Dynamics of European temperatures from 1500 to 2004 and analysis of their anomalies in the modern period

The object of the study is the change in seasonal and annual temperatures in the European territory from 1500 to 2004, obtained from open sources using proxy data (1500–1900) and instrumental data (1900–2004), as well as climate changes in the Northern Hemisphere and in the south of European Russia from 1961 to 2024 according to instrumental measurements. For the models of annual and seasonal European temperatures built by the sinusoidal regression method, periodicities were determined that simulate the process at a statistically significant level. Regression analysis showed that all trends are positive and, despite small R2 values, significant at the 5 % level. In a series of European annual temperatures, cold extremes occurred before the 20th century, and all warm extremes in the 20th and early 21st centuries. As a result of spectral analysis, it was found that for the European average annual temperature series from 1500 to 2004, the main periods were identified: 30-year and 3–4-year quasi-periodicity. Using the wavelet transform, the periodicities of the series were determined on different time scales, which demonstrated the fact that statistically significant periodicity scales in the time series of 1500-2004 are not only present but they evolve. The linear trend of annual temperatures in the Northern Hemisphere and the south of the European Russia in the modern period (1961-2024) demonstrates a steady increase at a rate of 0.24 °C/10 years and 0.28 °C/10 years. In the modern period, both for the Northern Hemisphere and for the south of the European Russia, intra-decadal periodicities of annual temperatures (2–3–4 years) are decisive. From the sinusoidal regression model, it follows that the 3-year periodicity that forms the series is defined as the main one already when using the first three harmonics in the model. In the formation of the temperature regime, 9–10-year periods are added, determined, probably, by the known cyclicity of solar activity.