Coupled Water Flow and Heat Transport in Seasonally Frozen Soils with Snow Accumulation

Abstract

A new numerical model was developed to calculate coupled water flow and heat transport in seasonally frozen soil and snow. Separate equations were presented to describe both unsaturated and saturated soil water flow. The effect of dissolved ions on soil water freezing point depression was included by combining an expression for osmotic head with the Clapeyron equation and the van Genuchten soil water retention function. The coupled water flow and heat transport equations were solved using the Thomas algorithm and Picard iteration. Ice pressure was always assumed zero, and frost heave was neglected. The new model was tested using data from an existing laboratory soil column freezing experiment and an ongoing field experiment in a high‐elevation rangeland soil. A dimensionless impedance factor describing the effect of ice pore blocking on soil hydraulic conductivity was treated as a calibration parameter for both cases. Calculated values of total water content for the laboratory soil column freezing experiment compared well with measured values, especially during the early stages of the experiment, as was also found by others. Modeling statistics for the rangeland field experiment showed varied performance for soil water content (RMSE = 0.02–0.06 m3 m−3; modeling efficiency [ME] = −4.06 to +0.72) and excellent performance for soil temperature (RMSE = 1.0–2.1°C; ME = 0.93–0.98), in accordance with earlier results with an older version of the model.