Paleothermometer

A paleothermometer is a methodology for determining past temperatures using a proxy found in a natural record such as a sediment, ice core, tree rings or TEX₈₆.

The isotopic ratio of ¹⁸O to ¹⁶O, usually in foram tests or ice cores. High values mean low temperatures. Confounded by ice volume - more ice means higher δ¹⁸O values.

Ocean water is mostly H₂¹⁶O, with small amounts of HD¹⁶O and H₂¹⁸O. In Standard Mean Ocean Water (SMOW) the ratio of D to H is ${\displaystyle 155.8*10^{-6}}$ and ¹⁸O/¹⁶O is ${\displaystyle 2005*10^{-6}}$. Fractionation occurs during changes between condensed and vapour phases: the vapour pressure of heavier isotopes is lower, so vapour contains relatively more of the lighter isotopes and when the vapour condenses the precipitation preferentially contains heavier isotopes. The difference from SMOW is expressed as δ¹⁸${\displaystyle O=1000*((^{18}O/^{16}O)/(^{18}O/^{16}O)_{SMOW}-1)}$; and a similar formula for δD. δ¹⁸O values for precipitation are always negative. The major influence on δ¹⁸O is the difference between ocean temperatures where the moisture evaporated and the place where the final precipitation occurred; since ocean temperatures are relatively stable the δ¹⁸O value mostly reflects the temperature where precipitation occurs. Taking into account that the precipitation forms above the inversion layer, we are left with a linear relation:

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