Abstract
All of the theory so far has been for the semi-Lagrangian methods in Cartesian coordinates. However, there are many geophysical processes that have to be modeled in spherical coordinates of some form. In this chapter we shall introduce semi-Lagrangian development on the sphere. As such this chapter comprises two parts: the first is associated with introducing how the vector calculus transfers to spherical coordinates, projections, numerical grids, as well as introducing the theory for spectral methods. The second part is associated with how semi-Lagrangian theory is applied to different models in spherical coordinates in multiple dimensions, where we will present finite difference and finite volume approaches, as well as semi-Lagrangian methods with spectral methods.
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