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Inversion of three-dimensional tidal currents in marginal seas by assimilating satellite altimetry. (English) Zbl 1225.76300
Summary: The four-dimensional variational data assimilation technology based on the theory of inverse problem is applied to simulate the three-dimensional tidal currents in the marginal seas by assimilating the satellite altimetry. The model is calibrated by the twin experiments where the prescribed open boundary conditions for a three-dimensional barotropic tidal model are successfully inverted. By assimilating the tidal harmonic constants derived from TOPEX/Poseidon altimeter data, the open boundary conditions are optimized and the M 2 tidal currents in the Bohai and Yellow Seas (BYS) are simulated in the practical experiment. During the assimilation, the cost function and the gradients of cost function with respect to the open boundary conditions have been decreased significantly. Although the current observations are not assimilated into the model, the cost function composed of the data misfit between model-produced and observed currents is still decreased from 1.00 to 0.09, which demonstrates the reasonability and feasibility of inverting tidal currents from satellite altimetry or other elevation measurements. The co-tidal charts and the near-surface M 2 tidal current ellipses obtained in the practical experiment are in good agreement with the observed tides and tidal currents in BYS.
MSC:
76U05Rotating fluids
86A05Hydrology, hydrography, oceanography
86A22Inverse problems in geophysics
Software:
L-BFGS
References:
[1]Munk, W. H.: Once again: once again-tidal friction, Prog. ocean. 40, 7-35 (1997)
[2]Teague, W. J.; Perkins, H. T.; Hallock, Z. R.: Current and tide observations in the southern yellow sea, J. geophys. Res. 103, 27783-27793 (1998)
[3]Egbert, G. D.; Ray, R. D.: Estimates of M2 tidal energy dissipation from TOPEX/poseidon altimeter data, J. geophys. Res. 106, 22475-22502 (2001)
[4]Fang, G. H.: Tide and tidal current charts for the marginal seas adjacent to China, Chin. J. Ocean. limnol. 4, 1-16 (1986)
[5]Choi, B. H.: A fine-grid three-dimensional M2 tidal model of the east China sea, Modelling marine system, 167-185 (1990)
[6]Guo, X. Y.; Yanagi, T.: Three-dimensional structure of tidal current in the east China sea and the yellow sea, J. oceanogr. 54, 651-668 (1998)
[7]Kang, S. K.; Lee, S. R.; Lie, H. J.: Fine grid tidal modeling of the yellow and east China seas, Cont. shelf. Res. 18, 739-772 (1998)
[8]Lee, J. C.; Jung, K. T.: Application of eddy viscosity closure models for the M2 tide and tidal currents in the yellow sea and the east China sea, Cont. shelf. Res. 19, 445-475 (1999)
[9]Lefevre, F.; Le Provost, C.; Lyard, F. H.: How can we improve a global ocean tide model at a regional scale? A test on the yellow sea and the east China sea, J. geophys. Res. 105, 8707-8725 (2000)
[10]Bao, X. W.; Gao, G. P.; Yan, J.: Three dimensional simulation of tide current characteristics in the east China sea, Oceanol. acta. 24, No. 2, 1-15 (2001)
[11]Lee, H. J.; Jung, K. T.; So, J. K.: A three-dimensional mixed finite-difference Galerkin function model for the oceanic circulation in the yellow sea and the east China sea in the presence of M2 tide, Cont. shelf. Res. 22, 67-91 (2002)
[12]He, Y. J.; Lu, X. Q.; Qiu, Z. F.: Shallow water tidal constituents in the bohai sea and the yellow sea from a numerical adjoint model with T/P altimeter data, Cont. shelf. Res. 24, 1521-1529 (2004)
[13]Lu, X. Q.; Zhang, J. C.: Numerical study on spatially varying bottom friction coefficient of a 2-D tidal model with adjoint method, Cont. shelf. Res. 26, 1905-1923 (2006)
[14]Byun, D. S.; Wang, X. H.: The effect of sediment stratification on tidal dynamics and sediment transport patterns, J. geophys. Res. 110, C03011 (2005)
[15]Yang, Z. Q.; Hamrick, J. M.: Variational inverse parameter estimation in a cohesive sediment transport model: an adjoint approach, J. geophys. Res. 108, No. C2, 3055 (2003)
[16]Wang, X. H.: Tide-induced sediment resuspension and the bottom boundary layer in an idealized estuary with a muddy bed, J. phys. Oceanogr. 32, 3113-3131 (2002)
[17]Ray, R. D.: Inversion of oceanic tidal currents from measured elevations, J. mar. Syst. 28, 1-18 (2001)
[18]Bennett, A. F.; Mcintosh, P. C.: Open ocean modeling as an inverse problem: tidal theory, J. phys. Oceanogr. 12, 1004-1018 (1982)
[19]Prevost, C.; Salmon, R.: A variational method for inverting hydrographic data, J. mar. Sci. 44, 1-34 (1986)
[20]Sasaki, Y.: Some basic formalisms in numerical variational analysis, Mon. weather. Rev. 98, 875-883 (1970)
[21]Thacker, W. C.; Long, R. B.: Fitting dynamics to data, J. geophys. Res. 93, 1227-1240 (1988)
[22]Navon, I. M.: Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn. atmos. Oce. special issue in honor of richard pfeffer 27, 55-79 (1998)
