Results of Calibration/Verification Exercises

ANNUAL MEAN RECONSTRUCTIONS:

                     Raw Data (1902-1980) 

           beta                          r^2(c)  g^2(b) 
           GLB   NH   DET   NIN  MULT    NIN     NIN 
raw data  1.00  1.00  1.00  1.00  1.00   0.51     0.44
 
         Eigenvector Filtering (1902-1980)

Grp EVs              beta 
                      GLB   NH   DET   NIN   MULT
a   1st 40            1.00  0.99  0.98  0.91  0.73
b   1st 20            0.99  0.99  0.97  0.74  0.58
c   1-5,7,9,11,14-16  0.95  0.93  0.87  0.72  0.40
d   1-5,7,9,11,15     0.95  0.93  0.78  0.70  0.38
e   1-3,5,6,8,11,15   0.92  0.83  0.69  0.65  0.31
f   1st 5             0.93  0.85  0.76  0.67  0.27 
g   1,2,5,11,15       0.92  0.83  0.70  0.55  0.23
h   1,2,11,15         0.90  0.78  0.61  0.53  0.21
i   1,2               0.91  0.76  0.57  0.50  0.18 
j   1                 0.88  0.73  0.53  0.09  0.12
--------------------------------------------------------------------------------------------------------------------------- 
Experiment                                 Calibration (1902-1980)                   Verification (pre 1902) 
#  year     tot inst EVs                   beta                       r^2(a) g^2(b)  beta                    r^2(c) g^2(b) 
                                           GLB   NH    DET   NIN   MLT  NIN   NI N   GLB   NH    MLTA  MLTB  NIN    NIN 
1  1820     112  24  11 (1-5,7,9,11,14-16) 0.77  0.76  0.56  0.48  0.30 0.51  0.29   0.76  0.69  0.22  0.55  0.14***0.28*** 
2  1800     102  15            "           0.76  0.75  0.54  0.50  0.27 0.52  0.30   0.75  0.68  0.19  0.45  0.10** 0.22**
3  1780      97  12            "           0.76  0.74  0.54  0.51  0.27 0.53  0.29   0.76  0.69  0.17  0.40  0.11** 0.20**
4  1760      93   8   9 (1-5,7,9,11,15)    0.76  0.74  0.52  0.49  0.26 0.52  0.29   0.75  0.70  0.17  0.33  0.10** 0.17*
5  1750      89   5   8 (1-3,5,6,8,11,15)  0.76  0.74  0.53  0.34  0.18 0.39  0.33   0.64  0.57  0.11  0.13  0.10** 0.19*
6  1730      79   3   5 (1,2,5,11,15)      0.74  0.71  0.47  0.23  0.15 0.30  0.29   0.65  0.61  0.11  0.13  0.05*  0.17*
7  1700      74   2            "           0.74  0.71  0.47  0.22  0.14 0.29  0.29   0.63  0.57  0.10  0.12  0.05*  0.15+ 
8  1600      57   1   4 (1,2,11,15)        0.72  0.67  0.42  0.05  0.14 0.19  0.23   0.61  0.53  0.12  0.10  0.02+  0.15**  
9  1500      28   0   2 (1,2)              0.51  0.42 -0.05  0.04  0.10 0.20  0.20   0.52  0.49  0.06  0.13  0.02+  0.11*
10 1450      24   0   2 (1,2)              0.50  0.41 -0.07 -0.01  0.09 0.18  0.23   0.55  0.51  0.04  0.10  0.015  0.06
11 1400      22   0   1 (1)                0.51  0.42 -0.04 -0.08  0.08 0.02  0.10   0.57  0.51  0.04  0.06  x      0.0
---------------------------------------------------------------------------------------------------------------------------
12 1820 (PR) 88    0  8 (1-3,5,6,8,11,15)  0.76  0.73 0.51  0.31  0.19  0.37  0.31   0.65  0.56  0.11  0.19  0.12** 0.29* 
13 1820 (IN) 24   24  2 (1,2)              0.32  0.28 -0.28 -0.27 0.10  0.07  0.20   0.30  0.37  0.11  0.26  0.00   0.16
14 1820 (ND) 42   24  7 (1-3,5,11,15,16)   0.50  0.50  0.13  0.05  0.17 0.22  0.18   0.56  0.53  0.17  0.47  0.09*  0.10 
15 1750 (ND) 19    2  2 (1,2)              0.46  0.47 0.05  0.21  0.09  0.30  0.27   0.28  0.27  0.06  0.10  0.03+  0.15

symbols: 
+  85% significant) * (90% significant) ** (95% significant) *** (99% significant)
x (unphysical positive correlation obtained) 
a (r^2 with NINO3 index)  b (g^2 w/ Quinn chron. c (r^2 w/ SOI) 
ND (all dendroclimatic indicators excluded) 
PR (no instrumental/historical proxy indicators only) 
IN (instrumental/historical indicators only) 

Table 1: Correlation and variance reduction Statistics. For reference, the values appropriate for the raw 1902-1980 data
are shown. The upper group (a-j) describes the resolved variance for different eigenvector group filterings of the raw
data. The middle group (experiments 1-11) describes the calibration and verification resolved variance statistics beta for
the optimal group of retained eigenvectors (as described in ``Methods--calibration'') as a function of the increasingly 
sparse multiproxy network available going back in time. The lower group (experiments 12-15) describes the calibration and 
verification resolved variance statistics for various sensitivity experiments in which key indicators (e.g., instrumental
data, non-instrumental data, dendroclimatic indicators) have been excluded from the network. 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, and the squared congruence statistic (g^2) with the historical Quinn El Nino chronology are also given.
For verification (see ``Methods--verification''), resolved variance statistics are also given for GLB, NH, and MULT
[the latter based on both (A) the 1854-1901 gridpoint data and the (B)  11 long instrumental temperature ``gridpoint
series available back to at least 1820 (5 back to 1760)] are provided. 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) and squared congruence 
g^2 with the Quinn (2) chronology (available back through 1525) are  explicity denoted by the indicated symbols. For the
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
2. Quinn, W.H. & Neal, V.T., The historical record of El Nino events, 
in Climate Since A.D. 1500 (eds Bradley, R.S. & Jones, P.D., 623-648, 
Routledge, 1992). 

BOREAL COLD-SEASON RECONSTRUCTIONS:

BOREAL WARM-SEASON RECONSTRUCTIONS: