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The present article is the third part of a series of papers devoted to theshallow water wave modelling. In this part, we investigate the derivation ofsome long wave models on a deformed sphere. We propose first a suitable for ourpurposes formulation of the full Euler equations on a sphere. Then, by applyingthe depth-averaging procedure we derive first a new fully nonlinear weaklydispersive base model. After this step, we show how to obtain some weaklynonlinear models on the sphere in the so-called Boussinesq regime. We have tosay that the proposed base model contains an additional velocity variable whichhas to be specified by a closure relation. Physically, it represents adispersive correction to the velocity vector. So, the main outcome of ourarticle should be rather considered as a whole family of long wave models.

Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry