Influence of metrics on determination of bifurcation points in time series of meteorological values

Abstract

The influence of a metric kind and a method of setting the "dividing" polynomial on the results of finding bifurcation points in time series of meteorological values has been studied. The bifurcation point reflects the moment of change of the established system mode, caused by a significant change in the factors that generate the process under study. This article searches for a moment when the direction of the process changes in the time series of measurement data as the boundary between local trends. Zero to third degree polynomials have served as an indicator for determining the position of the bifurcation point. As the metrics allowing to determine the optimal position of these polynomials within the time series under investigation the following ones have been considered: standard deviation, Euclidean metric, Manhattan and relative distance. The statistical significance of the split is checked using the Fischer test. The proposed algorithm has been tested on time series of instantaneous and averaged air temperature and atmospheric pressure. The degree of the initial variation unexplained by the model is used as an estimate of the approximation accuracy. The use of Manhattan distance as a metric has been found to be the best for the time series considered. The approach proposed in this paper can be applied in the future, in particular, when determining the start time of climate change in different regions of our planet