Statistical Uncertainty in Paleoclimate Proxy Reconstructions

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data‐forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences. Plain Language Summary Earth's surface environments have varied significantly throughout geologic time. Accurate quantification of these ancient environmental changes relies on proxies—materials that are known to change composition or morphology with the ambient environment. These approaches have provided insight into important questions across the Earth sciences, from the context and consequences of biological evolution and volcanic eruptions, to threshold behavior and long‐term feedbacks within the modern climate system. Although the uncertainty associated with an estimate of an environmental change is of equal importance to the estimate itself, uncertainties are widely either underestimated or else rely on proxy‐specific statistical models. Fortunately, a very good, and broadly applicable, estimate of uncertainty is extremely simple to calculate. In this paper we show that statistical uncertainty in proxy reconstructions is mostly due to the magnitude of scatter around the calibration line. We furthermore attempt to give the reader an intuition for how large reported uncertainties in proxy reconstructions should be, how and when they can be reduced, and where future efforts to reduce uncertainty should be directed. Key Points Statistical uncertainties in proxy reconstructions are dominated by unexplained variance in the calibration Proxy data should be presented as explicitly distinct from