A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept

Torben Kunz,Thomas Laepple,Andrew M Dolman

doi:10.5194/cp-16-1469-2020

Abstract

Abstract. Proxy records represent an invaluable source of information for reconstructing past climatic variations, but they are associated with considerable uncertainties. For a systematic quantification of these reconstruction errors, however, knowledge is required not only of their individual sources but also of their auto-correlation structure as this determines the timescale dependence of their magnitude, an issue that has been often ignored until now. Here a spectral approach to uncertainty analysis is provided for paleoclimate reconstructions obtained from single sediment proxy records. The formulation in the spectral domain rather than the time domain allows for an explicit demonstration and quantification of the timescale dependence that is inherent in any proxy-based reconstruction uncertainty. This study is published in two parts. In this first part, the theoretical concept is presented, and analytic expressions are derived for the power spectral density of the reconstruction error of sediment proxy records. The underlying model takes into account the spectral structure of the climate signal, seasonal and orbital variations, bioturbation, sampling of a finite number of signal carriers, and uncorrelated measurement noise, and it includes the effects of spectral aliasing and leakage. The uncertainty estimation method, based upon this model, is illustrated by simple examples. In the second part of this study, published separately, the method is implemented in an application-oriented context, and more detailed examples are presented.

Highlights

The central issues of climate sciences include the estimation, understanding, and prediction of climatic variations across ranges of space and timescales that are relevant to the specific field of study
– We assume a fixed proxy seasonality in the sense of applying every year the same seasonal timing of a prescribed proxy abundance period, characterized by the parameters τp and φc. For this reason we have to separate the supposed true climate signal into a stochastic component X(t) and a deterministic component Y (t) that represents the seasonal cycle because proxy seasonality implies an in-phase subsampling from Y (t) which, in turn, affects the amount of variance aliased from the seasonal cycle U(4),n and which may lead to a reconstruction bias Bn and associated uncertainty U(3),n
In the opposite extreme case where no seasonality is imposed at all, we do not need to separate the climate signal into X(t) and Y (t). In this case the total climate signal is fully recorded by the proxy, but its total variance is reduced by some factor because of habitat tracking if the habitat probability density function (PDF) of the proxy is narrower than the PDF of the climate signal

Summary

Introduction

The central issues of climate sciences include the estimation, understanding, and prediction of climatic variations across ranges of space and timescales that are relevant to the specific field of study. Once processes are studied that involve climate states or variations at times before the instrumental era or that involve timescales longer than this, reconstructions obtained from paleoclimate proxies become indispensable. Such proxy records reveal imprints of past climatic conditions created by, for example, impacts on the calcification of the shells of marine organisms (Nürnberg et al, 1996), preserved in sea sediments, on terrestrial pollen assemblages archived in lake sediments (Birks and Seppä, 2004), or on stable water isotopes that can be recovered from ice cores (Jouzel et al, 1997). An important task of the paleoclimate research field is to pro-

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