Statistical time series decomposition into significant components and application to European temperature

Summary

Time series of observed monthly mean temperatures of European stations and at grid points are decomposed into different kinds of trends (linear, progressive, degressive), constant or significantly changing annual cycles, episodic and harmonic components, extreme events and noise. A stepwise regression is used to test whether the components are significant. Special emphasis is given to extreme events which we distinguish from extreme values. While extreme values may likely occur by chance, it is very unlikely that extreme events would be in accordance with the features of the time series. On one hand, extreme events alter the estimates (and test results) of trends and other components. On the other hand, such components have to be known to recognize extreme events. To deal with this problem, an iterative procedure is introduced that converges fast to robust estimates of all the components.

Applying this procedure to the last 100 years of European temperatures reveals that the phase of the annual cycle is shifted backward within the year in western Europe but foreward in eastern Europe. In the latter region, the amplitude of the annual cycle has also increased significantly. Most of the trend components found in the time series are positive and linear. Nearly all detected extreme events are cold events which occurred in winter. Their number has significantly grown. Significant harmonic components with a period of 92.3 months (about 7.7 years) are found mainly in northern and western Europe.