“…There are several methods to estimate soil freeze and thaw depths in cold regions: (1) using soil temperature data to estimate freeze-thaw depths (Frauenfeld et al, 2004;Zhang et al, 2005), (2) estimating the depths from the freeze-thaw index, and (3) using numerical models to estimate depths (Zhang and Stamnes, 1998). Of these, the annual freezethaw index is most widely used to determine the seasonal freeze and thaw depths in cold regions, primarily by using the Stefan equation (Nelson et al, 1997;Shiklomanov and Nelson, 2002;Zhang et al, 2005;Anisimov et al, 2007;Smith et al, 2009).…”