It is rather well recognized that the global dynamics of the Sun-Earth relationship involves complex nonlinear phenomena. Here we present a preliminary attempt to characterize the influence and the timing of the solar magnetic activity on the near-Earth environment, based on quite novel tools based on concepts from information theory. In detail, we show two preliminary examples. In the first one, we investigate the time behaviour of the delayed mutual information applied to the solar wind forcing on ionospheric irregularities in a stormy period of November 2004; in the other example, we study the evolution of a possible measure of relative complexity for the diurnal variability of the vertical total electron content during the "Halloween Storm" of year 2003. The future use of data from the Galileo system will give a definitive improvement to the application of such techniques to Space Weather.