How Deep Is Cool: The Soil-Temperature Bound for Earth-Sheltered Food Storage, and the Depth That Holds a Store Between 0 and 4 °C

Earth-sheltered storage is widely recommended as refrigeration without machinery: dig a cellar, and the ground itself holds food cold. This paper computes, from the diffusion of the annual surface temperature cycle into soil, exactly when that advice works and when it cannot. For three stated soil diffusivities the damping depth of the annual cycle is 1.417 m in dry sandy soil, 2.241 m in moist loam, and 3.169 m in wet clay. In a stated cool continental climate (mean annual surface temperature 2.0 °C, annual amplitude 14.0 °C) a store first stays inside the 0–4 °C refrigeration band all year at depths of 2.76 m, 4.36 m, and 6.17 m in the three soils respectively. The popular rule that deeper digging always finds colder ground does not survive the arithmetic: at great depth the soil temperature tends to the mean annual surface temperature, so where that mean is itself warm no depth reaches refrigeration temperatures. In a stated temperate climate with mean 8.0 °C the deep soil sits at 8.0 °C, a full 4.0 °C above the top of the band; in a stated hot climate with mean 26.0 °C the deep soil sits at 26.0 °C, which is 22.0 °C above the band, and even the coldest moment at the surface itself is 18.0 °C. The deciding quantity for earth-sheltered refrigeration is therefore not depth but the mean annual temperature of the site.