Wavelets in the analysis of local time series of the Earth's surface air

The practical application of local smoothing and wavelet analysis methods for studying the spectral composition and coherent relationships of local average annual surface air temperatures with solar activity and the displacement of the Earth's North Pole is presented. A preliminary analysis of local time series of surface temperatures revealed the presence of emissions and their localization. It is shown that to eliminate the influence of outliers (short-term events) on the reliability of identifying a long-term nonlinear trend, the wavelet decomposition method, which filters high frequencies, is most suitable. Functional approximation models are constructed and compared at different levels of wavelet decomposition of the data. Time or scale smoothing is used to improve the reliability of the wavelet spectrum. Based on data on average annual surface air temperatures in Yalta (44.48⁰, 34.17⁰, = 72.0 m) for the time interval from 1869 to 2022, functional models of long-term trends were built and used to obtain short-term forecasts. Information about the linear relationship of events in the compared time series is obtained and discussed in the analysis of wavelet cross-correlation, wavelet coherence and phase coherence. Local similarities were discovered between data on surface air temperature and solar activity data (Wolf numbers) for a period of ∼(30-70) years, as well as oscillations with period of 11 years, manifested in the constancy of the phase difference and an increase in the modulus of wavelet coherence power over time. Localized similarities were also found in data on surface air temperature in Yalta and in data on displacements of the Earth's mean pole relative to the conventional beginning of EOP (IERS) CO1 in the interval of periods ∼ (30-70) years.