Physical and numerical analysis of long-wave modeling for tsunamis and tides

Numerical models are increasingly being used as tools in the analysis of ocean, coastal, and estuarine dynamics. This thesis examines finite element modeling of two types of long waves, tsunamis and tides, and scrutinizes the numerical representation of the physics governing their propagation.;The Eastern North Pacific Ocean is the domain used to evaluate the ability of numerical models to reproduce regional tidal observations. Inversion techniques identified the amplitudes and phases of tidal constituents along the open boundary based upon tide gauge observations. The goal of this study was not only to minimize RMS errors between the model and the observations, but to also accurately depict the physics as the waves propagate through the domain. This regional model of tides was further examined by contrasting results with global models, and by using regional model results as input to a local modeling study of the Columbia River.;Eliminating errors from tsunami models is more difficult than for tidal modeling, primarily because initial conditions for tsunamis, the movement of the ocean floor during the earthquake, are difficult to verify. Two approaches to overcoming this uncertainty were examined. First, more effective representations of plate movement in the subduction zone were used to compute probable deformations for future Cascadia subduction zone (CSZ) events. Computations for the CSZ allowed us to numerically simulate potential wave dynamics off the northwest coast of the United States resulting from future CSZ earthquakes. With proper parameterization, such computations also may be used for any tsunami event. Results of the CSZ simulations were used by the Oregon Department of Geology and Mineral Industries and the National Oceanic and Atmospheric Administration to provide state and local governments with tools to design effective hazard mitigation strategies. The second approach to eliminating errors in tsunami simulations was to identify and quantify the effects of factors that can alter the quality of the results. Such factors include tide and tsunami interactions, selection of model parameters, grid refinement, truncation errors, and energy errors. Methods were formulated to control and minimize these errors and to better preserve energy in the simulations.