AUTOMATIC CALIBRATION OF A WAVE MODEL WITH AN EVOLUTIONARY BAYESIAN METHOD

Rodrigo Alonso, Sebastián Solari

Abstract


Bayesian Inference has been widely applied with success in science and engineering. One of its main uses is the inference of model parameters in order to reconcile model outputs with evidence provided by measures. In this article we propose this application for coastal engineering problems. Specifically, it is proposed to infer the parameters of a numerical wave model used to downscale wave reanalysis data to a coastal site. The proposed method is applied to a case study on the Uruguayan Atlantic coast, where a few month wave measure data series is available and needs to be extended in order to be used on an engineering project. The wave model used is SWAN and the data in deep waters and the wind data were obtained from the ERA-Interim reanalysis. At first, the method was tested with one and two parameters, since in these cases it is possible to compare the obtained results with a plot of the target function. Finally it was used to calibrate four parameters of the wave model and assess the uncertainty introduced by the selection of a set of parameters.

Keywords


Bayesian inference; wave modelling; wave reanalysis downscaling; Markov chain Monte Carlo

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References


Booij, N., R. C. Ris, & L-H. Holthuijsen. 1999. A third-generation wave model for coastal regions: 1. Model description and validation. Journal of Geophysical Research: Oceans, 104(C4), 7649–7666.

Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N. and Vitart, F. 2011, The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q.J.R. Meteorol. Soc., 137: 553–597.

Gelman, A. G., and D. B. Rubin 1992. Inference from iterative simulations using multiple sequence. Stat. Sci 7, 457 - 472

Hamada, M.S, Wilson A. G., Reese C. S. and Martz H. F. 2008. Bayesian Reliability, Springer Series in Statistics, New York, 436 pp.

Hasselmann, K., 1974: On the spectral dissipation of ocean waves due to whitecapping, Bound.-layer Meteor., 6, 1-2, 107-127

Hasselmann, K., T.P. Barnett, E. Bouws, H. Carlson, D.E. Cartwright, K. Enke, J.A. Ewing, H. Gienapp, D.E. Hasselmann, P. Kruseman, A. Meerburg, P. Müller, D.J. Olbers, K. Richter, W. Sell and H. Walden, 1973: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP), Dtsch. Hydrogr. Z. Suppl., 12, A8

Pierson, W.J. and L. Moskowitz, 1964: A proposed spectral form for fully developed wind seas based on the similarity theory of S.A. Kitaigorodskii, J. Geophys. Res., 69, 24, 5181-5190

ter Braak, C.J.F. and J.A. Vrugt 2008. Differential Evolution Markov chain Monte Carlo with snooker updater. Stat Comput, 18, 435-446.

Vrugt , J.A., H. V. Gupta, W. Bouten and S. Sorooshian. 2003. A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resource Research, 39, NO. 8, 1201.

Vrugt , J.A.,C.J.F. ter Braak, M.P. Clark, J.M. Hyman and B.A. Robinson. 2008. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resource Research, 44, W00B09.

Vrugt , J.A.,C.J.F. ter Braak, C.G.H. Diks, B.A. Robinson, J.M. Hyman and D. Higdon. 2009. Accelerating Markov chain Monte Carlo simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling. International Journal of Nonlinear Science & Numerical Simulation, 10 (3), 271-288.

Vrugt , J.A. 2016., Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and Matlab implementation. Environmental Modelling & Software, 75, 273-316

WAMDI group, 1988: The WAM model - a third generation ocean wave prediction model, J. Phys. Oceanogr., 18, 1775-1810




DOI: https://doi.org/10.9753/icce.v35.waves.26