Ocean Dynamics

, Volume 60, Issue 6, pp 1497–1537 | Cite as

Multiscale two-way embedding schemes for free-surface primitive equations in the “Multidisciplinary Simulation, Estimation and Assimilation System”



We derive conservative time-dependent structured discretizations and two-way embedded (nested) schemes for multiscale ocean dynamics governed by primitive equations (PEs) with a nonlinear free surface. Our multiscale goal is to resolve tidal-to-mesoscale processes and interactions over large multiresolution telescoping domains with complex geometries including shallow seas with strong tides, steep shelfbreaks, and deep ocean interactions. We first provide an implicit time-stepping algorithm for the nonlinear free-surface PEs and then derive a consistent time-dependent spatial discretization with a generalized vertical grid. This leads to a novel time-dependent finite volume formulation for structured grids on spherical or Cartesian coordinates, second order in time and space, which preserves mass and tracers in the presence of a time-varying free surface. We then introduce the concept of two-way nesting, implicit in space and time, which exchanges all of the updated fields values across grids, as soon as they become available. A class of such powerful nesting schemes applicable to telescoping grids of PE models with a nonlinear free surface is derived. The schemes mainly differ in the fine-to-coarse scale transfers and in the interpolations and numerical filtering, specifically for the barotropic velocity and surface pressure components of the two-way exchanges. Our scheme comparisons show that for nesting with free surfaces, the most accurate scheme has the strongest implicit couplings among grids. We complete a theoretical truncation error analysis to confirm and mathematically explain findings. Results of our discretizations and two-way nesting are presented in realistic multiscale simulations with data assimilation for the middle Atlantic Bight shelfbreak region off the east coast of the USA, the Philippine archipelago, and the Taiwan–Kuroshio region. Multiscale modeling with two-way nesting enables an easy use of different sub-gridscale parameterizations in each nested domain. The new developments drastically enhance the predictive capability and robustness of our predictions, both qualitatively and quantitatively. Without them, our multiscale multiprocess simulations either were not possible or did not match ocean data.


Embedding schemes Multiscale ocean modeling Shelfbreak regions Coastal dynamics Tidal forcing  Multiresolution Multigrid CFD 



We are thankful to W.G. Leslie for his collaboration in the real-time experiments that formed the test-bed for this research and for his help in preparing the figures for this manuscript. We would like to thank C. Lozano and L. Lanerolle for many fruitful discussions during the development of our system. We thank O. Logutov for his tide research and discussions. We are very thankful to the reviewers for their careful and detailed reviews and their very useful suggestions. For our AWACS-SW06 effort, we thank G. Gawarkiewicz, P. Abbot and T. Duda for their ocean data and M. Taylor and J. Hare for their NMFS survey data. We also thank J. Evans, S. Glenn, and J. Wilkin for their real-time WRF atmospheric fluxes and the FNMOC teams for their own products. For our PhilEx effort, we thank A. Gordon, C. Villanoy, C. Lee, and J. Sprintall for their ocean data; H. Hurlburt and J. Metzger for large-scale boundary conditions; and H. Arango and J. Levin for discussions. We also thank B. Leben and CCAR for providing SSH anomaly data. For our QPE effort, we thank G. Gawarkiewicz, T. Duda, J. Sen, B. Cornuelle, J. Lynch, P. Niiler, L. Centurioni, C. Lee, R.-C. Lien, T. Sanford, L. Mayer, B. Calder, and Y.-T. Lin for data and discussions. We also thank J. Doyle, D. Marble, J. Nachimknin, and J. Cook as well as the FNMOC for providing us with atmospheric fluxes.


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Patrick J. HaleyJr.
    • 1
  • Pierre F. J. Lermusiaux
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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