About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 950926, 11 pages
http://dx.doi.org/10.1155/2013/950926
Research Article

Optimization of Open Boundary Conditions in a 3D Internal Tidal Model with the Adjoint Method around Hawaii

1Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266003, China
2Laboratory of Coast and Island Development, Nanjing University, Nanjing 210093, China

Received 4 January 2013; Accepted 13 March 2013

Academic Editor: Guanglu Zhou

Copyright © 2013 Anzhou Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. L. Rudnick, T. J. Boyd, R. E. Brainard et al., “From tides to mixing along the Hawaiian Ridge,” Science, vol. 301, no. 5631, pp. 355–357, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Munk and C. Wunsch, “Abyssal recipes II: energetics of tidal and wind mixing,” Deep-Sea Research Part I, vol. 45, no. 12, pp. 1977–2010, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. R. D. Ray and G. T. Mitchum, “Surface manifestation of internal tides generated near Hawaii,” Geophysical Research Letters, vol. 23, no. 16, pp. 2101–2104, 1996. View at Scopus
  4. R. D. Ray and G. T. Mitchum, “Surface manifestation of internal tides in the deep ocean: observations from altimetry and island gauges,” Progress in Oceanography, vol. 40, no. 1–4, pp. 135–162, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Munk, “Once again: once again—tidal friction,” Progress in Oceanography, vol. 40, no. 1–4, pp. 7–35, 1997. View at Publisher · View at Google Scholar · View at Scopus
  6. J. P. Martin, D. L. Rudnick, and R. Pinkel, “Spatially broad observations of internal waves in the upper ocean at the Hawaiian Ridge,” Journal of Physical Oceanography, vol. 36, no. 6, pp. 1085–1103, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. Z. Zhao, M. H. Alford, J. A. Mackinnon, and R. Pinkel, “Long-range propagation of the semidiurnal internal tide from the Hawaiian Ridge,” Journal of Physical Oceanography, vol. 40, no. 4, pp. 713–736, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. Z. Zhao, M. Alford, J. Girton, T. Johnston, and G. Carter, “Internal tides around the Hawaiian Ridge estimated from multisatellite altimetry,” Journal of Geophysical Research, vol. 116, Article ID C12039, 2011.
  9. Z. Zhao, M. Alford, and J. Griton, “Mapping low-mode internal tides from mulsatellite altimetry,” Oceanography, vol. 25, no. 2, pp. 42–51, 2012.
  10. S. K. Kang, M. G. G. Foreman, W. R. Crawford, and J. Y. Cherniawsky, “Numerical modeling of internal tide generation along the Hawaiian Ridge,” Journal of Physical Oceanography, vol. 30, no. 5, pp. 1083–1098, 2000. View at Scopus
  11. H. Simmons, R. Hallberg, and B. Arbic, “Internal wave generation in a global baroclinic tide model,” Deep-Sea Research II, vol. 51, pp. 3043–3068, 2004. View at Publisher · View at Google Scholar
  12. G. S. Carter, M. A. Merrifield, J. M. Becker et al., “Energetics of M2 barotropic-to-baroclinic tidal conversion at the Hawaiian Islands,” Journal of Physical Oceanography, vol. 38, no. 10, pp. 2205–2223, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. B. Powell, I. Janekovic, G. Carter, and M. A. Merrifield, “Sensitivity of internal tide generation in Hawaii,” Geophysical Research Letters, vol. 39, Article ID L10606, 2012.
  14. L. Rainville, T. M. S. Johnston, G. S. Carter et al., “Interference pattern and propagation of the M2 internal tide south of the Hawaiian Ridge,” Journal of Physical Oceanography, vol. 40, no. 2, pp. 311–325, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. E. D. Zaron and G. D. Egbert, “The impact of the M2 internal tide on data-assimilative model estimates of the surface tide,” Ocean Modelling, vol. 18, no. 3-4, pp. 210–216, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. I. Shulman, “Local data assimilation in specification of open boundary conditions,” Journal of Atmospheric and Oceanic Technology, vol. 14, no. 6, pp. 1409–1419, 1997. View at Scopus
  17. I. Shulman, J. K. Lewis, A. F. Blumberg, and B. N. Kim, “Optimized boundary conditions and data assimilation with application to the M2 tide in the yellow sea,” Journal of Atmospheric and Oceanic Technology, vol. 15, no. 4, pp. 1066–1071, 1998. View at Scopus
