date: Fri, 28 Jun 96 06:42:17 EDT
from: drdendro@lamont.ldgo.columbia.edu (edward cook)
subject: things
to: k.briffa@uea.ac.uk

Hi Keith,

Yesterday afternoon, just after I left Lamont to come home for vacaction, the NAO
manuscript arrived. Rose Mary called home to tell me that. She is mailing it out to
the beach house and it should arrive there around Monday or Tuesday. So, I will be
able to have a go at it out at the beach. But it will be difficult to get the changes
back to you before I come off the beach in a couple of weeks. Just thought I should
let you know.

Below is appended the results of reconstructing Roger's winter SENA slp pattern over
Europe from European tree rings. The results are not too bad. At least they are
acceptable at this time. His other slp patterns (I didn't try his NAO one) could not
be calibrated well enough to reconstruct, even the SCAND pattern, which I thought was
a trivial one to do. Don't know why. Anyway, here is all this stuff.

Cheers, Ed

		         ROGER'S WINTER SENA SLP PATTERN RECONSTRUCTION
				 
				     NOT PERFECT, BUT OKAY FOR A FIRST CUT


         PREDICTOR-PREDICTAND COMMON PERIOD: 1900 - 1978     79 years

         FOR THE CALIBRATION PERIOD:
              FIRST YEAR:                   1940
              LAST YEAR:                    1978
              TOTAL YEARS:                    39

         POINT-BY-POINT REGRESSION OPTION CHOSEN

         CRITERIA FOR SCREENING PREDICTORS:

         PROBABILITY LEVEL FOR SCREENING CORRELATIONS:    0.1000
         NUMBER OF TAILS FOR TESTING CORRELATIONS:         2
         EIGENVECTOR SELECTION CRITERION:                  EIGENVALUE-1
         REGRESSION MODEL SELECTION CRITERION:             T-STATISTIC
         MINIMUM T-VALUE FOR ACCEPTING PREDICTORS:           1.

         19 TREE-RING PREDICTORS PASSED FOR PREDICTAND  1

                       PRINCIPAL COMPONENT ANALYSIS OF PREDICTORS

         COMPONENT   EIGENVALUE   % VARIANCE   CUMULATIVE %   CUMULATIVE PRODUCT

              1        6.075        31.974        31.974            6.075
              2        3.161        16.636        48.610           19.202
              3        2.118        11.146        59.756           40.664
              4        1.487         7.825        67.581           60.458
              5        1.171         6.165        73.746           70.821
              6        1.087         5.723        79.469           77.009
              7        0.801         4.214        83.684           61.664
              8        0.756         3.981        87.664           46.641
              9        0.680         3.579        91.244           31.720
             10        0.413         2.175        93.419           13.108
             11        0.364         1.917        95.335            4.773
             12        0.251         1.323        96.658            1.199
             13        0.178         0.938        97.596            0.214
             14        0.132         0.694        98.290            0.028
             15        0.126         0.666        98.956            0.004
             16        0.104         0.549        99.505            0.000
             17        0.067         0.350        99.855            0.000
             18        0.026         0.138        99.993            0.000
             19        0.001         0.007       100.000            0.000

                                  REGRESSION MODEL RESULTS

         STEP  EIGEN  CORR  T-STAT   PROB   RSQ  CUM RSQ  ADJ RSQ  ADJ RE    AIC

           1     1  -0.452  -3.082*0.0039*0.204   0.204   0.183*   0.162    -4.58*
           2     2   0.451   3.076*0.0040*0.204   0.408   0.375*   0.344   -13.76*
           3     3   0.354   2.301*0.0258*0.125   0.533   0.493*   0.455   -20.53*
           4     4   0.167   1.029*0.3114 0.028   0.561   0.509*   0.460   -20.28 
           5     6   0.126   0.773 0.5498 0.016   0.577   0.513*   0.452   -18.91 
           6     5  -0.087  -0.530 0.6053 0.008   0.584   0.506    0.432   -16.63 

         BEST ORDER MODEL USING T-STATISTIC:  4
         PERCENT VARIANCE EXPLAINED:  56.09 %
         FULL MODEL F-RATIO:   10.86   PROB: .00001     4 AND   34 D.F.

