In climate research, a proxy variable is something that is probably not in itself of any great interest, but from which a variable of interest can be obtained.

Examples include:

1. Isotopic variations in ice cores can be used to infer temperature changes and ice sheet volume.
2. Beryllium 10 variations can be used to infer past solar irradiance.
3. Tree ring widths can be used to infer precipitation and temperature changes.

In all cases it is necessary to carefully calibrate the proxy against the variable of interest. Tree growth, for example, is sensitive to precipitation and temperature as well as a number of other signals, and is often most sensitive during certain seasons of the year. Ice core proxies are usually the most direct.

Water isotopes and temperature reconstruction

Ocean water is mostly , with small amounts of HD¹⁶O and . In standard mean ocean water (SMOW) the ratio of D to H is 155.8 * 10 ^{- 6} and O-18 to O-16 is 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 preferrentially contains heavier isotopes. The difference from SMOW is expressed as δ¹⁸O = 1000 * ((¹⁸O / ¹⁶O) / (¹⁸O / ¹⁶O)_SMOW - 1); and a similar formula for δD. δ values for precipitation are always negative. The major influence on δ 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 δ value mostly reflects the temperature where precipitation occurs. Taking into account that the precipiation forms above the inversion layer, we are left with a linear relation:

δ ¹⁸O = aT + b

which is empirically calibrated from measurements of temperature and δ as a = 0.00067 %/^oC for Greenland and 0.00076 %/^oC for East Antarctica. The calibration was initially done on the basis of spatial variations in temperature and it was assumed that this corresponded to temporal variations (Jouzel and Merlivat, 1984). More recently, borehole themometry has shown that for glacial-interglacial variations, a = 0.00033 %/^oC (Cuffey et al., 1995), implying that glacial-interglacial temperature changes were twice as large as previously believed.

Reference

1. E. W. Wolff, History of the atmosphere from ice cores; ERCA vlo 4 pp147-177