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