Sub-structures were found in the narrow line profiles of most objects suggesting that the line emitting region is a collection of individual clouds in motion relative to each other and producing different parts of the line profiles (see for instance Veilleux 1991, Espey et al. 1994 or Ferguson et al. 1997).
These findings induced us to assume that each of these clouds is characterized by a single density and that lines coming from the same emission-region should have the same profile and mean velocity. We therefore tried to model the spectra of KUG 1031+398 with the smallest possible number of line sets, each set including three Gaussians (modelling H and the N II6548, 6583 lines, or H and the O III4959, 5007 lines) having the same velocity shift and width, with the additional constraint that the intensity ratio of the two N II (respectively O III) lines was taken to be equal to the theoretical value of 3.00 (respectively 2.96) (Osterbrock 1974). In a physically meaningful and self-consistent model, the components found when fitting the blue and red spectra should have velocity shifts and widths compatible within the measurement errors.