Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

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.

Parameter estimation and prediction for groundwater contamination based on measure theory

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Projection-Based Model Reduction for Finite Element Approximation of Shallow Water Flows

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“…While ongoing work continues to improve the performance of core numerical methods for the SWE, it is clear that alternative approaches are needed to achieve the speedups necessary to make use of the SWE common in real-time simulation or sampling-intensive methods for risk assessment or uncertainty quantification [9]. Here, we consider global model reduction for the SWE via projection.…”

Development and Assessment of the Physically-Based 2D/1D Model “TRENOE” for Urban Stormwater Quantity and Quality Modelling

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