Heavy rain events constitute a major operational problem in the Mediterranean area. The present work tries to contribute to a better understanding of this problem by considering the possible indirect influence of surface depressions in the triggering and location of the heavy rain. The idea is that any surface low contributes to the organisation of the low-level flow. This then affects the creation/intensification of a low-level feeding current of warm and wet air that can sustain heavy rain if there is convective instability. Two approaches have been used: (a) a numerical and synoptic approach, Part 1, and (b) a statistical approach, Part 2. In Part 1, the differences between a control run and a numerical experiment without the Iberian mountains for the 'MAP Piedmont flood event' are discussed. Among other effects, the Iberian orography seems to intensify a secondary low near Liguria as well as increase the mixing ratio convergence and the rainfall intensity near it. A few other cases of heavy rain are also briefly reviewed in order to identify the presence of a Mediterranean depression in the vicinity.