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An Algorithm for Adaptive Assessment in Time Series Seasonal Oscillations and Its Testing Based on the Example of Variations in the CO2 Concentration in the Atmosphere

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Abstract

An adaptive model is proposed to describe time-varying seasonal effects. The seasonal average function is constructed using an iterative algorithm that provides a neat decomposition of the signal into a generalized trend, seasonal and residual components. By a trend, we mean long-term evolutionary changes in the average signal level, both unidirectional and chaotic, in the form of a slow random drift. This algorithm allows one to obtain unbiased estimates for each of the signal components, even in the presence of a significant number of missing observations. The series length is not required to be a multiple of an integer number of years. In contrast to the usual “Climate Normals” (CN) model, the considered adaptive model of seasonal effects assumes a continuous slow change in the properties of the seasonal component over time. The degree of allowable variability in seasonal effects from year to year is entered as a tunable parameter of the model. In particular, this allows one to show the dynamics of the growth of the amplitude of seasonal fluctuations in time in the form of a continuous (smooth) function without necessarily linking these changes to predetermined calendar epochs. The algorithm was tested on the atmospheric CO2 concentration monitoring series at Barrow, Mauna Loa, Tutuila, and South Pole stations located at different latitudes. The form of the seasonal variation was estimated, and the average amplitude of the seasonal variation and the rate of its change at each station were calculated. Noticeable differences in the dynamics of the studied parameters between stations are demonstrated. Mean amplitude of seasonal variation in CO2 concentration at Barrow, Mauna Loa, Tutuila, and South Pole stations in the epoch 2010–2019 was estimated as 18.15, 7.08, 1.30, and 1.26 ppm, respectively, and the average rate of increase in the amplitude of the seasonal variation in the increase in CO2 concentration in the interval 1976–2019 is 0.085, 0.0100, 0.0165, and 0.0031 ppm/year. In relative terms, the increase is 0.57 ± 0.03, 0.11 ± 0.02, 2.24 ± 0.24, and 0.27 ± 0.04% per year.

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ACKNOWLEDGMENTS

The possibilities of using the algorithm described in this paper are illustrated by the example of long-term observations of changes in the concentration of carbon dioxide in the atmosphere, which were prepared and posted on the Internet by K.W. Thoning, A.M. Crotwell and J.W. Mund (see (Thoning et al., 2020). We are grateful to them and to all their colleagues who took part in obtaining and posting this data on the Internet, and express our interest in cooperation.

Funding

This work was carried out according to project no. 0144-2019-0011 of the State Order of the Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences.

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    A. V. Deshcherevskii & A. Ya. Sidorin

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Deshcherevskii, A.V., Sidorin, A.Y. An Algorithm for Adaptive Assessment in Time Series Seasonal Oscillations and Its Testing Based on the Example of Variations in the CO2 Concentration in the Atmosphere. Izv. Atmos. Ocean. Phys. 58, 681–707 (2022). https://doi.org/10.1134/S0001433822070027

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