Effects of dating errors on nonparametric trend analyses of speleothem time series
A fundamental problem in paleoclimatology is to take fully into account the various error sources when examining proxy records with quantitative methods of statistical time series analysis. Records from dated climate archives such as speleothems add extra uncertainty from the age determination to the other sources that consist in measurement and proxy errors. This paper examines three stalagmite time series of oxygen isotopic composition (δ 18O) from two caves in western Germany, the series AH-1 from the Atta Cave and the series Bu1 and Bu4 from the Bunker Cave. These records carry regional information about past changes in winter precipitation and temperature. U/Th and radiocarbon dating reveals that they cover the later part of the Holocene, the past 8.6 thousand years (ka). We analyse centennial- to millennial-scale climate trends by means of nonparametric Gasser–Müller kernel regression. Error bands around fitted trend curves are determined by combining (1) block bootstrap resampling to preserve noise properties (shape, autocorrelation) of the δ 18O residuals and (2) timescale simulations (models StalAge and iscam). The timescale error influences on centennial- to millennial-scale trend estimation are not excessively large. We find a "mid-Holocene climate double-swing", from warm to cold to warm winter conditions (6.5 ka to 6.0 ka to 5.1 ka), with warm–cold amplitudes of around 0.5‰ δ 18O; this finding is documented by all three records with high confidence. We also quantify the Medieval Warm Period (MWP), the Little Ice Age (LIA) and the current warmth. Our analyses cannot unequivocally support the conclusion that current regional winter climate is warmer than that during the MWP.