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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 data. The NOAA data 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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