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The purpose of this study was to analyze the influence of solar activity described by the sunspot number (SSN) on certain terrestrial variables that might impact the Southeastern European climate at different spatio-temporal scales (the North Atlantic Oscillation Index, NAOI, and the Greenland–Balkan Oscillation Index, GBOI—on a large scale; the Palmer Hydrological Drought Index, PHDI—on a regional scale; the Danube discharge at the Orsova (lower basin), Q, representative of the Southeastern European climate—on a local scale). The investigations were carried out for the 20th century using the annual and seasonal averages. To find the connections between terrestrial (atmospheric and hydrological) parameters and SSN, the wavelet coherence were used both globally and in the time–frequency domain. The analyses were carried out for the time series and considered simultaneously (in the same year or season), as well as with lags from 1 to 5 years between the analyzed variables. For the annual values, the type of correlation (linear/non-linear) was also tested using elements from information theory. The results clearly revealed non-linear links between the SSN and the terrestrial variables, even for the annual average values. By applying the wavelet transform to test the solar influence on the terrestrial variables, it was shown that the connections depend on both the terrestrial variable, as well as on the considered lags. Since, in the present study, they were analyzed using wavelet coherence, but only the cases in which the coherence was significant for almost the entire analyzed time interval (1901–2000) and the terrestrial variables were in phase or antiphase with the SSN were considered. Relatively few results had a high level of significance. The analysis of seasonal averages revealed significant information, in addition to the analysis of annual averages. Thus, for the climatic indices, the GBOI and NAOI, a significant coherence (>95%) with the solar activity, associated with the 22-year (Hale) solar cycle, was found for the autumn season for lag = 0 and 1 year. The Hale solar cycle, in the case of the PHDI, was present in the annual and summer season averages, more clearly at lag = 0. For the Danube discharge at Orsova, the most significant SSN signature (~95%) was observed at periods of 33 years (Brüuckner cycle) in the autumn season for lags from 0 to 3 years. An analysis of the redundancy–synergy index was also carried out on the combination of the terrestrial variables with the solar variable in order to find the best synergistic combination for estimating the Danube discharge in the lower basin. The results differed depending on the timescale and the solar activity. For the average annual values, the most significant synergistic index was obtained for the combination of the GBOI, PHDI, and SSN, considered 3 years before Q. [ABSTRACT FROM AUTHOR]

This paper presents the extent to which the combination of extra-atmospheric and hydroclimatic factors can be deciphered to record their contribution to the evolution and forecasting of the Danube discharge (Q) in the lower basin. A combination of methods such as wavelet filtering and deep learning (DL) constitutes the basic method for discriminating the external factors (solar activity through Wolf numbers) that significantly contribute to the evolution and prediction of the lower Danube discharge. An ensemble of some of the most important factors, namely, those representing the atmospheric components, i.e., the Greenland-Balkan Oscillation Index (GBOI) and the North Atlantic Oscillation Index (NAOI); the hydroclimatic indicator, the Palmer Hydrological Drought Index (PHDI); and the extra-atmospheric factor, constitutes the set of predictors by means of which the predictand, Q, in the summer season, is estimated. The external factor has to be discriminated in the Schwabe and Hale spectra to make its convolutional contribution to the Q estimation in the lower Danube basin. An interesting finding is that adding two solar predictors (associated with the Schwabe and Hale cycles) to the terrestrial ones give a better estimation of the Danube discharge in summer, compared to using only terrestrial predictors. Based on the Nash–Sutcliffe (NS) index, a measure of performance given by the extreme learning machine (ELM), it is shown that, in association with certain terrestrial predictors, the contribution of the Hale cycle is more significant than the contribution of the Schwabe cycle to the estimation of the Danube discharge in the lower basin. [ABSTRACT FROM AUTHOR]

The aim of this research was to determine relationships between solar activity and variability of discharges of three Central European rivers: the Vistula, Odra and Warta in Poland in the multi-annual period of 1901–2020. Changes in precipitation and air temperature at Poznań meteorological station in the same period were also analyzed. The long-term variations in river runoff were investigated both from the point of view of temporal variability in relation to climate variations in the study area, and from the point of view of linear/non-linear links to solar activity, as described by the Wolf sunspot number. The wavelet transform analysis was used to highlight the frequency-time distribution of the coherences between solar and discharge variability. It was found that most of the links between solar activity and discharges were non-linear. [ABSTRACT FROM AUTHOR]

The aims of this study are to investigate the influence of large-scale atmospheric circulation quantified by indices such as the North Atlantic Oscillation index (NAOI), the Greenland-Balkan Oscillation index (GBOI) and blocking-type indices on the Lower Danube discharge. We separately analysed each season for the 1948–2000 period. In addition to the statistical linear procedure, we applied methods to quantify nonlinear connections between variables, as mutual information between predictors and predictand, using Shannon's information entropy theory. The nonlinear correlation information between climate indices and discharge is higher than that obtained from the linear measure, providing more insight into real connections. Also, the non-stationarity of the link between variables is highlighted by spectral coherence based on wavelet analysis. For the physical interpretation, we analyse composite maps over the Atlantic-European region. The most significant influence on the discharge of the Lower Danube Basin is given by the GBOI and blocking-type atmospheric circulation over Europe. [ABSTRACT FROM AUTHOR]

Of the internal factors, we tested the predictors from the fields of precipitation, temperature, pressure and geopotential at 500hPa. From the external factors, we considered the indices of solar/geomagnetic activity. Our analysis was achieved separately for each season, for two time periods 1901-2000 and 1948-2000. We applied developments in empirical orthogonal functions (EOFs), cross correlations, power spectra, filters, composite maps. In analysis of the correlative results, we took into account, the serial correlation of time series. For the atmospheric variables simultaneously, the most significant results (confidence levels of 95%) are related to the predictors, considering the difference between standardized temperatures and precipitation (TPP), except for winter season, when the best predictors are the first principal component (PC1) of the precipitation field and the Greenland-Balkan-Oscillation index (GBOI). The GBOI is better predictor for precipitation, in comparison with North Atlantic Oscillation index (NAOI) for the middle and lower Danube basin. The significant results, with the confidence level more than 95%, were obtained for the PC1-precipitation and TPP during winter/spring, which can be considered good predictors for spring/summer discharge in the Danube lower basin. Simultaneous, the significant signal of geomagnetic index (aa), was obtained for the smoothed data by band pass filter. For the different lags, the atmospheric variables respond to solar/geomagnetic activity after about 2-3 years. The external signals in the terrestrial variables are revealed also by power spectra and composite maps. The power spectra for the terrestrial variables show significant peaks that can be associated with the interannual variability, Quasi-Biennial Oscillation influence and solar/geomagnetic signals. The filtering procedures led to improvement of the correlative analyses between solar or geomagnetic activity and terrestrial variables, under the condition of a rigorous test of the statistical significance. [ABSTRACT FROM AUTHOR]