Permafrost Depth Calculator

Permafrost is defined thermally, not by ice content: ground that remains at or below 0 degrees C for at least two consecutive years. Its thickness follows from a simple steady conduction argument. Below the depth where seasonal swings die out, temperature rises linearly with depth at the geothermal gradient, so the base of permafrost sits where the mean annual ground temperature plus that gradient reaches the freezing point. This gives base depth equal to the magnitude of the mean annual ground temperature divided by the gradient. The gradient itself is the geothermal heat flux divided by thermal conductivity, so a continental flux near 50 mW per square meter through soil of 2.0 W per meter per kelvin produces about 0.025 degrees C per meter. A site at -12 degrees C then carries permafrost to roughly 480 m, while the deepest known permafrost, in the Yakutian basins of northeastern Siberia, approaches 1500 m. Zonation is conventionally set by areal coverage: continuous above 90 percent, discontinuous 50 to 90 percent, sporadic 10 to 50 percent, and isolated patches below 10 percent, corresponding roughly to mean annual air temperatures below -8, -8 to -4, -4 to -1, and near -1 degrees C. The depth of zero annual amplitude generally falls between 10 and 20 m. The largest limitation of the steady-state formula is time: thick Siberian permafrost is a relic of Pleistocene conditions and lags climate by thousands of years, so present thickness is not in equilibrium with present temperature. The calculation also ignores latent heat, unfrozen water films, salinity that depresses the freezing point in subsea permafrost, and the offset between air and ground temperature imposed by snow and vegetation.

Deep frozen ground was documented in Russia long before it had a scientific name. Between 1828 and 1837 the merchant Fyodor Shergin dug a shaft at Yakutsk to about 116 m and never reached unfrozen ground; Alexander von Middendorff measured temperatures in that shaft in the 1840s and extrapolated a frozen thickness of roughly 200 m, the first quantitative estimate of permafrost depth anywhere. The Shergin shaft settled a live debate over whether perennially frozen ground could exist at all at such depth. Russian and Soviet workers built the discipline around it. Mikhail Sumgin published the founding monograph on perennially frozen ground of the USSR in 1927, and a dedicated Soviet permafrost institute was later established, eventually centred at Yakutsk. The English word permafrost was coined by Siemon William Muller of the US Geological Survey in a 1943 wartime report prepared for military engineering in Alaska. Postwar construction, the Trans-Alaska Pipeline among the most demanding cases, forced systematic borehole thermal monitoring. The first International Conference on Permafrost convened at Purdue University in 1963, the International Permafrost Association formed in 1983, and the Global Terrestrial Network for Permafrost now aggregates borehole temperature records worldwide; a 2019 synthesis of that network reported warming near 0.3 degrees C per decade at continuous-zone sites.