  Windstorms are a primary natural hazard affecting Europe that are commonly
linked to substantial property and infrastructural damage and are responsible
for the largest spatially aggregated financial losses. Such extreme winds are
typically generated by extratropical cyclone systems originating in the North
Atlantic and passing over Europe. Previous statistical studies tend to model
extreme winds at a given set of sites, corresponding to inference in a Eulerian
framework. Such inference cannot incorporate knowledge of the life cycle and
progression of extratropical cyclones across the region and is forced to make
restrictive assumptions about the extremal dependence structure. We take an
entirely different approach which overcomes these limitations by working in a
Lagrangian framework. Specifically, we model the development of windstorms over
time, preserving the physical characteristics linking the windstorm and the
cyclone track, the path of local vorticity maxima, and make a key finding that
the spatial extent of extratropical windstorms becomes more localised as its
magnitude increases irrespective of the location of the storm track. Our model
allows simulation of synthetic windstorm events to derive the joint
distributional features over any set of sites giving physically consistent
extrapolations to rarer events. From such simulations improved estimates of
this hazard can be achieved both in terms of intensity and area affected.

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