Automatic Calibration of Bed Friction Coefficients to Reduce the Influence of Seasonal Variation: Case of the Gironde Estuary
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147, Issue 3
Abstract
An automatic procedure to identify the bed friction coefficient is tested on a 2D hydrodynamic model of the Gironde estuary (France). The proposed procedure involves an optimization algorithm based on evolution strategy, namely Covariance Matrix Adaptation Evolution Strategy. Without optimization, application of the same friction distribution to different hydrological conditions leads to significant relative error in water level prediction up to 20%–30%. For the tested configuration, 300 runs seemed to be sufficient to reach an optimal value whereas an additional 200 runs would help to gain an accuracy of a few millimeters (or 0.3%). In order to reach the same level of accuracy for the different hydrological configurations, it is necessary to adapt for each configuration of the bed friction coefficient. Such behavior tends to confirm a seasonal variation of the friction coefficient and this is particularly the case in the central part of the estuary. Different relationships of the friction coefficient according to the flowrate have been incorporated inside the 2D hydrodynamic model. These relationships effectively maintain an accurate prediction of the water levels close to 10% for a wide range of hydrological configurations.
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Data Availability Statement
Data, models, and code scripts used for coupling CMA-ES and TELEMAC-2D developed in this study are available from the corresponding author upon request. Water levels data are available at www.vigicrues.gouv.fr.
Acknowledgments
The research leading to these results has received funding from the Connecting Europe Facility (CEF)-Transport Sector under agreement (Innovation and Networks Executive Agency) No INEA/CEF/TRAN/M2014/1049680 through the project Gironde XL. The authors thank the National Hydrographic Service (SHOM) and the National Weather Agency (Météo-France) for providing bathymetric datasets, and predictions of tide-surge interactions. Dr. Tom Benson is kindly acknowledged for providing the Matlab toolbox used to postprocess TELEMAC-2D results. Map of France from Fig. 1 is extracted from Geoportail website (https://www.geoportail.gouv.fr/) held by National Institute of Geographic and Forest Information (IGN), which is a public administrative establishment placed under the joint authority of the ministries in charge of ecology and forestry.
Notation
The following symbols are used in this paper:
- g
- gravity acceleration (m/s2);
- h
- water depth in (m);
- K
- Strickler coefficient for the bed friction in (m1/3/s);
- depth-averaged flow velocity vector, with east–west U, north–south V components (m/s);
- Ζ
- free surface elevation (m);
- νt
- momentum diffusion coefficient (m2/s); and
- ρ
- density (m3/kg).
References
Allen, G. P. 1972. “Etude des processus sédimentaires dans l’estuaire de la Gironde.” Ph.D. thesis, Institut de Géologie du Bassin d'Aquitaine, Univ. of Bordeaux I.
Baeck, T., D. B. Fogel, and Z. Michalewicz. 2000a. Evolutionary computation 1: Basic algorithms and operators. Bristol, UK: Institute of Physics Publishing.
Baeck, T., D. B. Fogel, and Z. Michalewicz. 2000b. Evolutionary computation 2: Advanced algorithms and operators. Bristol, UK: Institute of Physics Publishing.
Bayer, P., and M. Finkel. 2004. “Evolutionary algorithms for the optimization of advective control of contaminated aquifer zones.” Water Resour. Res. 40 (6): W06506. https://doi.org/10.1029/2003WR002675.
Bellos, V., I. Nalbantis, and G. Tsakiris. 2018. “Friction modeling of flood flow simulations.” J. Hydraul. Eng. 144 (12): 04018073. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001540.
Benaouda, A. 2008. “Dynamique saisonnière des sediments en suspension dans l’estuaire de la Gironde: modélisation operationnelle de la reponse aux forcages hydrodynamiques.” [In French.] Ph.D. thesis, Environnements et Paléoenvironnements Océaniques et Continentaux, Université de Bordeaux 1.
Castaing, P. 1981. “Le transfert à l’océan des suspensions estuariennes—Cas de la Gironde.” Ph.D. thesis, Département de géologie et océanographie, Univ. of Bordeaux I.
Ch, S. C., and P. W. Tsai. 2007. “Computational intelligence based on the behavior of cats.” Int. J. Innov. Comput. Inf. Control 3 (1): 163–173.
Dorigo, M., and L. M. Gambardella. 1997. “Ant colony system: A cooperative learning approach to the traveling salesman problem.” IEEE Trans. Evol. Comput. 1 (1): 53–66. https://doi.org/10.1109/4235.585892.
Dréo, J., A. Pétrowski, P. Siarry, and E. Taillard. 2005. Metaheuristics for hard optimization. Berlin: Springer-Verlag.
