BOREAL COLD SEASON (Oct-Mar) RECONSTRUCTIONS: Raw Data (1902-1980) beta r^2(c) GLB NH DET NIN MULT NIN raw data 1.00 1.00 1.00 1.00 1.00 0.51 Eigenvector Filtering (1902-1980) Grp EVs beta GLB NH DET NIN MULT a 1st 8 0.89 0.76 0.64 0.75 0.27 b 1st 5 0.88 0.76 0.63 0.74 0.19 c 1st 2 0.86 0.72 0.55 0.73 0.11 --------------------------------------------------------------------------------------------------------------------------- Experiment Calibration (1902-1980) Verification (pre 1902) # year tot inst EVs beta beta r^2(c) GLB NH DET NIN MLT GLB NH MLTA NIN 1 1820 112 24 8 (1-8) 0.65 0.56 0.12 0.49 0.19 0.53 0.48 0.15 0.52*** 2 1780 102 15 " 0.66 0.57 0.15 0.46 0.17 0.53 0.48 0.14 0.53*** 3 1730 5 (1-5) 0.60 0.54 0.14 0.35 0.11 0.57 0.53 0.13 0.36*** 4 1700 74 2 " 0.59 0.53 0.14 0.32 0.11 0.56 0.52 0.13 0.38*** 5 1600 2 (1-2) 0.50 0.41 0.05 0.16 0.06 0.48 0.46 0.13 0.22** 6 1500 " 0.44 0.35 0.02 0.16 0.05 0.48 0.43 0.11 0.22** 7 1400 " 0.40 0.32 0.01 0.11 0.05 0.38 0.32 0.08 0.15* symbols: + 85% significant) * (90% significant) ** (95% significant) *** (99% significant) x (unphysical positive correlation obtained) a (r^2 with NINO3 index) c (r^2 w/ SOI) Table 1: Correlation and variance reduction Statistics. For reference, the values appropriate for the raw 1902-1980 data are shown. The upper group (a-c) describes the resolved variance for different eigenvector group filterings of the raw data. The middle group (experiments 1-7) describes the calibration and verification resolved variance statistics beta for the optimal group of retained eigenvectors as a function of the increasingly sparse multiproxy network available going back in time. In each case, the beginning year ``year'' is provided (note that all indicators in the multiproxy network date at least back to 1820), and for the sensitivity experiments the particular data excluded are noted by appropriate symbols. The total number (``tot''), and number of historical/instrumental records in the network (``inst'') are noted, along with the number and specific subset of retained eigenvectors (``EVs''). Calibration resolved variance (beta) for global average (``GLB''), northern hemisphere average (``NH''), detrended NH (``DET''), NINO3 index (``NIN'') and the full multivariate field (``MULT'') are provided. For NINO3, the squared correlation (r^2) with the actual NINO3 series from 1902-1980, is given. For verification, resolved variance statistics are also given for GLB, NH, and MULT [the latter based on (A) the 1854-1901 gridpoint data. Any positive value of beta is statistically significant at greater than 99% confidence as established from Monte Carlo simulations. The statistical significance of the verification r^2 of NINO3 with the Jones (1) Southern Oscillation Index (``SOI'',1865-1901: note that there is a difference in convention by one year with our winter half-season "year" and the winter "year" of the SOI). SOI-NINO3 reconstruction, only r^2 values corresponding to a physical r<0 are shown (with one-sided confidence intervals used for establishing significance). Unphysical r<0 is denoted by an ``x'' symbold.

REFERENCES:

1. Jones, P.D., personal communication