## 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 in this paper. 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. Finally, 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.

- Authors:

- Univ. of Colorado, Denver, CO (United States)
- Univ. of Texas, Austin, TX (United States)
- Colorado State Univ., Fort Collins, CO (United States)
- Univ. of Notre Dame, South Bend, IN (United States)

- Publication Date:

- Research Org.:
- Colorado State Univ., Fort Collins, CO (United States); Univ. of Colorado, Denver, CO (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1343755

- Alternate Identifier(s):
- OSTI ID: 1249698

- Grant/Contract Number:
- SC0009279; FG02-04ER25620; FG02-05ER25699; FC02-07ER54909; SC0001724; SC0005304; DGE-1110007; INL00120133; DE0000000SC9279; PO672TO001; 00069249; 00115474; B573139; B584647; B590495

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Advances in Water Resources

- Additional Journal Information:
- Journal Volume: 78; Journal ID: ISSN 0309-1708

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Manning’s n coefficient; measure theory; parameter estimation; set-valued inverse solutions; shallow water equations; stochastic inverse problems

### Citation Formats

```
Butler, Troy, Graham, L., Estep, D., Dawson, C., and Westerink, J. J. Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models. United States: N. p., 2015.
Web. doi:10.1016/j.advwatres.2015.01.011.
```

```
Butler, Troy, Graham, L., Estep, D., Dawson, C., & Westerink, J. J. Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models. United States. doi:10.1016/j.advwatres.2015.01.011.
```

```
Butler, Troy, Graham, L., Estep, D., Dawson, C., and Westerink, J. J. Tue .
"Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models". United States. doi:10.1016/j.advwatres.2015.01.011. https://www.osti.gov/servlets/purl/1343755.
```

```
@article{osti_1343755,
```

title = {Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models},

author = {Butler, Troy and Graham, L. and Estep, D. and Dawson, C. and Westerink, J. J.},

abstractNote = {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 in this paper. 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. Finally, 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.},

doi = {10.1016/j.advwatres.2015.01.011},

journal = {Advances in Water Resources},

number = ,

volume = 78,

place = {United States},

year = {2015},

month = {2}

}

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