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:
- Journal Article: 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. https://doi.org/10.1016/j.advwatres.2015.01.011
Butler, Troy, Graham, L., Estep, D., Dawson, C., and Westerink, J. J. 2015.
"Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models". United States. https://doi.org/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},
url = {https://www.osti.gov/biblio/1343755},
journal = {Advances in Water Resources},
issn = {0309-1708},
number = ,
volume = 78,
place = {United States},
year = {Tue Feb 03 00:00:00 EST 2015},
month = {Tue Feb 03 00:00:00 EST 2015}
}
Web of Science
Works referenced in this record:
Dimensionally Homogeneous Manning's Formula
journal, September 1992
- Yen, Ben Chie
- Journal of Hydraulic Engineering, Vol. 118, Issue 9
Open Channel Flow Resistance
journal, January 2002
- Yen, Ben Chie
- Journal of Hydraulic Engineering, Vol. 128, Issue 1
Resistance Coefficients for Inbank and Overbank Flow.
journal, June 1999
- Myers, W. R. C.; Knight, D. W.; Lyness, J. F.
- Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 136, Issue 2
Estimation of flow resistance in gravel-bedded rivers: A physical explanation of the multiplier of roughness length
journal, March 1992
- Clifford, N. J.; Robert, A.; Richards, K. S.
- Earth Surface Processes and Landforms, Vol. 17, Issue 2
Acting, predicting and intervening in a socio-hydrological world
journal, January 2014
- Lane, S. N.
- Hydrology and Earth System Sciences, Vol. 18, Issue 3
The potential of wetlands in reducing storm surge
journal, January 2010
- Wamsley, Ty V.; Cialone, Mary A.; Smith, Jane M.
- Ocean Engineering, Vol. 37, Issue 1
Flexible Roughness in Open Channels
journal, May 1973
- Kouwen, Nicholas; Unny, Tharakkal Eroman
- Journal of the Hydraulics Division, Vol. 99, Issue 5
A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part II: Synoptic Description and Analysis of Hurricanes Katrina and Rita
journal, February 2010
- Dietrich, J. C.; Bunya, S.; Westerink, J. J.
- Monthly Weather Review, Vol. 138, Issue 2
Hurricane Gustav (2008) Waves and Storm Surge: Hindcast, Synoptic Analysis, and Validation in Southern Louisiana
journal, August 2011
- Dietrich, J. C.; Westerink, J. J.; Kennedy, A. B.
- Monthly Weather Review, Vol. 139, Issue 8
Modeling floods in a dense urban area using 2D shallow water equations
journal, July 2006
- Mignot, E.; Paquier, A.; Haider, S.
- Journal of Hydrology, Vol. 327, Issue 1-2
On the spatial variation of resistance to flow in upland channel networks: RESISTANCE TO FLOW IN UPLAND CHANNEL NETWORKS
journal, October 2002
- Orlandini, Stefano
- Water Resources Research, Vol. 38, Issue 10
Deriving distributed roughness values from satellite radar data for flood inundation modelling
journal, September 2007
- Schumann, G.; Matgen, P.; Hoffmann, L.
- Journal of Hydrology, Vol. 344, Issue 1-2
Comparison of floodplain surface roughness parameters derived from land cover data and field measurements
journal, July 2012
- Medeiros, Stephen C.; Hagen, Scott C.; Weishampel, John F.
- Journal of Hydrology, Vol. 452-453
A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
journal, January 2011
- Breidt, J.; Butler, T.; Estep, D.
- SIAM Journal on Numerical Analysis, Vol. 49, Issue 5
A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis
journal, January 2012
- Butler, T.; Estep, D.; Sandelin, J.
- SIAM Journal on Numerical Analysis, Vol. 50, Issue 1
A numerical method for solving a stochastic inverse problem for parameters
journal, February 2013
- Butler, T.; Estep, D.
- Annals of Nuclear Energy, Vol. 52
A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest
journal, January 2014
- Butler, T.; Estep, D.; Tavener, S.
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 2, Issue 1
Identification of Manning's roughness coefficients in channel network using adjoint analysis
journal, January 2005
- Ding, Yan; Wang, Sam S. Y.
- International Journal of Computational Fluid Dynamics, Vol. 19, Issue 1
Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland): THUR RIVER BASIN BAYESIAN UNCERTAINTY ANALYSIS
journal, October 2007
- Yang, Jing; Reichert, Peter; Abbaspour, Karim C.
- Water Resources Research, Vol. 43, Issue 10
Bayesian calibration of a flood inundation model using spatial data: BAYESIAN CALIBRATION OF A FLOOD MODEL
journal, May 2011
- Hall, Jim W.; Manning, Lucy J.; Hankin, Robin K. S.
- Water Resources Research, Vol. 47, Issue 5
Uncertainty quantification and inference of Manning’s friction coefficients using DART buoy data during the Tōhoku tsunami
journal, November 2014
- Sraj, Ihab; Mandli, Kyle T.; Knio, Omar M.
