Coupled cellular automata for frozen soil processes

Abstract

Heat and water movement in variably saturated freezing soils is a strongly coupled phenomenon. The coupling is a result of the effects of sub-zero temperature on soil water potential, heat carried by water moving under pressure gradients, and dependency of soil thermal and hydraulic properties on soil water content. This study presents a one-dimensional cellular automata (direct solving) model to simulate coupled heat and water transport with phase change in variably saturated soils. The model is based on first-order mass and energy conservation principles. The water and energy fluxes are calculated using first-order empirical forms of Buckingham–Darcy’s law and Fourier’s heat law respectively. The liquid–ice phase change is handled by integrating along an experimentally determined soil freezing curve (unfrozen water content and temperature relationship) obviating the use of the apparent heat capacity term. This approach highlights a further subtle form of coupling in which heat carried by water perturbs the water content–temperature equilibrium and exchange energy flux is used to maintain the equilibrium rather than affect the temperature change. The model is successfully tested against analytical and experimental solutions. Setting up a highly non-linear coupled soil physics problem with a physically based approach provides intuitive insights into an otherwise complex phenomenon.