  18. V. Taillandier, V. Echevin, L. Mortier, and J. L. Devenon, “Controlling boundary conditions with a four-dimensional variational data-assimilation method in a non-stratified open coastal model,” Ocean Dynamics, vol. 54, no. 2, pp. 284–298, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. P. G. J. ten Brummelhuis, A. W. Heemink, and H. F. P. van den Boogaard, “Identification of shallow sea models,” International Journal for Numerical Methods in Fluids, vol. 17, no. 8, pp. 637–665, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. E. Kazantsev, “Boundary conditions control for a shallow-water model,” International Journal for Numerical Methods in Fluids, vol. 68, no. 5, pp. 625–641, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. I. Yu. Gejadze and G. J. M. Copeland, “Open boundary control problem for Navier-Stokes equations including a free surface: adjoint sensitivity analysis,” Computers & Mathematics with Applications, vol. 52, no. 8-9, pp. 1243–1268, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. R. Lardner, “Optimal assimilation of current and surface elevation data in a two-dimensional numerical tidal model,” Applied Mathematical Modelling, vol. 19, pp. 30–38, 1995.
  23. E. P. Myers and A. M. Baptista, “Inversion for tides in the Eastern North Pacific Ocean,” Advances in Water Resources, vol. 24, no. 5, pp. 505–519, 2001. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Zhang and X. Lu, “Inversion of three-dimensional tidal currents in marginal seas by assimilating satellite altimetry,” Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 49-52, pp. 3125–3136, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Z. Guo, A. Cao, and X. Lv, “Inverse estimation of open boundary conditions in the Bohai Sea,” Mathematical Problems in Engineering, vol. 2012, Article ID 628061, 9 pages, 2012. View at Publisher · View at Google Scholar
  26. A. Cao, Z. Guo, and X. Lv, “Inversion of two-dimensional tidal open boundary conditions of M2 constituent in the Bohai and Yellow Seas,” Chinese Journal of Oceanology and Limnology, vol. 30, no. 5, pp. 868–875, 2012.
  27. H. Chen, C. Miao, and X. Lv, “A three-dimensional numerical internal tidal model involving adjoint method,” International Journal for Numerical Methods in Fluids, vol. 69, no. 10, pp. 1584–1613, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. X. Lu and J. Zhang, “Numerical study on spatially varying bottom friction coefficient of a 2D tidal model with adjoint method,” Continental Shelf Research, vol. 26, no. 16, pp. 1905–1923, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. J. Zhang, X. Lu, P. Wang, and Y. P. Wang, “Study on linear and nonlinear bottom friction parameterizations for regional tidal models using data assimilation,” Continental Shelf Research, vol. 31, no. 6, pp. 555–573, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. L. Yu and J. O'Brien, “Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile,” Journal of Physical Oceanography, vol. 21, pp. 709–719, 1990. View at Publisher · View at Google Scholar
  31. C. Miao, H. Chen, and X. Lv, “An isopycnic-coordinate internal tide model and its application to the South China Sea,” Chinese Journal of Oceanology and Limnology, vol. 29, no. 6, pp. 1339–1356, 2011.
  32. M. Gunzburger, “Adjoint equation-based methods for control problems in incompressible, viscous flows,” Flow, Turbulence and Combustion, vol. 65, no. 3-4, pp. 249–272, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. G. I. Marchuk, “Perturbation theory and the statement of inverse problems,” in Fifth Conference on Optimization Techniques (Rome, 1973), vol. 4 of Lecture Notes in Comput. Sci., pp. 159–166, Springer, Berlin, Germany, 1973. View at Zentralblatt MATH · View at MathSciNet
  34. G. Marchuk, “Basic and adjoint equations of atmosphere and ocean dynamics,” MeteorologIya i GIdrologIya, vol. 2, no. 9, pp. 9–37, 1974.
  35. D. G. Cacuci, “Sensitivity theory for nonlinear systems. II. Extensions to additional classes of responses,” Journal of Mathematical Physics, vol. 22, no. 12, pp. 2803–2812, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  36. G. I. Marchuk, Adjoint Equations and Analysis of Complex Systems, vol. 295 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995. View at MathSciNet
  37. I. M. Navon, “Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography,” Dynamics of Atmospheres and Oceans, vol. 27, no. 1–4, pp. 55–79, 1998. View at Scopus
  38. R. A. Flather, “A tidal model of the north-west European continental shelf,” Memoires de la Societe Royale des Sciences de Liege, vol. 6, no. 10, pp. 141–164, 1975. View at Scopus