- Ocean Modelling, Vol. 83
Data assimilation within the Advanced Circulation (ADCIRC) modeling framework for the estimation of Manning’s friction coefficient
journal, April 2014
- Mayo, Talea; Butler, Troy; Dawson, Clint
- Ocean Modelling, Vol. 76
A wave equation model for finite element tidal computations
journal, September 1979
- Lynch, Daniel R.; Gray, William G.
- Computers & Fluids, Vol. 7, Issue 3
Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations
journal, January 2004
- Dawson, Clint; Proft, Jennifer
- Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 3-5
A Basin- to Channel-Scale Unstructured Grid Hurricane Storm Surge Model Applied to Southern Louisiana
journal, March 2008
- Westerink, Joannes J.; Luettich, Richard A.; Feyen, Jesse C.
- Monthly Weather Review, Vol. 136, Issue 3
A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation
journal, February 2010
- Bunya, S.; Dietrich, J. C.; Westerink, J. J.
- Monthly Weather Review, Vol. 138, Issue 2
Origin of the Hurricane Ike forerunner surge: HURRICANE IKE FORERUNNER
journal, April 2011
- Kennedy, Andrew B.; Gravois, Uriah; Zachry, Brian C.
- Geophysical Research Letters, Vol. 38, Issue 8
Gradient-based estimation of Manning’s friction coefficient from noisy data
journal, January 2013
- Calo, Victor M.; Collier, Nathan; Gehre, Matthias
- Journal of Computational and Applied Mathematics, Vol. 238
On the almost sure coverage property of Voronoi tessellation: the ℝ 1 case
journal, December 2001
- Khmaladze, Estate; Toronjadze, N.
- Advances in Applied Probability, Vol. 33, Issue 4
A numerical method for solving a stochastic inverse problem for parameters
journal, February 2013
- Butler, T.; Estep, D.
- Annals of Nuclear Energy, Vol. 52
Modeling floods in a dense urban area using 2D shallow water equations
journal, July 2006
- Mignot, E.; Paquier, A.; Haider, S.
- Journal of Hydrology, Vol. 327, Issue 1-2
Comparison of floodplain surface roughness parameters derived from land cover data and field measurements
journal, July 2012
- Medeiros, Stephen C.; Hagen, Scott C.; Weishampel, John F.
- Journal of Hydrology, Vol. 452-453
On the almost sure coverage property of Voronoi tessellation: the ℝ1 case
journal, December 2001
- Khmaladze, Estate; Toronjadze, N.
- Advances in Applied Probability, Vol. 33, Issue 04
Flow Resistance Estimation in Mountain Rivers
journal, April 1985
- Bathurst, James C.
- Journal of Hydraulic Engineering, Vol. 111, Issue 4
Remote Sensing and Fully Distributed Modeling for Flood Forecasting
journal, November 1989
- Tao, Tao; Kouwen, Nicholas
- Journal of Water Resources Planning and Management, Vol. 115, Issue 6
Scaling and Similarity in Rough Channel Flows
journal, December 2001
- Gioia, G.; Bombardelli, F. A.
- Physical Review Letters, Vol. 88, Issue 1
A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis
journal, January 2011
- Breidt, J.; Butler, T.; Estep, D.
- SIAM Journal on Numerical Analysis, Vol. 49, Issue 5
A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis
journal, January 2012
- Butler, T.; Estep, D.; Sandelin, J.
- SIAM Journal on Numerical Analysis, Vol. 50, Issue 1
Resistance Coefficients for Inbank and Overbank Flow.
journal, June 1999
- Myers, W. R. C.; Knight, D. W.; Lyness, J. F.
- Proceedings of the Institution of Civil Engineers - Water Maritime and Energy, Vol. 136, Issue 2
Works referencing / citing this record:
A research on the estimation of coefficient roughness in open channel applying entropy concept
journal, September 2018
- Choo, Yeon Moon; Yun, Gwan Seon; Choo, Tai Ho
- Environmental Earth Sciences, Vol. 77, Issue 17
Uncertainty quantification of two-phase flow problems via measure theory and the generalized multiscale finite element method
journal, November 2016
- Presho, M.; Mattis, S.; Dawson, C.
- Computational Geosciences, Vol. 21, Issue 2
Specification of Additional Information for Solving Stochastic Inverse Problems
journal, January 2019
- Uy, Wayne Isaac T.; Grigoriu, Mircea
- SIAM Journal on Scientific Computing, Vol. 41, Issue 5
Experimental Design : Optimizing Quantities of Interest to Reliably Reduce the Uncertainty in Model Input Parameters
preprint, January 2016
- Walsh, Scott
- arXiv
Forward and backward uncertainty quantification: methods, analysis, and applications
text, January 2019
- Tan, Uy, Wayne Isaac
- Cornell University Library