Application of the Extended Force-restore Model to Estimating Soil-frost Depth in the Tokachi District of Hokkaido, Japan

In the present study, we tested the applicability of the extended force-restore model (eFRM) to estimating soil-frost depth in the Tokachi district where the soil is a type of volcanic ash. The optimal thermal conductivity of the snow (TC-S) in each cold period varied from 0.074 to 0.172 W m^-1 K^-1, with root-mean-square errors (RMSEs) ranging from 0.020 to 0.039 m. The difference between observed and estimated maximum soil frost depth (SFD_max) was less than 0.03 m. The fixed TC-S through the six cold periods from 2001 to 2007 was optimized as the value of 0.173 W m^-1 K^-1 with minimum RMSE of 0.043 m. When this optimal value of TC-S was used to estimate SFD_max, the difference between the observed and estimated values was 0.04 m at most, with the exception of 2003-2004 and 2004-2005, when little soil-frost developed. Our results showed that even though we considered the TC-S to be invariant over time, the eFRM was able to estimate soil-frost depth with an accuracy of a few centimeters using only mean daily air temperature and snow depth as inputs.