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the Average Annual Global Temperature Data from NASA's Goddard Institute for Space Science for 1880 through 2009 |
Two very successful statistical analyses were carried out using the National Oceanic and Atmospheric Administration (NOAA) data and the Hadley Climate Research Unit data on average annual global temperature. Those analyses revealed that there has been a cycle in global temperature of about thirty year upswings followed by about thirty year downswings. This cycle is on top of a long term trend of about 0.5°C per century. This pattern has persisted for the 128 years of the NOAA data. and the 168 years of the Hadley CRU data.
The data set prepared by the Goddard Institute of Space Science (GISS) is another commonly accepted source of information on global temperature. Although NOAA, Hadley CRU and GISS are purportedly measuring the same thing their values for global temperature are not exactly the same; they are however highly correlated, as evidence by the graphs of the data shown below.
Although each pair is highly correlated the correlation between the NOAA data and the Hadley CRU data is notably stronger.
The first step is to fit a bent-line regression equation to the data. The procedure for how this done is given in Bent Line Regression. The resulting regression line along with the data are shown below.
The coefficient of determination (R²) for this regression is 0.8810.
The second step is to test for whether or not the slopes of the upswings significantly different and likewise for the slopes of the downswings. The ratios of the differences in slope to their standard deviations are 0.14 amd 0.94, respectively. Thus the slopes of corresponding episodes are not significantly different from zero at the 95 percent level of confidence.
The third step is to estimate a bent regression line in which the slopes of upswings are all equal and the slopes of the downswings are equal. The following graph shows this regression.
The coefficient of determination (R²) for this regression is 0.8789, nearly as high as the value for the unconstrained regression of 0.8810. The magnitude of the t-ratio for the trend variable is 2.2. For the cycle variable the t-ratio is 11.8, indicating that there is almost zero probability that the cycle pattern could have arisen purely due to chance. For the GISS data the cycle pattern goes back 129 years. The data from the Hadley Climate Research Units indicates that the cycle goes back at least about 160 years.
The magnitude of the long term trend can be computed from the difference of two points on the regression line which are at the same stage in the cycle. For the cycle minima at 1918 and 1975 the difference is 0.28271°C over a 57 year period. This is 0.00496°C per year or 0.496°C per century. This is essentially the same value as found using the NOAA data and the Hadley CRU data.
A long term trend of 0.00496°C per year means that the purely cyclic slope on an upswing is 0.01401°C per year and −0.00635°C per year on a downswing.
The average period of the full upswings was 25 years and for the full downswings 38 years. These figures are sensitive to the turning points established in maximizing the coefficient of determination for the regression. The gain in the coefficient of determination from the adjustment of the turning points was not large and could be foregone without too much loss in the statistical performance of the regression equation. Without the adjustments of the turning points the data indicates thirty year periods for both upswings and downswings in global temperature.
The Goddard Institute of Space Science (GISS) data indicates that the discernible cycle in average annual global temperature goes back 129 years from the present. The cycle involves upswings of roughly thirty years followed by downswings of roughly thirty years. In addition to the cycle there is a long term trend of about 0.5°C per century. This is probably due to human actions, which include changes in land use and the increase in water vapor in the atmosphere in arid areas from irrigation and landscape watering as well as anthropogenic carbon dioxide. The results support the results of the analysis of the global temperature data from NOAA.
(To be continued.)
Year AGT Anomaly (0.01°C) 1880 -25 1881 -20 1882 -22 1883 -24 1884 -30 1885 -30 1886 -25 1887 -35 1888 -27 1889 -15 1890 -37 1891 -27 1892 -32 1893 -31 1894 -33 1895 -27 1896 -16 1897 -12 1898 -24 1899 -17 1900 -9 1901 -15 1902 -27 1903 -31 1904 -34 1905 -24 1906 -20 1907 -38 1908 -34 1909 -35 1910 -33 1911 -33 1912 -34 1913 -32 1914 -15 1915 -9 1916 -31 1917 -40 1918 -32 1919 -20 1920 -19 1921 -13 1922 -24 1923 -20 1924 -21 1925 -16 1926 -1 1927 -13 1928 -11 1929 -25 1930 -7 1931 -1 1932 -6 1933 -18 1934 -7 1935 -11 1936 -3 1937 8 1938 11 1939 3 1940 5 1941 10 1942 3 1943 10 1944 20 1945 7 1946 -4 1947 0 1948 -4 1949 -7 1950 -15 1951 -4 1952 3 1953 11 1954 -10 1955 -10 1956 -17 1957 7 1958 8 1959 6 1960 -1 1961 8 1962 4 1963 8 1964 -21 1965 -11 1966 -3 1967 0 1968 -4 1969 8 1970 3 1971 -10 1972 0 1973 14 1974 -8 1975 -4 1976 -16 1977 13 1978 1 1979 9 1980 18 1981 26 1982 5 1983 26 1984 9 1985 5 1986 13 1987 26 1988 31 1989 20 1990 38 1991 35 1992 13 1993 14 1994 23 1995 38 1996 29 1997 40 1998 56 1999 32 2000 33 2001 48 2002 56 2003 55 2004 49 2005 63 2006 54 2007 57 2008 43 2009 57
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