enthalpy solvers, and multi-source observations to constrain scale-aware parameterizations, thereby improving the reliability of predictions of permafrost change and its impacts on global climate.