Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models. (April 2015)

• Record Type: Journal Article
• Authors: Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J.J.
• Is Part Of: Advances in water resources. Volume 78(2015)
• Page Start: 60
• Page End: 79
• Publication Date: 2015-04
• Subjects: Manning's n coefficient -- Measure theory -- Parameter estimation -- Set-valued inverse solutions -- Shallow water equations -- Stochastic inverse problems; Hydrology -- Periodicals; Hydrodynamics -- Periodicals; Hydraulic engineering -- Periodicals; 551.48
• DOI: 10.1016/j.advwatres.2015.01.011
• Languages: English
• ISSNs: 0309-1708

Abstract

Highlights: A physically relevant inverse problem is solved using a measure-theoretic framework. Uncertainties in Manning's n field for a shallow water equation model are quantified. A new notion of "condition" for the inverse problem is defined and analyzed. We use the condition in the determination of effective output quantities of interest. Abstract: The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.