         REGRESSION COEFFICIENTS IN TERMS OF ORIGINAL SCREENED PREDICTORS

                   NUMBER     VARIABLE     BETA     STD ERR
                      1           3      0.0529*    0.0080
                      2           7      0.0768*    0.0074
                      3           9      0.0960*    0.0107
                      4          11      0.0722*    0.0085
                      5          13      0.0684*    0.0065
                      6          15      0.0370*    0.0058
                      7          21      0.0054     0.0236
                      8          23      0.0078     0.0232
                      9          36      0.1164*    0.0097
                     10          41     -0.1821*    0.0232
                     11          64     -0.1033*    0.0135
                     12          66     -0.1143*    0.0167
                     13          76     -0.0719*    0.0192
                     14          78     -0.0635*    0.0140
                     15          90      0.1045*    0.0242
                     16         104      0.1510*    0.0291
                     17         108      0.1490*    0.0279
                     18         109      0.0412*    0.0051
                     19         110     -0.0966*    0.0050

                        MEAN     STD DEV     SKEW     KURTOSIS     SERIAL R

         ACTUAL      -0.0033      0.6624   0.0708      2.3356       0.0410
         ESTIMATE     0.3401      0.4961  -0.2278      2.8123      -0.2527
         RESIDUAL     0.0000      0.4389   0.2778      3.2588       0.1877

         DURBIN-WATSON STATISTIC =    1.5431     DEGREES-OF-FREEDOM =  4  AND  39

         POSITIVE RESIDUALS =  20                NEGATIVE RESIDUALS =  19
         EXPECTED NUMBER OF RUNS =     20.49     ACTUAL NUMBER OF RUNS =  34
         TOO FEW RUNS Z-SCORE =        4.551     PROB =  0.00000
         TOO MANY RUNS Z-SCORE =       4.226     PROB =  0.00001

         ACTUAL VS. ESTIMATES CORRELATION =       0.7489
         ESTIMATES VS. RESIDUALS CORRELATION =    0.0000
         ACTUAL VS. RESIDUALS CORRELATION =       0.6626
		 

                     THE CALIBRATION PERIOD IS:  1940 - 1978
                     THE VERIFICATION PERIOD IS: 1900 - 1939

         VERIFICATION WILL BE PERFORMED ON   1 SUCCESSFULLY CALIBRATED MODELS

                           CALIBRATION PERIOD RESULTS ON UNDIFFERENCED DATA

               PEARSON      ROBUST     SPEARMAN   >0 = GOOD       SIGN TEST     XPROD MEAN
              ----------  ----------  ----------  ----------  ----------------  ----------
         VAR  CORR   PCT  CORR   PCT  CORR   PCT   RE    CE   PLUS  MINUS  PCT  TSTAT  PCT
           1 0.749 0.000 0.758 0.000 0.749 0.000 0.561 0.561   31      8 0.000  3.1870.002

                          CALIBRATION PERIOD RESULTS ON 1ST-DIFFERENCED DATA

               PEARSON      ROBUST     SPEARMAN   >0 = GOOD       SIGN TEST     XPROD MEAN
              ----------  ----------  ----------  ----------  ----------------  ----------
         VAR  CORR   PCT  CORR   PCT  CORR   PCT   RE    CE   PLUS  MINUS  PCT  TSTAT  PCT
           1 0.804 0.000 0.812 0.000 0.779 0.000 0.644 0.644   32      6 0.000  3.5260.001

