Discontinuous Galerkin unsteady discrete adjoint method for real-time efficient tsunami simulations

An unsteady discrete adjoint implementation for a discontinuous Galerkin model solving the shallow water wave equations on the sphere is presented. Its use for tsunami simulations is introduced to reconstruct the initial condition automatically from buoy measurements. Based on this feature, a real-time tsunami model is developed, using several numerical tools such as a high-order discretization, hp-refinement, parallel dynamic load balancing and adjoint-based data assimilation. The model is able to reconstruct the tsunami source and accurately forecast its far-field propagation (e.g. from Japan to Chile, at a distance of about 17000 km) in a computational time 20 times faster than the physical propagation time, to which the data collecting time needs to be added. The work presented constitutes a step towards an efficient nonlinear tsunami warning model. Additional features could be added for more complete realistic forecasts.