Dung, N. V., B. Merz, A. Bárdossy, T. D. Thang, and H. Apel. 2011. “Multi-objective automatic calibration of hydrodynamic models utilizing inundation maps and gauge data.” Hydrol. Earth Syst. Sci. 15 (4): 1339–1354. https://doi.org/10.5194/hess-15-1339-2011.
Eberhart, R., and J. Kennedy. 1995. “A new optimizer using particle swarm theory.” In Proc., 6th Int. Symp. on Micro Machine and Human Science, 39–43. New York: IEEE.
Elshall, A. S., H. V. Pham, F. T.-C. Tsai, L. Yan, and M. Ye. 2015. “Parallel inverse modeling and uncertainty quantification for computationally demanding groundwater-flow models using covariance matrix adaptation.” J. Hydrol. Eng. 20 (8): 04014087. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001126.
Espana, R. M., A. M. Hernández-Díaz, J. M. Cecilia, and M. D. García-Román. 2017. “Evolutionary strategies as applied to shear strain effects in reinforced concrete beams.” Appl. Soft Comput. 57: 164–176. https://doi.org/10.1016/j.asoc.2017.03.037.
Fletcher, R. 1980. Practical methods of optimization: Volume 1 constrained optimization. New York: John Wiley & Sons.
Fletcher, R. 1981. Practical methods of optimization: Volume 2 unconstrained optimization. New York: John Wiley & Sons.
Goldberg, D. E. 1989. Genetic algorithm in search. optimization and machine learning. Boston, MA: Addison-Wesley Publishing Company.
Hansen, N. 2006. “The CMA evolution strategy: A comparing review.” In Towards a new evolutionary computation, edited by J. A. Lozano, P. Larrañaga, I. Inza, and E. Bengoetxea, 75–102. Berlin: Springer.
Hansen, N. 2016. “The CMA evolution strategy: A tutorial.” Accessed April 4, 2016. https://arxiv.org/abs/1604.00772.
Hansen, N., and A. Ostermeier. 1996. “Adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaption.” In Proc., 3rd IEEE Int. Conf. on Evolutionary Computation, 312–317. New York: IEEE Press.
Hansen, N., and A. Ostermeier. 2001. “Completely derandomized self-adaptation in evolution strategies.” Evol. Comput. 9 (2): 159–195. https://doi.org/10.1162/106365601750190398.
Hansen, N., S. D. Müller, and P. Koumoutsakos.2003. “Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES).” Evol. Comput. 11 (1): 1–18. https://doi.org/10.1162/106365603321828970.
Hervouet, J. M. 2007. Hydrodynamic of free surface flows modelling with the finite element method. New York: Wiley.
Holland, J. H. 1975. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. Ann Arbor, MI: U Michigan Press.
Huybrechts, N., G. V. Luong, Y. F. Zhang, C. Villaret, and M. A. Verbanck. 2011. “Dynamic routing of flow resistance and alluvial Bed-form changes from the lower to the upper regime.” J. Hydraul. Eng. 137 (9): 932–944. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000371.
Huybrechts, N., and C. Villaret. 2013. “Large-scale morphodynamic modelling of the Gironde Estuary, France.” Proc. Inst. Civ. Eng. Mar. Eng. 166 (2): 51–62. https://doi.org/10.1680/maen.2012.18.
Huybrechts, N., C. Villaret, and F. Lyard. 2012. “Optimized predictive Two-dimensional hydrodynamic model of the gironde estuary in france.” J. Waterw. Port Coastal Ocean Eng. 138 (4): 312–322. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000129.
Jalón-Rojas, I., S. Schmidt, and A. Sottolichio. 2015. “Turbidity in the fluvial Gironde Estuary (southwest France) based on 10-year continuous monitoring: Sensitivity to hydrological conditions.” Hydrol. Earth Syst. Sci. 19 (6): 2805–2819. https://doi.org/10.5194/hess-19-2805-2015.
Jalon-Rojas, I., A. Sottolichio, V. Hanquiez, A. Fort, and S. Schmidt. 2018. “To what extent multidecadal changes in morphology and fluvial discharge impact tide in a convergent (turbid) tidal river.” J. Geophys. Res.: Oceans 123 (5): 3241–3258. https://doi.org/10.1002/2017JC013466.
Kirkpatrick, S. D., C. Gelatt, and M. P. Vecchi. 1983. “Optimization by simulated annealing.” Science 220 (4598): 671–680. https://doi.org/10.1126/science.220.4598.671.
Laborie, V., F. Hissel, and P. Sergent. 2014. “Impact of climate change on Gironde estuary.” La Houille Blanche 6: 34–39. https://doi.org/10.1051/lhb/2014060.
Le Floch, J. 1961. “Propagation de la marée dynamique dans l’estuaire de la Seine et la Seine-Maritime.” Ph.D. thesis, Université de Paris.
