2.1.3 Freeze and thaw fronts (FTFs)
For the FTFs, Stefan’s equation (Jumikis 1977; Lunardini 1981; Woo et al. 2004; Zhang and Wu 2012; Xie et al. 2013; Gao et al. 2016; Gao et al. 2018) provided a basis to compute one-directional freeze and thaw in a soil column (Jumikis 1978), which was based on heat conduction and assumes that all heat that reached the freezing or thawing front was used for water freezing or melting. This method was frequently used by permafrost scientists to predict frost depth, and to simulate heat transfer during water phase transitions in frozen soil when little site-specific information are available. It could also be applied to calculate one-directional FTFs in a soil profile (Xie and Gough 2013; Gao et al. 2016). The FTFs were implemented into CAS-LSM here following Gao et al. (2018).