A Measure-Theoretic Algorithm for Estimating Bottom Friction in a Coastal Inlet: Case Study of Bay St. Louis during Hurricane Gustav (2008)

Abstract

The majority of structural damage and loss of life during a hurricane is due to storm surge, thus it is important for communities in hurricane-prone regions to understand their risk due to surge. Storm surge in particular is largely influenced by coastal features such as topography/bathymetry and bottom roughness. Bottom roughness determines how much resistance there is to the flow. Manning’s formula can be used to model the bottom stress with the Manning’s n coefficient, a spatially dependent field. Given a storm surge model and a set of model outputs, an inverse problem may be solved to determine probable Manning’s n fields to use for predictive simulations. The inverse problem is formulated and solved in a measure-theoretic framework using the state-of-the-art Advanced Circulation (ADCIRC) storm surge model. The use of measure theory requires minimal assumptions and involves the direct inversion of the physics-based map from model inputs to output data determined by the ADCIRC model. Thus, key geometric relationships in this map are preserved and exploited. By using a recently available subdomain implementation of ADCIRC that significantly reduces the computational cost of forward model solves, the authors demonstrate the method on a case study using data obtained from an ADCIRC hindcast study of Hurricane Gustav (2008) to quantify uncertainties in Manning’s n within Bay St. Louis. However, the methodology is general and could be applied to any inverse problem that involves a map from model input to output quantities of interest.