Moldwin, M. 2016. “Tidal river dynamics.” Eos 97, 1–3. https://doi.org/10.1029/2018EO049541.
Moler, C., and J. Little. 2020. “A history of MATLAB.” Proc. ACM Program. Lang. 4: 81. https://doi.org/10.1145/3386331.
Morvan, H. P., D. K. Knight, N. G. Wright, X. Tang, and A. J. Crossley. 2008. “The concept of roughness in fluvial hydraulics and its formulation in 1-D, 2-D and 3-D numerical simulation models.” J. Hydraul. Res. 46 (2): 191–208. https://doi.org/10.1080/00221686.2008.9521855.
Mouradi, R.-S., C. Goeury, O. Thual, F. Zaoui, and P. Tassi. 2020. “Physically interpretable machine learning algorithm on multidimensional non-linear fields.” J. Comput. Phys. 428: 110074. https://doi.org/10.1016/j.jcp.2020.110074.
Orseau, S., N. Huybrechts, P. Tassi, S. Kaidi, and F. Klein. 2021. “NavTEL: Open-source decision support tool for ship routing and underkeel clearance management in Estuarine Channels.” J. Waterw. Port Coastal Ocean Eng. 147 (2): 04020053. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000610.
Orseau, S., N. Huybrechts, P. Tassi, D. Pham Van Bang, and F. Klein. 2020. “Two-dimensional modeling of fine sediment transport with mixed sediment and consolidation: Application to the Gironde Estuary, France.” Int. J. Sediment Res. In press.
Pairaud, I. L., F. Lyard, F. Auclair, T. Letellier, and P. Marsaleix. 2008. “Dynamics of the semi-diurnal and quarter-diurnal internal tides in the Bay of biscay. part 1: Barotropic tides.” Cont. Shelf Res. 28 (10–11): 1294–1315. https://doi.org/10.1016/j.csr.2008.03.004.
Pawlowicz, R., B. Beardsley, and S. Lentz. 2002. “Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE.” Comput. Geosci. 28 (8): 929–937. https://doi.org/10.1016/S0098-3004(02)00013-4.
Qi, P., and Z. Y. Sun. 1995. “Analysis of channel scouring and deposition of the Lower Yellow River.” Int. J. Sediment Res. 10 (2): 21–34.
Rudolph, G. 1994. “Convergence analysis of canonical genetic algorithms.” IEEE Trans. Neural Networks 5 (1): 96–101. https://doi.org/10.1109/72.265964.
Schureman, P. 1958. Manual of harmonic analysis and prediction of tides. Washington, DC: US Dept. of Commerce, Coast and Geodetic Survey.
Smaoui, H., A. Maqsoud, and S. Kaidi. 2019. “Transmissivity identification by combination of CVFEM and genetic algorithm: Application to the coastal aquifer.” Math. Probl. Eng. 2019: 3463607. https://doi.org/10.1155/2019/3463607.
Smaoui, H., L. Zouhri, and S. Kaidi. 2018. “Combination of FEM and CMA-ES algorithm for transmissivity identification in aquifer systems.” Hydrol. Processes 32 (2): 264–277. https://doi.org/10.1002/hyp.11412.
Sottolichio, A. 1999. “Modélisation de la dynamique des structurs turbides (bouchon vaseux et crème de vase) dans l’estuaire de la Gironde.” Ph.D. thesis, Environnements et Paléoenvironnements Océaniques et Continentaux, Univ. of Bordeaux I.
Sottolichio, A., and P. Castaing. 1999. “A synthesis on seasonal dynamics of highly-concentrated structures in the Gironde Estuary.” C. R. L’Acad. Sci. 329: 795–800.
Sottolichio, A., P. Le Hir, and P. Castaing. 2001. “Modelling mechanisms for the turbidity maximum stability in the Gironde Estuary, France.” Coastal Estuarine Fine Sediment Process. 3: 373–386. https://doi.org/10.1016/S1568-2692(00)80132-1.
Storn, R., and K. Price. 1997. “Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces.” J. Global Optim. 11 (4): 341–359. https://doi.org/10.1023/A:1008202821328.
van Maren, D. S., J. C. Winterwerp, and J. Vroom. 2015. “Fine sediment transport into the hyper-turbid lower Ems River: The role of channel deepening and sediment-induced drag reduction.” Ocean Dyn. 65 (4): 589–605. https://doi.org/10.1007/s10236-015-0821-2.
van Rijn, L. C. 2007. “Unified view of sediment transport by currents and waves. I: Initiation of motion, Bed roughness, and Bed-load transport.” J. Hydraul. Eng. 133 (6): 649–667. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:6(649).
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Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147 • Issue 3 • May 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jul 9, 2020
Accepted: Nov 24, 2020
Published online: Mar 4, 2021
Published in print: May 1, 2021
Discussion open until: Aug 4, 2021
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