Using Approximation by Piecewise Linear Functions in the Empirical Analysis of Changes and Variability of Climate Data Series

A method for analyzing climate data series is proposed that makes it possible to identify fast and slow components of variability. The method uses approximation of time series by piecewise linear functions. An algorithm is substantiated that provides the best approximation in the mean square sense; i.e., it allows to obtain the least squares estimate. Using the program implementing this algorithm, the method is applied to the analysis of time series of annual mean air temperature in the surface layer. The analysis is carried out for the series of globally averaged temperature and average for the Northern and Southern hemispheres (HadCRUT5 Analysis version 5.0.2.0). The usefulness of the proposed tool of empirical analysis is demonstrated; based on the results, it is possible to decide the expediency of a more in-depth investigation into the climate data series with statistical means.