Reliability Assessment of Computational River Models
Publication: Journal of Irrigation and Drainage Engineering
Volume 148, Issue 6
Abstract
Application of numerical flood models in hydraulic engineering, loss and risk analysis, and urban policy making has increased significantly in recent years. While those models are widely being used, verification of underlying solvers and quality control (QC) of flood inundation results are still scarce among the hydraulic engineering community. This paper provides comprehensive verification methods/tools to fill this gap of knowledge. In this paper, the implementation of different code/solution verification procedures to build confidence in flood models was presented. The model verification approaches covered in this study includes: method of exact solution (MES), method of manufactured solution (MMS), Richardson extrapolation (RE), and the grid convergence index (GCI). Three test cases (steady subcritical flow, smooth transcritical flow, and dam-break shock formation) were used during the analyses to uncover all possible error/limitations in a shallow-water-wave solver. The asymptotic regime of convergence was used to select appropriate discretization sizes. The results from the MES and MMS indicate matched values for the observed and formal order of accuracy. For most of the discretization sizes, the observed order of accuracy indicates better performance for the water depth values than for the velocities. Although formal order of convergence is not achieved in some cases, the solution verification results show acceptable convergence behavior in the error norms as the grid resolution is refined. The RE and the GCI were successfully implemented for generating reference solutions and estimating the numerical uncertainty upper and lower bounds. Overall, this study provides a complete framework with essential set of tests to fully build a confidence in a flood model (1D or 2D) before applying it to solve real-world problems.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The first author was supported by the Center of Management Utilization and Protection of Water Resources at Tennessee Technological University.
References
ASME. 2009. Standard for verification and validation in computational fluid dynamics and heat transfer. ASME V&V 20. New York: ASME.
Birhanu, D., H. Kim, C. Jang, and S. Park. 2016. “Flood risk and vulnerability of Addis Ababa city due to climate change and urbanization.” Procedia Eng. 154 (Jan): 696–702. https://doi.org/10.1016/j.proeng.2016.07.571.
Blessing, R., A. Sebastian, and S. D. Brody. 2017. “Flood risk delineation in the United States: How much loss are we capturing?” Nat. Hazard. Rev. 18 (3): 04017002. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000242.
Bradford, S. F., and B. F. Sanders. 2002. “Finite-volume model for shallow water flooding of arbitrary topography.” J. Hydraul. Eng. 128 (3): 289–298. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:3(289).
Brunner, G. W., and CEIWR-HHT. 2018. “Benchmarking of the HEC-RAS Two-dimensional Hydraulic modelling capabilities.” Accessed November 12, 2021. http://www.hec.usace.army.mil/software/hec-ras/documentation/RD-51_Benchmarking_2D.pdf.
Center for Research on Epidemiology of Disaster (CRED) and United Nations Offices for Disaster Risk Reduction (UNISDR). 2015. “The human cost of weather related disasters 1995-2015.” Accessed November 15, 2021. https://www.unisdr.org/2015/docs/climatechange/COP21_WeatherDisastersReport_2015_FINAL.pdf.
Changnon, S. A. 2008. “Assessment of flood losses in the United States.” J. Contemp. Water Res. Educ. 138 (1): 38–44. https://doi.org/10.1111/j.1936-704X.2008.00007.x.
Cordier, S., H. Coullon, O. Delestre, C. Laguerre, M. H. Le, D. Pierre, and G. Sadaka. 2013. “Fullswof_paral: Comparison of two parallelization strategies (MPI and SkelGIS) on a software designed for hydrology applications.” ESAIM Proc. 43 (Dec): 59–79. https://doi.org/10.1051/proc/201343004.
Delestre, O., C. Lucas, P. A. Ksinant, F. Darboux, C. Laguerre, T. N. T. Vo, F. James, and S. Cordier. 2013. “SWASHES: A compilation of shallow water analytic solutions for hydraulic and environmental studies.” Int. J. Numer. Methods Fluids 72 (3): 269–300. https://doi.org/10.1002/fld.3741.
Dhillon, D. S., F. A. Bombardelli, W. E. Fleenor, and K. Zamani. 2014. On the issues associated with 2-D modeling for flood mapping purposes. Washington, DC: FEMA, California Department of Water Resources.
Dullo, T. T., G. K. Darkwah, S. Gangrade, M. Morales-Hernandez, M. B. Sharif, A. J. Kalyanapu, S.-C. Kao, S. Ghafoor, and M. Ashfaq. 2021a. “Assessing climate-change-induced flood risk in the Conasauga River watershed: An application of ensemble hydrodynamic inundation modelling.” Nat. Hazards Earth Syst. Sci. 21 (6): 1739–1757. https://doi.org/10.5194/nhess-21-1739-2021.
Dullo, T. T., S. Gangrade, M. Morales-Hernandez, M. B. Sharif, S.-C. Kao, A. J. Kalyanapu, S. Ghafoor, and K. J. Evans. 2021b. “Simulation of hurricane Harvey flood event through coupled hydrologic-hydraulic models: Challenges and next steps.” J. Flood Risk Manage. 14 (3): 1–26. https://doi.org/10.1111/jfr3.12716.
