Filaments and the magnetic configuration. I. Observation of the solar case

International audienceContext. The emission of Ca and Hα is correlated for the Sun, but this does not seem to be true for other stars. We previously demonstrated that this lack of correlation could be due to the presence of filaments. Aims. We aim to establish a link between the activity level, the magnetic configuration, and the number of filaments, and therefore with observables of other stars that the Sun. Methods. We studied the relationship between the filaments and the magnetic configuration using a large scale approach on MDI/SOHO magnetograms and a large sample of filaments. We validated the reconstruction of synthetic time series of filament surface coverage representative of the magnetic configuration, and then apply it to observations over a full solar cycle. Results. We derived quantitative criteria that relates the presence of filaments to the properties at polarity inversion lines, hereafter PIL, magnetic field gradient, and unipolar areas on the solar surface (size and distance to these areas). We also observed that the number of PIL pixels is anti-correlated with the activity level, and the increase in filament surface coverage is due to the modification of the PIL pixel properties. We reconstructed synthetic time series of filaments that are in good agreement with observations. Conclusions. This work validates our method, which will later be applied to solar and stellar simulations