A Cycle and Trend Analysis of the Average Annual Global Temperature Data from the Hadley Climate Research Unit of the University of East Anglia for 1850 through 2008

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A Cycle and Trend Analysis of the
Average Annual Global Temperature Data
from the Hadley Climate Research Unit
of the University of East Anglia
for 1850 through 2008

A very successful statistical analysis was carried out using the National Oceanic and Atmospheric Administration (NOAA) data on average annual global temperature which 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. The NOAA only goes back to 1880, but there is evidence that the pattern goes back at least another thirty years.
The Hadley Climate Research Unit (Hadley CRU) at the University of East Anglia in the U.K. provides average global temperature data back to 1850. (This data is appended to this webpage.) In 2009 there was revealed very serious breaches of intellectual integrity on the part of top level people at Hadley CRU which cast doubt on the products of that organization. Those breaches of intellectual integrity however generally involved endeavors other than the compilation of measured temperature data. The average annual global temperature figures for the period 1880 to the present from NOAA and Hadley CRU do not differ in significant ways. Therefore it is worthwhile to use the Hadley CRU to incorporate the information for the period from 1850 to 1880 into the analysis of trend and cycle in average global temperature. It is only in the period of time after 2000 when global temperature changes seemed to flatten and become negative that the temperature figures generated by organizations such as Hadley CRU and Goddard Institute for Space Research, which are controlled by CO2 global warming alarmist-activists, became suspect.
The temperature data are given as temperature anomalies, meaning the deviations from a long term average temperature. The first step in the analysis is to discern approximate turning points in the data.

Source: Hadley CRU
These turning points, from visual inspection of the above graph, turn out to be simply 1880, 1910, 1940, 1970 and 2000. The selection of 1970 was not from visual inspection; it came as a result of the spacing of all the other turning points thirty years apart. The second step was to create a variable for each turning point which was zero before the turning point and afterwards the number of years past the turning point. The trend variable was the number of years since 1850. These variables allowed the fitting of a bent line regression to the data.
The coefficient of determination (R²) for the regression is 0.8511, which means that 85.1 percent of the variation in the global temperature is explained by a sequence of linear upswings and downswings. It alsomeans 14.9 percent of the variation was not explained by a sequence of linear upswings and downswings. The standard error of the estimate for the regression is 0.100 °C. A plot of the regression estimate along with the data is shown below.

The slopes of the regression line for the upswings from 1910 to 1940 and from 1970 to 2000 are remarkably close. Their numerical values are 0.0.01648°C per year and 0.01698°C per year, respectively. The slopes of the two downswings, from 1879 to 1910 and from 1940 to 1970, were not as close as the slopes of the two upswings but also not dramatically different, being decreases of 0.00265°C per year and 0.00389°C per year, respectively. Both sets of figures for slopes include the long term trend slope along with the slopes of the episodes of upswings or downswings. At this point the two cannot be separated.
The coefficients for the bent line regression give a measure of the significance of the changes in slope. The measure is the t-ratio for the coefficients, the ratio of the value of the coefficient to its standard deviation. To be statistically significant at the 95 percent level of confidence the t-ratio must be of magnitude of about 2.0 or higher. For the change in slope at 1879 the t-ratio was -2.27. At 1910 it was 8.54, at 1940 -7.35 and at 1970 8.74. These are all statistically significant. At 2000 the t-ratio for the change in slope was only -1.47.
The turning points years were then varied to maximize the coefficient of determination for the regression. Those adjusted turning points were 1879, 1910, 1939, 1971, 2005. The coefficient of determination for the bent line regression with these adjusted turning points is 0.8538, a marginal improvement over the R² of 0.8511 for the regression with the original turning points.
The similarity of the slopes for the upswings and for the downswings suggest a cycle. A regression was carried out in which the slopes of all the upswings were required to be equal and likewise for the slopes of all the downswings. The R² for the the cycle regression is 0.7342. When the turning points were adjusted to maximize the coefficient of determination for the regression the R² rose to 0.8314.. These turning points were 1865, 1916, 1939, 1969 and 2005. The maximized coefficient of determination of 0.8314 is nearly the same as for the unconstrained regression, 0.8538. The standard error for the regression was about 0.106°C, again nearly the same as the figure of 0.100°C found for the unconstrained regression.
The magnitudes of the t-ratios for the trend and cycle variables in this regression were 18.6 and 13.9, both highly significantly.
The regression estimates and the data are displayed below.

