**The classical mechanics of weather**

Ideal fluid dynamics may be viewed as a continuum version of classical
mechanics, which implies strong geometric properties of the equations of motion
including symmetries, invariants, and variational principles. One of the key
numerical challenges in numerical weather prediction is the question how to
preserve these structures under spatial and temporal truncation. I will talk
about a Lagrangian particle method that leads to a finite dimensional system
of Newtonian equations of motion with a number of desirable conservation
properties. Applications include the spherical shallow-water equations and a
vertical slice model. The emphasis on conservative discretizations will be
motived by a simple example which will be related to ensemble weather prediction.

*Sebastian Reich*

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