Ocean Dynamics

, Volume 63, Issue 5, pp 489–505 | Cite as

Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

  • Ivan D. Garcia
  • Ghada El Serafy
  • Arnold Heemink
  • Henk Schuttelaars


Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.


Bathymetry Morphology Data assimilation Delft3D Morphodynamic modeling Model order reduction Variational Adjoint free 


  1. Altaf M, Heemink A, Verlaan M (2009) Inverse shallow-water flow modeling using model reduction. Int J Multiscale Comput Eng 7:577–594CrossRefGoogle Scholar
  2. Baur W, Strassen V (1983) The complexity of partial derivatives. Theor Comput Sci 22:317–330CrossRefGoogle Scholar
  3. Brander R (1999) Field observations on the morphodynamic evolution of a low-energy rip current system. Mar Geol 157:199–217CrossRefGoogle Scholar
  4. Cao Y, Zhu J, Navon I, Luo Z (2007) A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Int J Numer Methods Fluids 53:1571–1583CrossRefGoogle Scholar
  5. Daescu D, Carmichael G (2010) An adjoint sensitivity method for the adaptive location of the observations in air quality modeling. Technical report. Institute for Mathematics and its Applications, University of MinnesotaGoogle Scholar
  6. Deltares (2009a) Delft3D-FLOW user’s manual, ver 3.14 edition. Deltares, Rotterdamseweg 185, Delft, The Netherlands, http://oss.deltares.nl/web/delft3d/manuals
  7. Deltares (2009b) Delft3D-Wave user’s manual, ver 3.14 edition. Deltares, Rotterdamseweg 185, Delft, The Netherlands, http://oss.deltares.nl/web/delft3d/manuals
  8. Errico R (1997) What is an adjoint model? Bull Am Meteorol Soc 78:2577–2591CrossRefGoogle Scholar
  9. Giering R, Kaminski T (1998) Recipes for adjoint code construction. ACM Trans Math Softw (TOMS) 24:437–474CrossRefGoogle Scholar
  10. Griewank A (1989) On automatic differentiation. In: Iri M, Tanabe K (eds) Appears in mathematical programming: recent developments and applications. Kluwer, Amsterdam, pp 83–108Google Scholar
  11. Kaleta M, Hanea R, Heemink A, Jansen J (2010) Model-reduced gradient-based history matching. Comput Geosci 15:135–153CrossRefGoogle Scholar
  12. Le Dimet F, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38:97–110CrossRefGoogle Scholar
  13. Lesser G, Roelvink J, Kester JV, Stelling G (2004) Development and validation of a three-dimensional morphological model. Coast Eng 51:883–915CrossRefGoogle Scholar
  14. Pelc J, Ehouarn S, Laurent B, El Serafy G, Heemink A (2012) Application of model reduced 4D-Var to a 1D ecosystem model. Ocean Model 57–58:43–58CrossRefGoogle Scholar
  15. Ranasinghe R, Symonds G, Black K, Holman R (2004) Morphodynamics of intermediate beaches: a video imaging and numerical modeling study. Coast Eng 51:629–655CrossRefGoogle Scholar
  16. Roelvink J (2006) Coastal morphodynamic evolution techniques. Coast Eng 53:277–287CrossRefGoogle Scholar
  17. Roelvink J, Aarninkhof S, Wijnberg K, Reniers A (2003) Quantification of 2D subtidal bathymetry from video. TU Delft Report, prepared for Rijkswaterstaat, RIKZ, Z 3536. Deltares, Delft.Google Scholar
  18. Scott T, Mason D (2007) Data assimilation for a coastal area morphodynamic model: Morecambe Bay. Coast Eng 54:91–109CrossRefGoogle Scholar
  19. Short A (1993) Beaches of the New South Wales Coast; a guide to their nature, characteristics, surf and safety. Technical report. Australian Beach Safety and Management Program, SydneyGoogle Scholar
  20. Short A, Trenaman N (1992) Wave climate of the sydney region, an energetic and highly variable ocean wave regime. Mar Freshw Res 43:765–791CrossRefGoogle Scholar
  21. Smit M, Reniers A, Ruessink B, Roelvink D (2008) The morphological response of a nearshore double sandbar system to constant wave forcing. Coast Eng 55:761–770CrossRefGoogle Scholar
  22. Smith P, Dance S, Baines M, Nichols N, Scott T (2009) Variational data assimilation for parameter estimation: application to a simple morphodynamic model. Ocean Dyn 59:697–708CrossRefGoogle Scholar
  23. Smith P, Dance S, Nichols N (2011) A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling. In: 10th ICFD conference series on numerical methods for fluid dynamics (ICFD 2010), vol 46, pp 436–441Google Scholar
  24. Talagrand O, Courtier P (1987) Variational assimilation of meteorological observations with the adjoint vorticity equation. I: theory. Q J R Meteorol Soc 113:1311–1328CrossRefGoogle Scholar
  25. Thornhill G, Mason D, Dance S, Lawless A, Nichols N, Forbes H (2012) Integration of a 3D variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay. Coast Eng 69:82–96CrossRefGoogle Scholar
  26. Turner I, Aarninkhof S, Holman R (2006) Coastal imaging applications and research in Australia. J Coast Res 221:37–48CrossRefGoogle Scholar
  27. Uunk L (2008) Automated collection of intertidal beach bathymetries from Argus video images. Msc thesis, University of Twente, TwenteGoogle Scholar
  28. van Dongeren A, Plant N, Cohen A, Roelvink D, Haller D, Catalan P (2008) Beach wizard: nearshore bathymetry estimation through assimilation of model computations and remote observations. Coast Eng 55:1016–1027CrossRefGoogle Scholar
  29. van Rijn L (1993) Principles of sediment transport in rivers estuaries and coasts seas. Aqua Publications, AmsterdamGoogle Scholar
  30. van Rijn L (2007a) Unified view of sediment transport by currents and waves. I: initiation of motion, bed roughness, and bed-load transport. J Hydraul Eng 133:649–667CrossRefGoogle Scholar
  31. van Rijn L (2007b) Unified view of sediment transport by currents and waves. II: suspended transport. J Hydraul Eng 133:668–689CrossRefGoogle Scholar
  32. van Rijn L (2007c) Unified view of sediment transport by currents and waves. III: graded beds. J Hydraul Eng 133:761–775CrossRefGoogle Scholar
  33. Vermeulen P, Heemink A (2006) Model-reduced variational data assimilation. Mon Weather Rev 134:2888–2899CrossRefGoogle Scholar
  34. Wright L, Short A (1984) Morphodynamic variability of surf zones and beaches: a synthesis. Mar Geol 56:93–118CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ivan D. Garcia
    • 1
  • Ghada El Serafy
    • 1
  • Arnold Heemink
    • 2
  • Henk Schuttelaars
    • 2
  1. 1.DeltaresDelftThe Netherlands
  2. 2.DIAMTU DelftDelftThe Netherlands

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