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Optimal assimilation of current and surface elevation data in a two-dimensional numerical tidal model. (English) Zbl 0879.76010

The author studies an inverse problem for a two-dimensional oceanographic model in which kinematic nonlinearities are neglected but nonlinear friction is included. Data from current meters and/or tide gauges are used to calculate the bottom friction coefficient, water depth and wind drag coefficient. The norm of discrepancies between theoretical and measured values at the data stations is minimized. Gradients of that norm are calculated by an adjoint scheme, numerical optimization is carried out by Nash’s truncated Newton package. By tests with synthetic data it was found that the method works well for initial guesses within \(20-25\%\) of the true values. Convergence was more likely if both current and surface elevation data were used rather than only one of them.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M25 Other numerical methods (fluid mechanics) (MSC2010)
86A05 Hydrology, hydrography, oceanography
35R30 Inverse problems for PDEs

Software:

L-BFGS; tn; Algorithm 500
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Full Text: DOI

References:

[1] Bennett, A. F.; McIntosh, P. C., Open ocean modelling as an inverse problem: Tidal theory, J. Phys. Oceanog., 12, 1004-1018 (1982)
[2] Prevost, C.; Salmon, R., A variational method for inverting hydrographic data, J. Mar. Sci., 44, 1-34 (1986)
[3] Thacker, W. C.; Long, R. B., Fitting dynamics to data, J. Geophys. Res., 93, 1227-1240 (1988)
[4] Panchang, V. G.; O’Brien, J. J., On the determination of hydraulic model parameters using the adjoint state formulation, (Davies, A. M., Modelling marine systems (1989), CRC Press: CRC Press Boca Raton, FL), 6-18
[5] Tziperman, E.; Thacker, W. C., An optimal-control/adjointequations approach to studying the oceanic general circulation, J. Phys. Oceanog., 19, 1471-1485 (1989)
[6] Smedstad, O. M., Data assimilation and parameter estimation in oceanographic models, (Ph.D. Thesis (1989), Geophysical Fluid Dynamics Institute, Florida State University: Geophysical Fluid Dynamics Institute, Florida State University Tallahassee, FL)
[7] Smedstad, O. M.; O’Brien, J. J., Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model, Progr. Oceanog., 26, 179-241 (1991)
[8] Yu, L.; O’Brien, J. J., Variational estimation of the wind stressdrag coefficient and the oceanic viscosity profile, J. Phys. Oceanog., 21, 709-719 (1991)
[9] Yu, L.; O’Brien, J. J., On the initial condition in parameter estimation, J. Phys. Oceanog., 22, 1361-1364 (1992)
[10] Das, S. K.; Lardner, R. W., On the estimation of parameters of hydraulic models by assimilation of periodic tidal data, J. Geophys. Res. (Ocans), 96, 15.187-15.196 (1991)
[11] Marotzke, J., The role of integration time in determining a steady state through data assimilation, J. Phys. Oceanog., 22, 1556-1567 (1992)
[12] Lardner, R. W., Optimal control of open boundary conditions for a numerical tidal model, Comput. Meth. Appl. Mech. Eng., 102, 367-387 (1993), (1993) · Zbl 0767.76036
[13] Lardner, R. W.; Das, S. K., Optimal estimation of eddy viscosity for a quasi-three-dimensional numerical tidal and storm-surge model, Int. J. Numer. Meth. Fluids, 18, 295-312 (1994) · Zbl 0794.76057
[14] Navon, I. M., A review of variational and optimization methods in meteorology, (Sasaki, Y., Variational methods in geosciences (1986), Elsevier: Elsevier New York), 29-34
[15] Das, S. K.; Lardner, R. W., Variational parameters estimation for a two-dimensional numerical tidal model, Int. J. Numer. Meth. Fluids, 15, 313-327 (1992) · Zbl 0825.76109
[16] Lardner, R. W.; Al-Rabeh, A. H.; Gunay, N., Optimal estimation of parameters for a two-dimensional hydrodynamical model of the Arabian Gulf, J. Geophys. Res., 98, 18.229-18.242 (1993)
[17] Nash, S. A., Newton-type minimization via the Lanczos method, SIAM J. Numer. Anal., 21, 770-778 (1984) · Zbl 0558.65041
[18] Nash, S. G.; Nocedal, J., A numerical study of the limited memory BFGS method and the truncated Newton method for large scale optimization, (Tech. Rep. NAM 2 (1989), Northwestern University: Northwestern University Evanston, IL) · Zbl 0756.65091
[19] Lardner, R. W.; Smoczynski, P., A vertical/horizontal splitting algorithm for three-dimensional tidal and storm-surge computations, (Proc. Poy. Soc. London, A430 (1990)), 263-284 · Zbl 0703.76013
[20] Shanno, D. F.; Phua, K. H., Remark on algorithm 500, a variable metric method for unconstrained minimization, ACM Trans. Math. Software, 6, 618-622 (1980)
[21] Navon, I. M.; Legler, D. M., Conjugate gradient methods for large-scale minimization in meteorology, Mon. Wea. Rev., 115, 1479-1502 (1987)
[22] Leendertse, J. J., Aspects of a computational model for long period water-wave propagation, Rand Corp. Rep. (1967), RM-5294-PR
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