                           VERIFICATION PERIOD RESULTS ON UNDIFFERENCED DATA

               PEARSON      ROBUST     SPEARMAN   >0 = GOOD       SIGN TEST     XPROD MEAN
              ----------  ----------  ----------  ----------  ----------------  ----------
         VAR  CORR   PCT  CORR   PCT  CORR   PCT   RE    CE   PLUS  MINUS  PCT  TSTAT  PCT
           1 0.398 0.005 0.451 0.002 0.523 0.000 0.122 0.121   28     12 0.009  1.4210.080

                          VERIFICATION PERIOD RESULTS ON 1ST-DIFFERENCED DATA

               PEARSON      ROBUST     SPEARMAN   >0 = GOOD       SIGN TEST     XPROD MEAN
              ----------  ----------  ----------  ----------  ----------------  ----------
         VAR  CORR   PCT  CORR   PCT  CORR   PCT   RE    CE   PLUS  MINUS  PCT  TSTAT  PCT
           1 0.478 0.001 0.495 0.001 0.561 0.000 0.228 0.228   27     12 0.012  3.4820.001
		   

   ROGER'S SEASONAL SENA (4x,4f9.2)

YEAR     WIN      SPR      SUM      AUT  
1900    -1.44     0.24    -0.08     1.11
1901     0.13    -0.26    -0.63    -1.44
1902    -0.41    -0.58    -0.36     0.12
1903     1.57    -0.17    -0.12    -0.24
1904    -0.34     0.60     0.26    -0.45
1905     0.72     0.13    -0.56    -1.31
1906     0.13     0.14     0.07     0.00
1907    -0.33    -0.19     0.59     0.40
1908     0.23    -0.07     0.39     1.29
1909     0.06     0.24     0.51    -0.37
1910    -1.32    -0.11    -0.76     0.14
1911    -0.38    -0.69     1.14    -0.07
1912    -0.10     0.43    -1.01     0.59
1913     0.43    -0.36     0.27     0.06
1914     0.06     0.86    -0.65     0.38
1915    -0.25     0.57     0.00    -0.47
1916     0.61    -0.32    -0.72    -0.11
1917    -1.25     0.52     0.61     0.53
1918     1.22     0.32     0.68     0.04
1919    -0.32     0.56     1.40     1.10
1920     0.51     1.15     0.16     0.44
1921     0.75    -0.18    -0.05     1.56
1922    -0.39     1.13    -0.20    -0.33
1923     0.08     0.12     0.72     0.17
1924    -0.87     0.37    -1.17     0.44
1925     1.70    -0.64    -0.68     0.06
1926     0.22     0.03    -0.14     0.20
1927     0.05     0.55    -0.65    -0.99
1928    -0.18    -0.60     0.40     0.26
1929    -0.63     0.07     0.21    -0.55
1930    -0.20    -1.10    -1.17    -0.74
1931    -1.16    -0.41    -0.79    -0.20
1932     1.21    -0.28    -0.59    -1.57
1933    -0.29     0.31    -0.60    -0.22
1934     0.83    -0.85    -1.51    -0.17
1935    -0.38     0.02     0.25    -1.51
1936    -0.75    -1.76    -0.33    -0.14
1937     0.55     0.14    -0.76    -1.03
1938     0.14     0.60    -0.31    -0.20
1939    -0.88    -1.17    -0.17    -1.30
1940    -0.01     0.03     0.33    -0.05
1941     0.39    -0.78     0.22     0.97
1942    -0.32    -0.20     0.45    -0.22
1943     0.29     1.34     0.20    -0.43
1944     0.29     0.31    -1.34    -1.19
1945     0.27     2.08     0.65     0.42
1946     0.87    -0.19    -0.06    -0.28
1947    -1.06     1.22    -0.22     1.32
1948    -0.42     0.19    -0.28    -0.02
1949     1.36     0.53     0.24     1.32
1950    -0.10    -0.31    -0.97    -0.32
1951    -1.22    -0.82     0.12    -0.02
1952     0.06     0.12     0.28    -1.41
1953    -0.63     0.68    -0.15     0.45
1954    -0.24    -0.59    -0.67     0.51
1955    -0.67     0.23    -0.42    -1.15
1956    -0.94     0.27    -0.24     0.31
1957     1.08    -0.09     0.35     0.08
1958     0.63     0.69    -0.06     0.87
1959     0.19     0.24     0.79     1.12
1960    -0.13     0.10    -0.75    -1.27
1961    -0.53     0.55     0.47    -0.01
1962     0.11    -0.45     0.75    -0.06
1963    -1.22    -0.32    -0.51    -0.08
1964     0.40     0.20    -0.01     0.48
1965    -0.68     0.33     0.24    -0.18
1966    -0.06     0.44    -0.16    -0.58
1967     0.17    -0.12     1.00    -0.11
1968     0.06     0.30     0.72     0.01
1969    -0.87    -0.29     0.32    -0.26
1970    -0.62     0.06    -0.02    -0.05
1971     0.38    -0.89     0.16     1.77
1972     0.54    -0.66     0.25    -0.56
1973     1.29     0.67     0.57     0.04
1974     0.43    -0.69     0.14    -1.28
1975     1.01    -0.18     0.23     1.38
1976    -0.19    -0.44     0.99    -0.89
1977    -0.49     0.35    -0.97     1.09
1978     0.45    -0.57     0.54     0.11
1979    -0.71    -0.09     0.52     0.68
1980     0.29    -1.09    -0.38     0.41
1981     0.11    -0.36     0.88    -0.49
1982    -0.14     0.49     0.66     0.57
1983     1.99    -0.10     0.64     0.43
1984    -0.01    -1.23     0.80    -0.45
1985    -0.30    -0.81     0.02     1.51
1986    -0.52    -0.07    -0.22     0.60