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 1916 and 1969 the difference is 0.2725°C over a 53 year period; 0.00514°C per year or 0.514°C per century. This is essentially the same value as found using the NOAA data.
A long term trend of 0.00514°C per year means that the purely cyclic slope on an upswing is 0.01106°C per year and −0.00848°C per year on a downswing.
The average period of the full upswings was 30 years and for the full downswings 40 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.
Conclusion

The Hadley CRU data indicates that the discernible cycle in average annual global temperature goes back 160 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.)
Data Appendix

Year AGT Anomaly (°C) 1850 -0.447 1851 -0.292 1852 -0.294 1853 -0.337 1854 -0.307 1855 -0.321 1856 -0.406 1857 -0.503 1858 -0.513 1859 -0.349 1860 -0.372 1861 -0.412 1862 -0.540 1863 -0.315 1864 -0.516 1865 -0.297 1866 -0.303 1867 -0.334 1868 -0.291 1869 -0.313 1870 -0.302 1871 -0.344 1872 -0.255 1873 -0.331 1874 -0.397 1875 -0.418 1876 -0.403 1877 -0.091 1878 0.023 1879 -0.265 1880 -0.260 1881 -0.242 1882 -0.246 1883 -0.298 1884 -0.381 1885 -0.362 1886 -0.275 1887 -0.387 1888 -0.337 1889 -0.192 1890 -0.431 1891 -0.378 1892 -0.484 1893 -0.505 1894 -0.444 1895 -0.420 1896 -0.211 1897 -0.243 1898 -0.432 1899 -0.314 1900 -0.223 1901 -0.302 1902 -0.431 1903 -0.509 1904 -0.554 1905 -0.412 1906 -0.329 1907 -0.507 1908 -0.559 1909 -0.564 1910 -0.548 1911 -0.581 1912 -0.491 1913 -0.489 1914 -0.305 1915 -0.213 1916 -0.434 1917 -0.506 1918 -0.388 1919 -0.331 1920 -0.314 1921 -0.261 1922 -0.381 1923 -0.347 1924 -0.360 1925 -0.274 1926 -0.162 1927 -0.254 1928 -0.255 1929 -0.376 1930 -0.165 1931 -0.124 1932 -0.155 1933 -0.297 1934 -0.159 1935 -0.184 1936 -0.152 1937 -0.034 1938 0.009 1939 -0.001 1940 0.018 1941 0.077 1942 -0.031 1943 -0.028 1944 0.120 1945 -0.007 1946 -0.205 1947 -0.197 1948 -0.204 1949 -0.211 1950 -0.309 1951 -0.169 1952 -0.074 1953 -0.027 1954 -0.251 1955 -0.281 1956 -0.349 1957 -0.073 1958 -0.010 1959 -0.072 1960 -0.123 1961 -0.023 1962 -0.021 1963 0.002 1964 -0.295 1965 -0.216 1966 -0.147 1967 -0.149 1968 -0.159 1969 -0.010 1970 -0.067 1971 -0.190 1972 -0.056 1973 0.077 1974 -0.213 1975 -0.170 1976 -0.254 1977 0.019 1978 -0.063 1979 0.049 1980 0.077 1981 0.120 1982 0.011 1983 0.177 1984 -0.021 1985 -0.038 1986 0.029 1987 0.179 1988 0.18 1989 0.103 1990 0.254 1991 0.212 1992 0.061 1993 0.105 1994 0.171 1995 0.275 1996 0.137 1997 0.351 1998 0.546 1999 0.296 2000 0.270 2001 0.409 2002 0.464 2003 0.473 2004 0.447 2005 0.482 2006 0.422 2007 0.405 2008 0.327

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