A numerical model for water and heat transport in freezing soils with nonequilibrium ice‐water interfaces
Abstract A one‐dimensional numerical model of heat and water transport in freezing soils is developed by assuming that ice‐water interfaces are not necessarily in equilibrium. The Clapeyron equation, which is derived from a static ice‐water interface using the thermal equilibrium theory, cannot be readily applied to a dynamic system, such as freezing soils. Therefore, we handled the redistribution of liquid water with the Richard's equation. In this application, the sink term is replaced by the freezing rate of pore water, which is proportional to the extent of supercooling and available water content for freezing by a coefficient, β. Three short‐term laboratory column simulations show reasonable agreement with observations, with standard error of simulation on water content ranging between 0.007 and 0.011 cm 3 cm −3 , showing improved accuracy over other models that assume equilibrium ice‐water interfaces. Simulation results suggest that when the freezing front is fixed at a specific depth, deviation of the ice‐water interface from equilibrium, at this location, will increase with time. However, this deviation tends to weaken when the freezing front slowly penetrates to a greater depth, accompanied with thinner soils of significant deviation. The coefficient, β, plays an important role in the simulation of heat and water transport. A smaller β results in a larger deviation in the ice‐water interface from equilibrium, and backward estimation of the freezing front. It also leads to an underestimation of water content in soils that were previously frozen by a rapid freezing rate, and an overestimation of water content in the rest of the soils.
Key Points: The Clapeyron equation does not sufficiently describe the dynamic ice‐water interfaces found in freezing soils A numerical model is developed by assuming ice‐water interfaces are not necessarily in thermal equilibrium
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