Using approximation by piecewise linear functions in empirical analysis of changes and variability of climate data series

Abstract

A method for the analysis of climate data series is proposed, which
allows 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.,
allows to obtain the least squares estimate. Using the program implementing this

algorithm, the proposed 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 of which it
is possible to decide on the feasibility of further, more in-depth investigation of the
climate data series with statistical means.