This report is the documentation of a new model for large scale solution of the Boussinesq equations. The equations are briefly presented with emphasis on the inclusion of spherical coordinates and the Coriolis force. We have chosen to start with the standard Boussinesq formulation, but have modified it to achieve improved dispersion properties for moderately short waves. This formulation is put into the context of Boussinesq equations in general in an appendix. Describing first the discretization in detail, we design higher order numerical differences, analyse dispersion, stability and the convergence rate of the iteration scheme used at each time step. The performance of the present model is also compared to state of the art models (FUNWAVE/COULWAVE). A selection of tests are performed to validate the code and assess the applicability and accuracy of the method. The tests include eigenoscillations in basins, solitary wave propagation, comparison with pre-existing models, diffraction of incident solitary waves by a vertical cylinder and trans-Atlantic propagation of a hypothetical tsunami from the La Palma island. The latter case is pursued further in a companion paper. All tests indicate that the model is correctly coded, efficient and robust.