Table 1. Overview of the reconstruction methods and data-model comparison.

“Refs” indicate key References. “Annual proxies only” indicates whether a method only incorporates proxy data of annual or higher resolution. The last two columns present the variance ratios and correlations between multi-decadal (30-200 year bandpass filtered) models and data, respectively, over the period 1300-2000 (Fig. 2). Ensemble medians are provided for each reconstruction method and 2.5th and 97.5th percentiles in square brackets. Percentage of ensemble members with correlations larger than expected from noise in parenthesis. Details see Methods. Unfiltered data and results for each model simulation are shown in Supplementary Tables 1-3.

	Refs	Annual resolved proxies only	model/data variance ratios	model vs. data correlations
Composite plus scaling (CPS)	26, 27	yes	0.96 [0.39, 2.49]	0.64 [0.44, 0.80] (99.6%)
Principal component regression (PCR)	27, 28	yes	1.01 [0.39, 2.65]	0.60 [0.38, 0.77] (99.4%)
Optimal information extraction (OIE)	29	no	1.13 [0.48, 3.02]	0.61 [0.43, 0.83] (99.5%)
Regularized errors in variables (M08)	26	no	1.01 [0.41, 2.59]	0.65 [0.49, 0.79] (99.8%)
Pairwise comparison (PAI)	30	no	0.63 [0.25, 1.65]	0.63 [0.43, 0.79] (99.7%)
Bayesian hierarchical model (BHM)	31	yes	1.12 [0.47, 2.91]	0.53 [0.37, 0.66] (98.9%)
Offline data assimilation (DA)	32	yes	1.15 [0.44, 3.02]	0.62 [0.40, 0.86] (99.6%)