Paleoclimatic inference from stable isotope profiles of accretionary biogenic hardparts - A quantitative approach to the evaluation of incomplete data

Variation in δ¹⁸O of invertebrate and vertebrate skeletons has been widely employed to estimate annual means and seasonal ranges of temperature from many geologic settings. Among incertitudes encountered in employing this approach is the influence of unconstrained noise in environmental signals, cessation of hardpart accretion during reproduction and/or seasonal temperature extremes, biasing of calculated mean temperatures toward seasons of maximum growth rate, and dependence on the most extreme δ¹⁸O values observed for estimating annual temperature range. To better constrain paleoclimatic interpretations, we describe several applications of a computational approach that address many of these uncertainties. It is predicated on the presumption that annual variation in isotope composition across an accretionary skeleton represents sinusoidal variation in temperature and/or the composition of ambient fluids. The analysis resolves a best-fit sinusoid for any portion of the data. Output consists of determinations of mean annual δ¹⁸O, seasonal range in δ¹⁸O, and sine period, which reflects hardpart growth rate. The procedure can be employed over some window of values within any data series, and can be reiterated to arrive at solutions for all possible windows. The technique allows for quantitative interpretation of mean values and annual amplitudes of δ¹⁸O variation for every window, regardless of whether or not that window actually spans a seasonal isotope extreme. Moreover, it affords equal interpretational weight for every analysis in the data set, in that mean annual and seasonal variation values estimated for each window are derived from eyery analysis in the data set. It is therefore not necessary to estimate mean annual δ¹⁸O as simply the arithmetic mean of all analyses, and estimates of seasonality can be derived from data within any window rather than depending only on those several analyses that fall at compositional extremes. In order to demonstrate the utility this methodology to the interpretation of paleoclimatological data, we have applied it to published temperature data from several modern climatological data sets, and to published δ¹⁸O data from a Paleogene Gulf Coast fish otolith, a modern Arabian Sea coral, a Miocene Texan equine tooth, and an Eocene bivalve from England. Each yields robust estimates of mean annual temperatures or isotopic compositions, and of seasonal ranges in these values. In addition, unique features of data from each of these examples illustrate the power of this method to shed light on climatological and/or biological phenomena that are also unique to each system.