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