  Solving the shallow water equations efficiently is critical to the study of
natural hazards induced by tsunami and storm surge, since it provides more
response time in an early warning system and allows more runs to be done for
probabilistic assessment where thousands of runs may be required. Using
Adaptive Mesh Refinement (AMR) speeds up the process by greatly reducing
computational demands, while accelerating the code using the Graphics
Processing Unit (GPU) does so through using faster hardware. Combining both, we
present an efficient CUDA implementation of GeoClaw, an open source
Godunov-type high-resolution finite volume numerical scheme on adaptive grids
for shallow water system with varying topography. The use of AMR and spherical
coordinates allows modeling transoceanic tsunami simulation. Numerical
experiments on several realistic tsunami modeling problems illustrate the
correctness and efficiency of the code, which implements a simplified
dimensionally-split version of the algorithms. This implementation is shown to
be accurate and faster than the original when using CPUs alone. The GPU
implementation, when running on a single GPU, is observed to be 3.6 to 6.4
times faster than the original model running in parallel on a 16-core CPU.
Three metrics are proposed to evaluate relative performance of the model, which
shows efficient usage of hardware resources.