 WINTER SENA RECONSTRUCTION FROM EUROPEAN TREE RINGS
 1701    0.028
 1702    0.514
 1703   -0.452
 1704   -0.244
 1705   -0.134
 1706   -0.083
 1707   -0.230
 1708   -0.008
 1709   -0.791
 1710    0.442
 1711    0.314
 1712    0.719
 1713   -0.087
 1714    0.153
 1715    0.830
 1716   -0.611
 1717   -0.740
 1718    0.377
 1719   -0.361
 1720   -0.567
 1721   -1.070
 1722   -0.820
 1723   -0.170
 1724   -0.110
 1725    0.314
 1726    0.059
 1727   -0.121
 1728   -0.797
 1729   -0.113
 1730    0.076
 1731   -0.347
 1732    0.045
 1733   -0.181
 1734   -0.254
 1735    0.231
 1736    0.285
 1737    0.096
 1738    0.384
 1739    0.261
 1740    0.247
 1741    0.353
 1742    0.511
 1743    0.275
 1744    0.182
 1745   -0.172
 1746    0.160
 1747   -0.027
 1748    0.392
 1749    0.299
 1750    0.815
 1751   -0.540
 1752    0.353
 1753    0.674
 1754    0.598
 1755    0.190
 1756    0.190
 1757   -0.142
 1758   -0.693
 1759   -0.147
 1760   -0.175
 1761    0.088
 1762    0.108
 1763   -1.027
 1764   -0.846
 1765    0.062
 1766    0.261
 1767   -0.105
 1768   -0.331
 1769   -0.526
 1770   -0.116
 1771    0.003
 1772    0.158
 1773    0.020
 1774    0.356
 1775    0.403
 1776   -0.237
 1777    0.057
 1778   -0.120
 1779    0.640
 1780   -0.064
 1781    0.106
 1782   -0.353
 1783   -0.161
 1784   -0.171
 1785    0.518
 1786   -0.473
 1787    0.101
 1788   -0.067
 1789   -0.174
 1790   -0.395
 1791    0.328
 1792   -0.547
 1793   -0.130
 1794   -0.030
 1795   -0.615
 1796    0.198
 1797    0.115
 1798    0.134
 1799   -0.082
 1800   -0.475
 1801   -0.081
 1802    0.633
 1803   -0.050
 1804    0.301
 1805    0.018
 1806   -0.536
 1807    0.490
 1808    0.256
 1809    0.411
 1810   -0.158
 1811   -0.229
 1812   -0.558
 1813   -0.623
 1814   -0.285
 1815    0.016
 1816    0.029
 1817   -0.042
 1818   -0.039
 1819    0.297
 1820   -0.119
 1821   -0.168
 1822   -0.219
 1823    0.439
 1824   -0.180
 1825   -0.143
 1826    0.958
 1827    0.534
 1828   -0.228
 1829   -0.544
 1830    0.033
 1831    0.110
 1832    0.048
 1833   -0.536
 1834    0.156
 1835   -0.025
 1836    0.032
 1837   -1.220
