A Three-Dimensional Solifluction Model: From Governing Equations to a Numerical Model Package

Solifluction is an important geomorphological process, mainly driven by seasonal freeze–thaw cycles that mobilize the upper soil layers and contribute significantly to landscape evolution. Despite its relevance, there is currently no numerical package available for simulating solifluction in a physically based manner. In this study, we present a new three-dimensional numerical model, soli3d, developed to simulate this phenomenon by deriving the governing physical partial differential equations and explicitly solving them using numerical discretization.The model integrates mass conservation, momentum conservation, and heat transfer. The thawed soil layer is treated as a viscous fluid, and the corresponding momentum equations are derived following principles from fluid mechanics. Topographic evolution is tracked using a Volume of Fluid (VOF) method. Soil temperature profiles are computed by solving the heat transfer equation in the vertical direction. The viscosity of the thawed soil is assumed to depend on temperature, soil and vegetation properties. The soli3d software package uses the finite difference method (FDM) to discretize and solve the governing equations. The vertical domain is represented by multiple layers, while the horizontal plane is discretized using uniform, structured rectangular grids. The soli3d model (see soli3d link [https://github.com/computationalgeography/soli3d]) is available as an open-source Python implementation utilizing the LUE environmental modelling framework (see link [https://zenodo.org/records/16792016]) for efficient parallel and distributed computing.To assess the model performance, soli3d is validated using a set of benchmark test cases. The results demonstrate the capability of the model to reproduce key characteristics of solifluction processes and provide a foundation for future applications.