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Error estimation and potential biases

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We followed a similar error analysis approach as used recently for temperature reconstruction inferred from ice core measurements (50). Uncertainties for the MC-FIT record come from the isotope measurement error and the error resulting from the selected TF. Uncertainties that encompass hydrogen isotope measurement uncertainty of 1‰ are ±0.21°, ±0.26°, and ± 0.35°C (225 samples) for TFs of 0.60, 0.48, and 0.36‰/°C, respectively (linear regression). It is ±0.31°, ±0.39°, and ±0.52°C (42 samples) for a 1.5‰ measurement uncertainty. The domain error arising from the TF choice is nonlinear and asymmetric and displayed in Fig. 2 and fig. S6 as upper and lower boundaries (blue-shaded interval) of each single TF temperature reconstruction. Whereas the change in TFs will induce an offset in MC-FIT and result in a change of MC-FIT amplitudes, the variability remains robust and is mainly dependent on measurement uncertainty. Thus, the record moves in the uncertainty band, but the variability will hardly be affected. Errors given in the text for the interval means were calculated with the following formula: $σinterval=√σmeas2+σmean2n$. The uncertainty of a change is given as the sum of the σinterval. The good δD interlaboratory reproducibility (12) documents that the loss of water by diffusion through the calcite or during measurements is negligible, leaving only evaporation before enclosure to alter δDfi that would tend to produce enriched isotope values and thus higher temperature estimates. Drip water δDdw is enriched compared to the correspondent value of direct precipitation by ~10‰. Yet, evidence that δDfi provides a direct record of past precipitations is given through its modern calibration and high correlation between δDfi and δ18Ofi (slope, 7.92 ± 0.07; R2 = 0.98) (15). We would further like to mention that the recent water balance (precipitation − evaporation) (15) potentially indicates slightly positive values in summer, implying reduced water infiltration and thus bias toward negative temperature values. If this would be true, then the reconstructed temperature would exhibit an offset of ~−3°C, resulting from autumn, winter, and spring (AWS) water infiltration based on instrumental temperature data. The comparison between the regional CCSM3 model simulations for the MAAT and the AWS for the past 14,000 years also results in a mean offset of ~−3°C. Nevertheless, the assumption is made that the water balance is constant over time. We also have no control on seasonality changes of infiltration and precipitation in the past, and we assume that annual infiltration is fairly constant over time. Potential changes in the large-scale atmospheric pattern, i.e., North Atlantic Oscillation or changes in the moisture source, were not taken into account.

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