I will describe a novel dynamically adaptive wavelet method for the shallow water equations on a staggered C-grid I have developed with Thomas Dubos during my sabbatical visit to LMD. Pressure is located at the centres of the primal grid (hexagons) and velocity is located at the edges of the dual grid (triangles). Distinct biorthogonal second generation wavelet transforms are developed for the pressure and the velocity. These wavelet transforms ensure that mass is conserved and that there is no numerical generation of potential vorticity when solving the shallow water equations. Appropriate thresholding of the wavelet coefficients allows error control in both the quasi-geostrophic and inertia-gravity wave regimes. The shallow water equations are discretized on the dynamically adapted multiscale grid using the TRiSK scheme [Ringler/etal:2010]. The conservation and error control properties of the method are verified by applying it to a propagating inertia--gravity wave packet and rotating shallow water turbulence. The method has been designed so it can be easily extended to the icosahedral subdivision of the sphere. This work is the first step in developing a fully adaptive general circulation model (GCM) for ocean and atmosphere modelling.