Improved Stefan Equation Correction Factors to Accommodate Sensible Heat Storage during Soil Freezing or Thawing

In permafrost regions, the thaw depth strongly controls shallow subsurface hydrologic processes that in turn dominate catchment runoff. In seasonally freezing soils, the maximum expected frost depth is an important geotechnical engineering design parameter. Thus, accurately calculating the depth of soil freezing or thawing is an important challenge in cold regions engineering and hydrology. The Stefan equation is a common approach for predicting the frost or thaw depth, but this equation assumes negligible soil heat capacity and thus exaggerates the rate of freezing or thawing. The Neumann equation, which accommodates sensible heat, is an alternative implicit equation for calculating freeze-thaw penetration. This study details the development of correction factors to improve the Stefan equation by accounting for the influence of the soil heat capacity and non-zero initial temperatures. The correction factors are first derived analytically via comparison to the Neumann solution, but the resultant equations are complex and implicit. Explicit equations are obtained by fitting polynomial functions to the analytical results. These simple correction factors are shown to significantly improve the performance of the Stefan equation for several hypothetical soil freezing and thawing scenarios. Copyright (c) 2015 John Wiley & Sons, Ltd.