Successful statistical analyses were carried out for the trend and cycles in average global temperature using the data of the National Oceanic and Atmospheric Administration (NOAA), the Hadley Climate Research Unit of the University of East Anglia, and the Goddard Institute for Space Science of NASA. 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 and GISS data. and the 168 years of the Hadley CRU data.

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 Data

The first step in a trend and cycle analysis is to fit a bent-line regression equation to the data. The procedure for how this done is given in Bent Line Regression. For example, the resulting regression line along with the GISS data are shown below.

The data are in the form of the temperature anomalies; i.e., the deviations of annual temperatures from a long term average. Goddard reports its temperatures in hundredths of a degree Celsius whereas the other two just use degrees Celsius.

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 for the GISS data.

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 GISS data 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 for the upswings and downswings is 32 years. The average global temperatures can be forecast (and backcast in the cases of the NOAA and GISS data) by continuing the cycle and the trend. The results of these forecasts are shown below:

Conclusion

The NOAA, Hadley CRU, GISS 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 two years followed by downswings of roughly thirty two 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.

(To be continued.)