Eça, L., G. Vaz, and M. Hoekstra. 2017. “Iterative errors in unsteady flow simulations: Are they really negligible?” In Proc., 20th Numerical Towing Tank Symp. (NUTTS2017). Red Hook, NY: Curran Associates.
Federal Emergency Management Agency (FEMA). 2002. “National flood insurance program: Program description. Federal Emergency Management Agency/Federal Insurance Mitigation Administration.” Accessed November 15, 2021. https://s3-us-gov-west-1.amazonaws.com/dam-production/uploads/20130726-1447-20490-2156/nfipdescrip_1_.pdf.
Feng, Y., K. Zamani, H. Yang, H. Wang, F. Wang, and B. Jeremić. 2020. “Procedures to build trust in nonlinear elastoplastic integration algorithm: Solution and code verification.” Eng. Comput. 36 (4): 1643–1656. https://doi.org/10.1007/s00366-019-00787-0.
Ferziger, P., and M. Peric. 2002. Computational methods for fluid dynamics. 3rd ed. Berlin, Heidelberg: Springer-Verlag.
Gould, A. M. 2010. “Finite volume solution of the unsteady free surface flow equations.” Accessed November 17, 2021. https://eprints.usq.edu.au/18654/1/Gould_2010.pdf.
Goutal, N., and F. Maurel. 1997. Proceedings of the second workshop on dam-break wave simulation. Paris, France: Electricite de France, Dept. Laboratoire National d’Hydraulique, Groupe Hydraulique Fluviale.
Harimi, I., and A. R. Pishevar. 2013. “Evaluating the capability of the flux-limiter schemes in capturing strong shocks and discontinuities.” Shock Vib. 20 (2): 287–296. https://doi.org/10.1155/2013/528358.
Hemez, F. M., and J. R. Kamm. 2008. “A brief overview of the state-of-the-practice and current challenges of solution verification.” In Vol. 62 of Computational methods in transport: Verification and validation, edited by F. Graziani, 229–250. Berlin, Heidelberg: Springer.
Judi, D. R., S. J. Burian, and T. N. McPherson. 2011. “Two-dimensional fast-response flood modeling: Desktop parallel computing and domain tracking.” J. Comput. Civ. Eng. 25 (3): 184–191. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000064.
Kalyanapu, A. J., S. Shankar, E. R. Pardyjak, D. R. Judi, and S. J. Burian. 2011. “Assessment of GPU computational enhancement to a 2D flood model.” Environ. Modell. Software 26 (8): 1009–1016. https://doi.org/10.1016/j.envsoft.2011.02.014.
Khoshghalb, A., O. Ghaffaripour, K. Zamani, and A. Tootoonchi. 2019. “Code verification in computational geomechanics: Method of manufactured solutions (MMS).” Comput. Geotech. 116 (Dec): 103178. https://doi.org/10.1016/j.compgeo.2019.103178.
Kollat, J. B., J. R. Kasprzyk, W. O. A. C. ThomasMiller Jr., A. C. Miller, and D. Divoky. 2012. “Estimating the impacts of climate change and population growth on flood discharges in the United States.” J. Water Resour. Plann. Manage. 138 (5): 442–452. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000233.
Liang, L., and L. Kavvas. 2008. “Modeling of solute transport and macrodispersion by unsteady stream flow under uncertain conditions.” J. Hydrol. Eng. 13 (6): 510–520. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:6(510).
MATLAB. 2015. Symbolic math toolbox: User’s guide. Natick, MA: The MathWorks.
Merwade, V., F. Olivera, M. Olivera, and S. Edleman. 2008. “Uncertainty in flood inundation mapping: Current issues and future directions.” J. Hydrol. Eng. 13 (7): 608–620. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:7(608).
Neal, J., G. Shumann, and P. Bates. 2012. “A subgrid channel model for simulating river hydraulics and floodplain inundation over large and data sparse areas.” Water Resour. Res. 48 (11): W11506. https://doi.org/10.1029/2012WR012514.
Neelz, S., and G. Pender. 2013. “Benchmarking the latest generation of 2D hydraulic flood modelling packages.” Accessed November 12, 2021. https://www.gov.uk/government/publications/benchmarking-the-latest-generation-of-2d-hydraulic-flood-modelling-packages.
Ntelekos, A. A., M. Oppenheimer, J. A. Smith, and A. J. Miller. 2010. “Urbanization, climate change and flood policy in the United States.” Clim. Change 103 (3): 597–616. https://doi.org/10.1007/s10584-009-9789-6.
Oberkampf, W. L., and F. G. Blottner. 1998. “Issues in computational fluid dynamics code verification and validation.” AIAA J. 36 (5): 687–695. https://doi.org/10.2514/2.456.
Oberkampf, W. L., and C. J. Roy. 2010. Verification and validation in scientific computing, 318–330. Cambridge: Cambridge University Press.