 1838    0.208
 1839   -0.668
 1840    0.316
 1841   -0.316
 1842   -0.835
 1843   -0.102
 1844    0.074
 1845    0.004
 1846    0.025
 1847   -0.138
 1848    0.054
 1849    0.202
 1850   -0.180
 1851    0.098
 1852    0.018
 1853   -0.384
 1854    0.512
 1855   -0.439
 1856    0.026
 1857    0.084
 1858    0.228
 1859    0.176
 1860   -0.323
 1861    0.050
 1862   -0.528
 1863    0.261
 1864    0.493
 1865    0.176
 1866   -0.304
 1867   -0.234
 1868    0.317
 1869    0.098
 1870    0.112
 1871   -0.402
 1872    0.036
 1873    0.191
 1874    0.282
 1875    0.134
 1876    0.100
 1877   -0.388
 1878    0.093
 1879   -0.740
 1880   -0.159
 1881    0.250
 1882    0.359
 1883   -0.218
 1884    0.062
 1885    0.449
 1886    0.453
 1887    0.113
 1888   -0.619
 1889    0.083
 1890    0.333
 1891   -0.126
 1892   -1.482
 1893   -0.655
 1894    0.202
 1895   -0.006
 1896    0.476
 1897   -0.179
 1898    0.223
 1899   -0.012
 1900   -0.584
 1901   -0.080
 1902   -0.810
 1903   -0.516
 1904   -0.258
 1905    0.091
 1906    0.264
 1907    0.037
 1908   -0.345
 1909    0.118
 1910   -0.622
 1911    0.024
 1912   -0.133
 1913   -0.152
 1914    0.121
 1915   -0.025
 1916    0.076
 1917   -0.335
 1918    0.165
 1919   -0.058
 1920    0.943
 1921    0.741
 1922   -0.414
 1923    0.432
 1924   -0.018
 1925    0.154
 1926   -0.373
 1927   -0.225
 1928   -0.415
 1929   -0.522
 1930    1.014
 1931   -0.086
 1932   -0.027
 1933    0.596
 1934    0.472
 1935    0.012
 1936   -0.403
 1937    0.266
 1938    0.609
 1939   -0.871
 1940   -0.741
 1941    0.219
 1942   -0.530
 1943    0.467
 1944    0.383
 1945    0.188
 1946    0.358
 1947   -1.096
 1948   -0.445
 1949    1.190
 1950   -0.152
 1951   -1.026
 1952    0.263
 1953   -0.010
 1954    0.011
 1955   -0.624
 1956   -0.096
 1957    0.795
 1958   -0.387
 1959    0.347
 1960    0.093
 1961   -0.396
 1962    0.015
 1963   -0.756
 1964    0.705
 1965   -0.701
 1966    0.138
 1967    0.327
 1968   -0.037
 1969   -0.001
 1970    0.230
 1971    0.313
 1972    0.031
 1973    0.501
 1974    0.402
 1975    0.012
 1976    0.134
 1977   -0.454
 1978    0.200


