The goal of this project is to improve the predictive capabilities of computational models of the coastal ocean, by combining a novel measure-theoretic approach for inverse sensitivity with experimental data. Advanced computer models of the coastal ocean, such as the Advanced Circulation (ADCIRC) model, can be used in predictive mode to estimate storm surge as hurricanes approach landfall for the purposes of emergency evacuation and response. However, the accuracy of ADCIRC, and other computer models, relies on the painstaking process of model calibration based on uncertain input parameters. The investigators study the estimation and model sensitivity for certain critical parameters, in particular bathymetry, bottom friction, and wind stress. Applying the solution to the inverse problem for prediction is complicated by two issues. First, the map from the input data and parameter space to the observable space generally reduces the dimension which implies the inverse problem has set-valued solutions. Second, even though the models considered in this project provide deterministic physical descriptions, all of the data available is subject to natural stochastic variability as well as experimental/observational error and uncertainty generally described stochastically. The measure-theoretic algorithm computes a probability measure over the entire parameter space from which an ensemble of model selections may be chosen to deliver reliable predictions of critical quantities of interest such as maximum water elevation along the coast. The PIs study various mathematical issues including estimation of various sources of error inherent in a non-intrusive implementation of the measure-theoretic approach. The use of experimental data and the ADCIRC model creates a unique opportunity for verification and validation of proposed methods.
Quantitative predictions of coastal ocean conditions is central to long-range studies of coastal sustainability, the development of priorities and policies for the restoration and maintenance of coastal ecosystems, enhancing the economic vitality of coastal communities, and assessing risk of coastal populations to natural disasters. While coastal predictions of various complexity have been under development and used routinely for decades now, a series of events over the past seven years has driven a revolution. Namely, Hurricane Katrina (2005), in devastating fashion, demonstrated the perils of underestimating the vulnerability of coastal communities to storm surge. Following on the heels of Katrina were hurricanes Rita (2005), Gustav (2008) and Ike (2008), which all caused tremendous damage to communities along the northern Gulf of Mexico, and more recently the Deepwater Horizon Oil Spill, which occurred off the coast of Louisiana and threatened the entire Gulf ecosystem. These events spurred a serious and sustained effort to improve the ability to predict coastal ocean conditions. However, the prediction of coastal conditions beyond what can be observed, e.g. predicting future maximum storm surge from current and near past coastal observation data in real-time, is an exceedingly challenging mathematical, statistical, and computational problem. In this project, the investigators study and apply state-of-the-art techniques in order to improve the predictive capabilities of coastal ocean models used to predict storm surge. The computational methodology and tools developed under this project are applicable to other problems in coastal engineering, marine science, material science and other engineering disciplines. Technology transfer of the mathematical and numerical methodologies developed under this project will occur with the coastal ocean modeling community, and with agencies such as the U.S. Army Corps of Engineers, NOAA, the Department of Homeland Security, state and local agencies, industry, and other universities in the U.S. and abroad.
