Similarity estimators for irregular and age-uncertain time series

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.

Warmer and wetter or warmer and dryer? Observed versus simulated covariability of Holocene temperature and rainfall in Asia

“…Age uncertainty in one or both of the proxy reconstructions will bias the correlation towards zero [32], contrary to what would be needed to reconcile proxies and observations.…”

“…This results in a bandpassed time series from which a timescale-dependent Pearson correlation can be estimated robustly against irregular sampling of the time series [32]. Significance testing is based on 2000 Monte Carlo simulations using AR1 surrogates with the lag-1 autocorrelation estimated from the f low -detrended proxy time series, and with the original temporal sampling [32]. In a first screening step the original time series had to overlap with more than 50 samples.…”

“…Both instrumental and model timeseries were linearly detrended and analyzed using timescale dependent Gaussian kernel correlation [32] as for the proxy data. The correlation map fields shown in Fig.…”

Reconstructing Late Holocene North Atlantic atmospheric circulation changes using functional paleoclimate networks

“…Rehfeld and Kurths, 2014, for a comparison of possible measures). Specifically, to determine the strength of co-variability between two paleoclimate records, a suitable similarity measure has to be able to cope with unevenly sampled and/or discontinuous time series.…”

Estimation of sedimentary proxy records together with associated uncertainty

“…Even though the proxy record is a derived measurement, it is still, in its essence, a measurement, and the representation of any measured quantity without an uncertainty (error) of measurement can lead to misleading conclusions. For instance, the assessment of correlations between data sets can be dramatically influenced by whether or not the uncertainty of the data is properly represented (see Rehfeld and Kurths, 2014;Heitzig, 2013, Intro. ).…”