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.

Cycle Trend Analysis of the GISS Data

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.

Conclusion

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.)

Data Appendix

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