Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.
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.
Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO 80202.
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T
Butler
Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, Texas 78712.
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L
Graham
Department of Statistics, Colorado State University, Fort Collins, CO 80523.
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D
Estep
Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, Texas 78712.
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C
Dawson
Department of Civil & Environmental Engineering & Earth Sciences, University of Notre Dame, South Bend, IN.
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JJ
Westerink
ADCIRC; Manning’s n cofficient; condition; generalized contour; induced probability measure; measure theory; parameter estimation; set-valued inverse solutions; shallow water equations; stochastic inverse problems; storm surge