Abstract

Abstract. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.

Highlights

  • Time series are often used to assess the properties of the processes that generated them, in climate science (Rehfeld et al, 2011) and in many other scientific fields ranging from ecology (Lhermitte et al, 2011) to astrophysics (Scargle, 1989)

  • Age uncertainty clearly affects all estimators of similarity for time series, and it is an illusion that it would be possible to mitigate the effects of uncertainty on the time axis for any type of analysis depending on observation times

  • In this paper we have investigated similarity estimators that do not require regular sampling in time and can capture linear and nonlinear relationships

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Summary

Introduction

Time series are often used to assess the properties of the processes that generated them, in climate science (Rehfeld et al, 2011) and in many other scientific fields ranging from ecology (Lhermitte et al, 2011) to astrophysics (Scargle, 1989). Time series similarity measures quantify the degree of statistical association and are, in the geoscientific context, often equated with Pearson correlation (Chatfield, 2004). They help to identify the strength of dependencies between climate processes and potential lead–lag relationships. For modern-day weather stations, both daily temperature and the time of observations are logged precisely. To identify relationships between distant weather evolution, time series of temperature anomalies can be compared.

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