Results of Calibration/Verification Exercises

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