  The present two-part paper provides a Lagrangian perspective of the final
southern warming in 2002, during which the stratospheric polar vortex (SPV)
experienced a unique splitting. Part I focuses on the understanding of
fundamental processes for filamentation and ultimately for vortex splitting on
a selected isentropic surface in the middle stratosphere. Part II discusses the
three-dimensional evolution of the selected sudden warming event. We approach
the subject from a dynamical systems viewpoint and search for Lagrangian
coherent structures using a Lagrangian descriptor as a tool. In this Part I we
work in the idealized framework of a kinematic model that allows for an
understanding of the contributing elements of the flow in late September during
the splitting. We introduce a definition of kinematic SPV boundary based on a
criterion for binning parcels inside and outside the vortex according to their
values of the Lagrangian descriptor and associated PDF. This definition is
justified by using arguments that go beyond heuristic considerations based on
the potential vorticity. Next, we turn to the filamentation proceses along this
kinematic boundary, and the role of Lagrangian structures in the SPV splitting.
We determine a criterion for splitting based on the structure of the evolving
unstable and unstable manifolds.
