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

Abstract

[1] 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.INDEX TERMS: 3322 Meteorology and Atmospheric Dynamics: Land/atmosphere interactions; 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; 1823 Hydrology: Frozen ground; 1878 Hydrology: Water/energy interactions; 1863 Hydrology: Snow and ice (1827); KEYWORDS: soil temperature, force-restore method, frozen soil Citation: Hirota, T., J. W. Pomeroy, R. J. Granger, and C. P. Maule, An extension of the force-restore method to estimating soil temperature at depth and evaluation for frozen soils under snow,

Estimating surface moisture availability for evaporation on bare soil from routine meteorological data and its parameterization without soil moisture

“…However, our method has the advantage of needing only routine metrological data without needing special measurements. Also, by using daily mean values, the estimated value cancels out the error of each hourly estimation (Hirota et al 1995;Hirota et al 2001) and the effect of soil thermal properties on the calculation of annual variations in the mean daily soil surface temperature is small, compared to the effect on diurnal variations (Hirota et al 1995;Hirota et al 2002). Therefore, this method can reduce the effect of observation error on the estimated value.…”

“…C1(d) (1+2d/Da). Tym is relatively invariant with depth until a depth of several meters (Hirota et al 1995;Hirota et al 2002), therefore Tym can be adopted for any depth up to several meters.…”

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

“…To estimate soil frost depth, the eFRM developed by Hirota et al (2002) was used. The model combines the merits of two traditional methods: the heat conduction equation (e.g., Campbell, 1985) and the force-restore model (e.g., Bhumralkar, 1975).…”

“…The extended force-restore model (Hirota et al, 2002; hereafter referred to as eFRM) has been validated using data from a Canadian farm whose soils were characterized as fine-textured chernozems, and in that study, the model successfully estimated the soil temperature profile from only mean air temperature and snow depth data. In the present study, we tested the applicability of the eFRM to estimating soil-frost depth in the Tokachi district of Hokkaido, Japan, an area where the soil freezes seasonally and the annual maximum frost depth has decreased significantly in the last 20 years (Hirota et al, 2006).…”

Decreasing Soil-Frost Depth and Its Relation to Climate Change in Tokachi, Hokkaido, Japan

“…However, the amount and timing of snowfall can also have significant effects, because the thickness of snow cover greatly influences the energy exchange at the ground surface (Fukuda 1982;Tsuchiya 1985;Sharratt et al 1999). Previous studies on soil freezing processes have mostly been conducted at a relatively small number of local sites over a short period of time (e.g., Osterkamp and Romanovsky 1997;Stä hli et al 1999;Hirota et al 2002;Iwata and Hirora 2005;Hirota et al 2005). Therefore, we have limited understanding of long-term interactions between climate and soil frost over a regional scale.…”