Pielke, R. A., Jr., and M. W. Downton. 2000. “Precipitation and damaging floods: Trends in the United States, 1932-97.” J. Clim. 13 (20): 3625–3637. https://doi.org/10.1175/1520-0442(2000)013%3C3625:PADFTI%3E2.0.CO;2.
Pielke, R. A., Jr., M. W. Downton, and J. Z. Barnard Miller. 2002. “Flood damage in the United States, 1926-2000: A reanalysis of National Weather Service Estimates. Boulder, CO: UCAR.” Accessed November 14, 2021. https://sciencepolicy.colorado.edu/flooddamagedata/flooddamagedata.pdf.
Roache, P. J. 1994. “Perspective: A method for uniform reporting of grid refinement studies.” J. Fluids Eng. 116 (3): 405–413. https://doi.org/10.1115/1.2910291.
Roache, P. J. 1997. “Quantification of uncertainty in computational fluid dynamics.” Annu. Rev. Fluid Mech. 29 (1): 123–160. https://doi.org/10.1146/annurev.fluid.29.1.123.
Roache, P. J. 1998. Verification and validation in computational science and engineering. New Mexico: Hermosa Publisher.
Roache, P. J. 2002. “Code verification by the method of manufactured solutions.” J. Fluids Eng. 124 (1): 4–10. https://doi.org/10.1115/1.1436090.
Roache, P. J., and P. M. Knupp. 1993. “Completed richardson extrapolation.” Commun. Numer. Methods Eng. 9 (5): 365–374. https://doi.org/10.1002/cnm.1640090502.
Roy, C. J. 2003. “Grid convergence error analysis for mixed-order numerical schemes.” AIAA J. 41 (4): 595–604. https://doi.org/10.2514/2.2013.
Roy, C. J. 2005. “Review of code and solution verification procedures for computational simulation.” J. Comput. Phys. 205 (1): 131–156. https://doi.org/10.1016/j.jcp.2004.10.036.
Roy, C. J., and W. L. Oberkampf. 2011. “A comprehensive framework for verification, validation and uncertainty quantification in scientific computing.” Comput. Methods Appl. Mech. Eng. 200 (25–28): 2131–2144. https://doi.org/10.1016/j.cma.2011.03.016.
Salari, K., and P. Knupp. 2000. “Code verification by the method of manufactured solutions.”. Alburquerque, NM: USDOE.
Sampson, C. C., A. M. Smith, P. B. Bates, J. C. Neal, L. Alfieri, and J. E. Freer. 2015. “A high-resolution global flood hazard model.” Water Resour. Res. 51 (9): 7358–7381. https://doi.org/10.1002/2015WR016954.
Sanders, B. F. 2018. “MATLAB-Source codes for 1D and 2D flood models.” Accessed June 8, 2018. http://sanders.eng.uci.edu/matlabcodes.html.
Sanders, B. F., and S. F. Bradford. 2002. “High-resolution, monotone solution of the adjoint shallow-water equations.” Int. J. Numer. Methods Fluids 38 (2): 139–161. https://doi.org/10.1002/fld.206.
Sanders, B. F., and S. F. Bradford. 2006. “Impact of Limiters on Accuracy of High-Resolution Flow and Transport Models.” J. Eng. Mech. 132 (1): 87–98. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:1(87).
Stoker, J. J. 1957. Water waves: The mathematical theory with applications. London, UK: Interscience.
UNISDR. 2015. Making development sustainable: The future of disaster risk management. global assessment report on disaster risk reduction. Geneva, Switzerland: United Nations Office for Disaster Risk Reduction.
USEPA. 2018. “Green infrastructure: Manage flood risk.” Accessed November 12, 2021. https://www.epa.gov/green-infrastructure/manage-flood-risk.
Winsemius, H. C., et al. 2016. “Global drivers of future river flood risk.” Nat. Clim. Change 6 (4): 381–385. https://doi.org/10.1038/nclimate2893.
Wu, C., G. Huang, and Y. Zheng. 1999. “Theoretical solution of dam-break shock wave.” J. Hydraul. Eng. 125 (11): 1210–1215. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:11(1210).
Yamazaki, D., S. Kanae, H. Kim, and T. Oki. 2011. “A physically based description of floodplain inundation dynamics in a global river routing model.” Water Resour. Res. 47 (4): W04501. https://doi.org/10.1029/2010WR009726.
Zamani, K. 2015. “Efficient and reliable mathematical modeling techniques for multi-phase environmental flows.” Ph.D. Dissertation, Dept. of Civil and Environmental Engineering, Univ. of California.
Zamani, K., and F. A. Bombardelli. 2014. “Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers.” Environ. Fluid Mech. 14 (4): 711–742. https://doi.org/10.1007/s10652-013-9325-0.
Zoppou, C., and S. Roberts. 2003. “Explicit schemes for dam-break simulations.” J. Hydraul. Eng. 129 (1): 11–34. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:1(11).
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Received: Jun 4, 2021
Accepted: Jan 17, 2022
Published online: Mar 16, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 16, 2022
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