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.

This study addresses the causal links between external factors and the main hydro-climatic variables. There is a gap in the literature on the description of a complete chain in addressing the structures of direct causal links of solar activity on the terrestrial variables. This is why, the present study uses the extensive facilities of the application of information theory in view of recent advances in different fields. Also, by other methods (e.g. neural networks) first are tested the existence non-linear links of solar-terrestrial influences on hydro-climate system. The results are promising related to the solar impact on terrestrial phenomena which is discriminant in space-time domain. The implications prove robust for determining the causal measure of climate variables under direct solar impact which makes it easier to consider solar activity in climate models, by appropriate parametrizations. This study found that hydro-climatic variables are sensitive to solar impact only for certain frequencies (periods) and these have a coherence with the Solar-Flux only for some lags of the Solar-Flux (in advance).