Statistical uncertainty in paleoclimate proxy reconstructions

WashU affiliated authors: H.L.O. McClelland, A.S. Bradley (Dept. of Earth and Planetary Sciences)

Abstract: 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 OLS 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, non-parametric 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 towards 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 behaviour 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 the 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 reducing uncertainty should be directed.