The physical properties of Interplanetary Coronal Mass Ejections (ICMEs) and therefore of magnetic clouds (a sub-class of ICMEs) and their preceding shocks can be measured locally by interplanetary spacecraft. However, those data are local, and they do not provide the global shape of those structures a priori.

In a series of work reviewed in this talk, we have proposed a new approach using statistical methods to investigate a data-constrained shape both for the flux rope axis in magnetic clouds and for the ICME shocks.

These methods rely on the computation from the data of a parameter that defines the location of the interplanetary spacecraft along the detected structures. From the distribution of this parameter and by comparing how some synthetic distributions can very well fit the observed distributions of interplanetary events, we derive the generic shape of the ICMEs. I will also show how such statistical methods can give us some clues about the budgets of magnetic field flux and helicity inside magnetic clouds.

Such studies allow us to construct a generic shape of an ICME at Earth.