Research Article

A POD reduced-order 4D-Var adaptive mesh ocean modelling approach

  1. F. Fang1,*,
  2. C. C. Pain1,
  3. I. M. Navon2,
  4. M. D. Piggott1,
  5. G. J. Gorman1,
  6. P. E. Farrell1,
  7. P. A. Allison1,
  8. A. J. H. Goddard1

Article first published online: 9 SEP 2008

DOI: 10.1002/fld.1911

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Volume 60, Issue 7, pages 709–732, 10 July 2009

Additional Information

How to Cite

Fang, F., Pain, C. C., Navon, I. M., Piggott, M. D., Gorman, G. J., Farrell, P. E., Allison, P. A. and Goddard, A. J. H. (2009), A POD reduced-order 4D-Var adaptive mesh ocean modelling approach. International Journal for Numerical Methods in Fluids, 60: 709–732. doi: 10.1002/fld.1911

Author Information

  1. 1

    Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, SW7 2AZ, U.K.

  2. 2

    Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, U.S.A.

*Applied Modelling and Computation Group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, SW7 2AZ, U.K.

Publication History

  1. Issue published online: 19 MAY 2009
  2. Article first published online: 9 SEP 2008
  3. Manuscript Accepted: 28 JUL 2008
  4. Manuscript Revised: 25 JUL 2008
  5. Manuscript Received: 14 DEC 2007

Funded by

  • UK's Natural Environment Research Council. Grant Numbers: NER/A/S/2003/00595, NE/C52101X/1, NE/C51829X/1
  • Engineering and Physical Sciences Research Council. Grant Number: GR/R60898
  • Leverhulme Trust. Grant Number: F/07058/AB
  • Imperial College High Performance Computing Service
  • Grantham Institute for Climate Change
  • NSF. Grant Numbers: ATM-0201808, CCF-0635162

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Keywords:

  • inverse;
  • adjoint;
  • POD;
  • reduced-order modelling;
  • ocean model;
  • finite element;
  • unstructured adaptive mesh

Abstract

A novel proper orthogonal decomposition (POD) inverse model, developed for an adaptive mesh ocean model (the Imperial College Ocean Model, ICOM), is presented here. The new POD model is validated using the Munk gyre flow test case, where it inverts for initial conditions. The optimized velocity fields exhibit overall good agreement with those generated by the full model. The correlation between the inverted and the true velocity is 80–98% over the majority of the domain. Error estimation was used to judge the quality of reduced-order adaptive mesh models. The cost function is reduced by 20% of its original value, and further by 70% after the POD bases are updated.

In this study, the reduced adjoint model is derived directly from the discretized reduced forward model. The whole optimization procedure is undertaken completely in reduced space. The computational cost for the four-dimensional variational (4D-Var) data assimilation is significantly reduced (here a decrease of 70% in the test case) by decreasing the dimensional size of the control space, in both the forward and adjoint models. Computational efficiency is further enhanced since both the reduced forward and adjoint models are constructed by a series of time-independent sub-matrices. The reduced forward and adjoint models can be run repeatedly with negligible computational costs.

An adaptive POD 4D-Var is employed to update the POD bases as minimization advances and loses control, thus adaptive updating of the POD bases is necessary. Previously developed numerical approaches Fang et al. (Int. J. Numer. Meth. Fluids 2008) are employed to accurately represent the geostrophic balance and improve the efficiency of the POD simulation. Copyright © 2008 John Wiley & Sons, Ltd.

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