An extension of the force-restore method to estimating soil temperature at depth and evaluation for frozen soils under snow

The force-restore method (FRM) was originally developed for estimating diurnal fluctuations in the ground surface temperature. Because of its relatively simple parameterization, it is commonly applied in meteorological and other models for this purpose. Its application to the calculation of deeper soil temperatures, to frozen soils, and to soils under snow covers has heretofore not been possible. This study demonstrates an extension of the FRM that permits accurate estimates of seasonal variation in mean daily deep soil temperature. The extended FRM is shown to provide a lower boundary condition for the heat conduction method, permitting a combination of the two approaches that avoids some limitations of each. The combined approach provides representations of the mean daily soil temperature, soil temperature at depth in frozen soils, and ground surface temperature under a snow cover. Diurnal variations can also be calculated. The extended method and combined approaches are tested using field site measurements collected in cold weather periods in Saskatchewan, Canada, and are found to provide a reasonable representation of measurements.