Discussion of A Simple Thaw-Freeze Algorithm for a Multi-Layered Soil using the Stefan Equation' by Xie and Gough (2013)

Xie and Gough (2013) developed an algorithm to expand the application of the well-known Stefan equation in order to predict the freeze or thaw depth in multi-layered soils. This discussion paper demonstrates that the development of this algorithm is premised on mathematical expressions that are not physically tenable. A previously proposed equation for applying the Stefan approach to multi-layered soils is herein derived from first principles using the appropriate governing equations, boundary conditions and initial conditions. Numerical methods are employed to demonstrate the accuracy of this equation derived from first principles. This approach can be implemented in existing cold regions hydrology models to estimate the active layer thickness in permafrost regions underlain by layered soils. Copyright (c) 2015 John Wiley & Sons, Ltd.