Kelly et al. (Coast Eng J 57(4):1-30, 2015) present a finite volume dynamic adaptive mesh model based on Osher's approximate Riemann solver for the prediction of storm surges over complex landscapes. Here, the model described in that paper is extended to use distributed memory parallel block tree-based mesh refinement via the PARAMESH library. The resulting model, called the fully adaptive storm tide (FAST) model, can thus be run on massively parallel supercomputers. In this paper, we validate the FAST model by conducting numerical simulations of the storm surges due to hurricanes Wilma (2005) on Lake Okeechobee and Ike (2008) in the Gulf of Mexico. The storm surge due to Wilma on Lake Okeechobee is interesting as it can be considered as an almost idealized case which comprises a closed system. The case of hurricane Ike is more complex as it involves a coastline and additional features such as barrier islands and tidally controlled boundaries. For both cases, results obtained using the FAST model compare favorably with the measured water elevation and high-water mark data. Moreover, we show that, with sufficient computational resource, low runtimes are possible for real-world surge simulations. The FAST model therefore has the potential to run the ensemble predictions necessary to account for the variability that is inherent in hurricane forecasting.