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At places with an annual mean temperature lower than −20°C on the Greenland and Antarctic ice sheets, the temperature at a depth of 10 m is close to the annual mean at the surface and at the level of the meteorological shelter. With temperatures higher than about −35°C the size and sign of the différences vary. With lower temperatures the 10 m temperature becomes increasingly lower than the air temperature, at the coldest Antarctic station, “Plateau”, by nearly 4 deg.
F. Loewe (Thu,) studied this question.