Simulating soil heat transfer with excess ice, erosion and deposition, guaranteed energy conservation, adaptive mesh refinement, and accurate spin-up (FreeThawXice1D)

Abstract. Thawing permafrost with excess ground ice can cause surface subsidence, damage to infrastructure, and long-term environmental changes. Accurate simulation of the depth, timing, and magnitude of excess-ice melt is important but remains difficult due to nonlinear phase-change dynamics, limitations in model resolution, and the computational challenges of conserving energy over long timescales. Many models blur key features such as the depth of thaw fronts, leading to uncertainty in assessing related hazards.

To address this, we developed a one-dimensional heat-transfer model that can accurately represent the melting of excess ice along with changes in soil geometry due to erosion or deposition. Innovations include adaptive mesh refinement around the melting point, separate treatment of excess and pore ice, and a two-step spin-up routine that ensures thermal equilibrium in deep profiles. The model uses a semi-implicit scheme with a nested Newton solver that guarantees energy conservation and convergence at large time steps.

Test cases show that model resolution and regridding influence the timing and magnitude of surface subsidence and thaw penetration. Tracking permafrost change requires representing the dynamic ground-surface elevation and reporting measurements either relative to it or as heights above a fixed datum. Cases with erosion or deposition demonstrate that even modest changes to surface geometry can alter subsurface thermal regimes, and delay or accelerate ice melt.

FreeThawXice1D provides a reliable and extensible tool for research, model testing, and scenario analysis. Its robust numerics and accuracy make it suitable for improving the realism of long-term permafrost simulations and supporting adaptation decisions in cold regions.