In this talk, we present recent progress on the design of a compact scheme for convective equations on the sphere. In numerical climatology, the simplest system consists of the shallow water equations on the rotating earth, in linear or nonlinear form. We show that a centered eulerian scheme presents attractive properties for this purpose. This kind of scheme can be considered as a discrete counterpart of the equations with a minimal numerical diffusion. This property is essential to preserve the accuracy of the approximation in space after a large number of time iterations. We will present the main properties of the spatial and temporal approximation as well as numerical results obtained with this approach on a series of tests cases of the literature.