Though formally a mathematician, I have always seen mathematics as a tool to develop solutions to real world problems. The problem that most interests me is coastal flooding due to tides and hurricane storm surges. These phenomena are often studied using computational models. The models numerically solve the shallow water equations (SWEs), providing estimates of water heights and currents.
I am a researcher and developer of the coastal ocean model ADCIRC, which was the model with which I began my career; it was the model used in my doctoral thesis research. ADCIRC is a high fidelity model that solves a modified form of the SWEs using the finite element method. It can be run in serial and in parallel, and can be coupled to the wave model, SWAN.
I also have expertise with the storm surge model SLOSH, which is the operational forecast model of the National Weather Service. This model also solves a modified version of the SWEs, but using finite differences. It is very efficient and is often used for probabalistic forecasting.
Much of my research has been developed with the goal of improving these types of models so they can be used to better serve coastal communities. The approach I have taken thusfar includes state and parameter estimation, which I have performed using statistical data assimilation methods (i.e. extensions of the classical Kalman filter). I also work to improve the models through more accurate descriptions of the model forcing, e.g. the wind field representation.
I have also used the models to analyze the risk of coastal inundation for vulnerable regions, including the US North Atlantic coast. This work was part of a multi-institutional, interdisciplinary research effort to design structures that will mitigate the effects of storm surges. For this work, we also considered the effects of climate change. For more information on this effort, visit structuresofcoastalresilience.org.
More recently, I have begun to study waves and numerical wave modeling for the assessment of renewable wave energy with my students and collaborators. We are also studying the impact of wave energy conversion on coastal erosion. My students and I have also done work towards understanding risk perception of vulnerable groups to inform storm surge risk communication. We are also currently developing a framework for real-time data assimilation for storm surges during a hurricane, and impacts of climate change on hurricane storm surge predictors.