[23]Panchang, V. G.; O’brien, J. J.: On the determination of hydraulic model parameters using the adjoint state formulation, Modelling marine system, 6-18 (1989)
[24]Smedstad, O. M.; O’brien, J. J.: Variational data assimilation and parameter estimation in an equatorial Pacific ocean model, Prog. ocean. 26, 179-241 (1991)
[25]Yu, L. S.; O’brien, J. J.: Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile, J. phys. Oceanogr. 21, 709-719 (1991)
[26]Yu, L. S.; O’brien, J. J.: On the initial condition parameter estimation, J. phys. Oceanogr. 22, 1361-1364 (1992)
[27]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. methods. Fluids 18, 295-312 (1994) · Zbl 0794.76057 · doi:10.1002/fld.1650180305
[28]Lardner, R. W.; Song, Y.: Optimal estimation of eddy viscosity and friction coefficients for a quasi-three-dimensional numerical tidal model, Atmos. ocean. 33, No. 3, 581-611 (1995)
[29]Marotzke, J.; Giering, R.; Zhang, Q. K.: Construction of the adjoint MIT ocean general circulation model and application to atlantic heat transport sensitivity, J. geophys. Res. 104, 29529-29548 (1999)
[30]Heemink, A. W.; Mouthaan, E. E. A.; Roest, M. R. T.: Inverse 3-D shallow water flow modeling of the continental shelf, Cont. shelf. Res. 22, 465-484 (2002)
[31]Peng, S. Q.; Xie, L.: Effect of determining initial conditions by four-dimensional variational data assimilation on storm surge forecasting, Ocean. model. 14, 1-18 (2006)
[32]Zhang, J. C.; Lu, X. Q.: Parameter estimation for a three-dimensional numerical barotropic tidal model with adjoint method, Int. J. Numer. methods. Fluids 57, 47-92 (2008)
[33]D.E. Cartwright, R.D. Ray, B.V. Sanchez, A computer program for predicting oceanic tidal currents, NASA Tech Memo 104578, Goddard Space Flight Center, 1992.
[34]Headrick, R. H.; Spiesberger, J. L.; Bushong, P. J.: Tidal signals in basin-scale acoustic transmissions, J. acoust. Soc. am. 93, 790-802 (1993)
[35]Mcintosh, P. C.; Bennett, A. F.: Open ocean modeling as an inverse problem: M2 tides in bass strait, J. phys. Oceanogr. 14, 601-614 (1984)
[36]Egbert, G. D.; Bennett, A. F.; Foreman, M. G. G.: Topex/poseidon tides estimated using a global inverse method, J. geophys. Res. 99, 24821-24852 (1994)
[37]Kantha, L. H.: Barotropic tides in the global oceans from a nonlinear tidal model assimilating altimetric tides 1. Model description and results, J. geophys. Res. 101, 25283-25308 (1995)
[38]Shum, C. K.; Woodworth, P. L.; Andersen, O. B.: Accuracy assessments of recent global ocean tide models, J. geophys. Res. 102, 25173-25194 (1997)
[39]Egbert, G. D.; Ray, R. D.: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data, Nature 405, 775-778 (2000)
[40]Zou, J. P.; Hsieh, W. H.; Navon, I. M.: Sequential open-boundary control by data assimilation in a limited area model, Mon. weather. Rev. 123, No. 9, 2899-2909 (1995)
[41]Anderson, D. L. T.; Sheinbaum, J.; Haines, K.: Data assimilation in ocean models, Rep. prog. Phys. 59, 1209-1266 (1996)
[42]Gunzburger, M.: Adjoint equation-based methods for control problems in incompressible, viscous flows, Flow, flow, turb. Comb. 65, 249-272 (2000) · Zbl 0996.76024 · doi:10.1023/A:1011455900396
[43]Sirkes, Z.; Tziperman, E.: Finite difference of adjoint or adjoint of finite difference?, Mon. weather. Rev. 125, No. 12, 3373-3378 (1997)
[44]Casulli, V.; Cheng, R. T.: Semi-implicit finite difference methods for the three dimensional shallow water flow, Int. J. Numer. methods. Fluids 15, 629-648 (1992) · Zbl 0762.76068 · doi:10.1002/fld.1650150602
[45]Navon, I. M.; Zou, X.; Derber, J.; Sela, J.: Variational data assimilation with an adiabatic version of NMC spectral model, Mon. weather. Rev. 120, 1433-1446 (1992)
[46]Alekseev, A. K.; Navon, I. M.; Steward, J.: Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems, Optim. meth. Software 24, No. 1, 63-87 (2009) · Zbl 1189.90221 · doi:10.1080/10556780802370746
[47]Zou, X.; Navon, I. M.; Sela, J. G.: Control of gravity oscillations in variational data assimilation, Mon. weather. Rev. 121, No. 1, 272-289 (1993)
[48]Fang, G. H.; Wang, Y. G.; Wei, Z. X.: And east China seas from 10 years of T/P altimetry, J. geophys. Res. 109, C11006 (2004)
[49]Tikhonov, A. N.: Regularization of incorrectly posed problems, Sov. math. Dokl. 4, 1624-1627 (1963) · Zbl 0183.11601
[50]Yeh, W. W. G.: Review of parameter identification procedures in groundwater hydrology: the inverse problem, Water. resour. Res. 22, 95-108 (1986)
[51]Liu, D. C.; Nocedal, J.: On the limited memory method for large scale optimization, Math. program. B 45, No. 3, 503-528 (1989) · Zbl 0696.90048 · doi:10.1007/BF01589116
[52]Yang, Z.; Hamrick, J. M.: Optimal control of salinity boundary condition in a tidal model using a variational inverse method, Estu. coas. Shelf sci. 62, 13-24 (2005)