Quantification and propagation of errors when converting vertebrate biomineral oxygen isotope data to temperature for palaeoclimate reconstruction

Abstract

Oxygen isotope analysis of bioapatite in vertebrate remains (bones and teeth) is commonly used to address questions on palaeoclimate from the Eocene to the recent past. Researchers currently use a range of methods to calibrate their data, enabling the isotopic composition of precipitation and the air temperature to be estimated. In some A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT2 situations the regression method used can significantly affect the resulting palaeoclimatic interpretations. Furthermore, to understand the uncertainties in the results, it is necessary to quantify the errors involved in calibration. Studies in which isotopic data are converted rarely address these points, and a better understanding of the calibration process is needed. This paper compares regression methods employed in recent publications to calibrate isotopic data for palaeoclimatic interpretation and determines that least-squares regression inverted to x = (y − b) / a is the most appropriate method to use for calibrating causal isotopic relationships. We also identify the main sources of error introduced at each conversion stage, and investigate ways to minimise this error. We demonstrate that larger sample sizes substantially reduce the uncertainties inherent within the calibration process: typical uncertainty in temperature inferred from a single sample is at least ±4ºC, which multiple samples can reduce to ±1-2ºC. Moreover, the gain even from one to four samples is greater than the gain from any further increases. We also show that when converting δ 18 O precipitation to temperature, use of annually averaged data can give significantly less uncertainty in inferred temperatures than use of monthly rainfall data. Equations and an online spreadsheet for the quantification of errors are provided for general use, and could be extended to contexts beyond the specific application of this paper.Palaeotemperature estimation from isotopic data can be highly informative for our understanding of past climates and their impact on humans and animals. However, for such estimates to be useful, there must be confidence in their accuracy, and this includes an assessment of calibration error. We give a series of recommendations for assessing uncertainty when making calibrations of δ 18 O bioapatite -δ 18 O precipitationTemperature. Use of these guidelines will provide a more solid foundation for palaeoclimate inferences made from vertebrate isotopic data.

The Influence of Social Status and Ethnicity on Diet in Mediaeval Tallinn as Seen Through Stable Isotope Analysis

“…As the local baseline value is uncertain and given the difficulties in converting human oxygen isotope values into drinking water values associated with conversion equations and error propagation (see discussions in Pollard et al 2011;Pryor et al 2014), the oxygen isotope results will be discussed as unconverted values. The data are given in the Appendix and shown in Fig.…”

Synchronized proxy‐based temperature reconstructions reveal mid‐ to late Holocene climate oscillations in High Arctic Svalbard

“…The composite errors for the reconstructions, factoring in both measurement uncertainty and calibration error, were calculated according to Pryor et al . (). They range from 1.4 to 3.6‰ (mean 1.6‰) and 1.9 to 4.5 °C (mean 2.1 °C) for the δ 18 O lake water and MAT reconstructions, respectively.…”

“…The d 18 O chir values were used to estimate mean annual values of d 18 O lake water and MAT following Wooller et al (2004) and Verbruggen et al (2011). The composite errors for the reconstructions, factoring in both measurement uncertainty and calibration error, were calculated according to Pryor et al (2014). They range from 1.4 to 3.6‰ (mean 1.6‰) and 1.9 to 4.5˚C (mean 2.1˚C) for the d 18 O lake water and MAT reconstructions, respectively.…”

The early colonial atlantic world: New insights on the African Diaspora from isotopic and ancient DNA analyses of a multiethnic 15th–17th century burial population from the Canary Islands, Spain

“…It is unclear, which equation can be considered the most appropriate, however as Pollard et al () combines the data from all of the other studies, this equation will be used preferentially. Nevertheless, as each conversion equation increases the error associated with the drinking water value (see Pryor et al, ), the data are considered as carbonate VPDB values wherever possible.…”