图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际多尺度计算工程期刊
影响因子: 1.016 5年影响因子: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.v7.i6.70
pages 577-594

Inverse Shallow-Water Flow Modeling Using Model Reduction

Muhammad Umer Altaf
Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands
Arnold W. Heemink
Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands
Martin Verlaan
Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

ABSTRACT

The idea presented in this paper is variational data assimilation based on model reduction using proper orthogonal decomposition. An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability, and only the dominant eigenvectors of this matrix are used to define a model subspace. An approximate linear reduced model is obtained by projecting the original model onto this reduced subspace. Compared to the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. Thus, it does not require the implementation of the adjoint of the tangent linear model. The minimization process is carried out in reduced subspace and hence reduces the computational cost. Twin experiments using an operational storm surge prediction model in the Netherlands, the Dutch Continental Shelf Model are performed to estimate the water depth, with the findings that the approach with relatively little computational cost and without the burden of implementation of the adjoint model can be used in variational data assimilation.

REFERENCES

  1. Ten-Brummelhuis, P. G. J., Heemink, A.W., and van den Boogard, H. F. P., Identification of shallow sea models. DOI: 10.1002/fld.1650170802

  2. Lardner, R.W., Al-Rabeh, A. H., and Gunay, N., Optimal Estimation of Parameters for a Two Dimensional Hydrodynamical Model of the Arabian Gulf. DOI: 10.1029/93JC01411

  3. Ulman, D. S., andWilson, R. E., Model Parameter Estimation for Data Assimilation Modeling: Temporal and Spatial Variability of the Bottom Drag Coefficient. DOI: 10.1029/97JC03178

  4. Heemink, A. W., Mouthaan, E. E. A., and Roest, M. R. T., Inverse 3D Shallow-Water Flow Modeling of the Continental Shelf. DOI: 10.1016/S0278-4343(01)00071-1

  5. Kaminski, T., Giering, R., and Scholze, M., An Example of an Automatic Differentiationbased Modeling System. DOI: 10.1007/3-540-44843-8_11

  6. Antoulas, A. C., Approximation of Large-Scale Dynamical Systems.

  7. Pearson, K., On Lines and Planes of Closest Fit to Points in Space. DOI: 10.1080/14786440109462720

  8. Kepler, G. M., Tran, H. T., and Banks, H. T., Reduced-Order Compensator Control of Species Transport in CVD Reactor.

  9. Prabhu, R. D., Scott, C. S., and Changly, Y., The Influence of Control on Proper Orthogonal Decomposition of Wall-Bounded Turbulent Flows. DOI: 10.1063/1.1333038

  10. Alfonsi, G., Restanob, C., and Primaveral, L., Coherent Structures of the Flow around a Surface-Mounted Cubic Obstacle in Turbulent Channel Flow. DOI: 10.1016/S0167-6105(02)00429-4

  11. Cao, Y., Zhu, J., Luo, Z., and Navon, I. M., Reduced Order Modeling of the Upper Tropical Pacific Ocean Model Using Proper Orthogonal Decomposition. DOI: 10.1016/j.camwa.2006.11.012

  12. Gunzburger, M. D., Reduced-Order Modeling, Data Compression and the Design of Experiments.

  13. Le Dimet, F. X., and Talagrand, O., Variational Algorithms for Analysis and Assimilation of Meteorological Observations: Theoratical Aspects. DOI: 10.1111/j.1600-0870.1986.tb00459.x

  14. Lawless, A. S., Nichols, N. C., Boess, C., and Bunse-Gerstner, A., Using Model Reduction Methods within Incremental 4DVAR. DOI: 10.1175/2007MWR2103.1

  15. Daescu, D. N., and Navon, I. M., A Dual Weighted Approach to Order Reduction in 4DVAR Data Assimilation. DOI: 10.1175/2007MWR2102.1

  16. Fang, F., Pain, C. C., Navon, I. M., Piggott, D., Gorman, G. J., Farrell, P. E., Allison, P. A., and Goddard, A. J. H., Reduced order modeling of an adaptive mesh ocean model. DOI: 10.1002/fld.1841

  17. Fang, F., Pain, C. C., Navon, I. M., Piggott, D., Gorman, G. J., Allison, P. A., and Goddard, A. J. H., A POD Reduced-Order Unstructured Mesh Ocean Modelling Method for Moderate Reynolds Number Flows. DOI: 10.1016/j.ocemod.2008.12.006

  18. Delay, F., Buoro, A., and de Marsily, G., Empirical Orthogonal Functions Analysis Applied to the Inverse Problem in Hydrogeology: Evaluation of Uncertainty and Simulation of New Solutions. DOI: 10.1023/A:1012298023051

  19. Vermeulen, P. T. M., Heemink, A. W., and Valstar, J. R., Inverse Modeling of Groundwater Flow Using Model Reduction. DOI: 10.1029/2004WR003698

  20. Vermeulen, P. T. M., and Heemink, A. W., Model-Reduced Variational Data Assimilation. DOI: 10.1175/MWR3209.1

  21. Courant, R., and Hilbert, D., Methods of Mathematical Physics.

  22. Sirovich, L., Choatic Dynamics of Coherent Structures. DOI: 10.1016/0167-2789(89)90123-1

  23. Cao, Y., Zhu, J., Navon, I. M., and Luo, Z., A Reduced-Order Approach to Fourdimensional Variational Data Assimilation Using Proper Orthogonal Decomposition. DOI: 10.1002/fld.1365

  24. Leendertse, J., Aspects of a Computational Model for Long-Period Water Wave Propagation.

  25. Stelling, G. S., On the Construction of Computational Methods for ShallowWater Flow Problem.

  26. Verboom, G. K., de Ronde, J. G., and van Dijk, R. P., A Fine Grid Tidal Flow and Storm Surge Model of the North Sea. DOI: 10.1016/0278-4343(92)90030-N

  27. Mouthaan, E., Heemink, A. W., and Robaczewska, K., Assimilation of ERS-1 Altimeter Data in a Tidal Model of the Continental Shelf. DOI: 10.1007/BF02226308

  28. Verlaan, M., Zijderveld, A., Vries, H., and Kroos, J., Operational Storm Surge Forcasting in the Netherlands: Developments in Last Decade. DOI: 10.1098/rsta.2005.1578

  29. Verlaan, M., Mouthaan, E., Kuijper, E., and Philippart, M., Parameter Estimation Tools for Shallow Water Flow Models.

  30. Verlaan, M., Efficient Kalman Filtering Algorithms for Hydrodynamic Models.

  31. Ten-Brummelhuis, P. G. J., Parameter Estimation in Tidal Flow Models with Uncertain Boundary Conditions.

  32. Velzen, N., and Verlaan, M., Costa a Problem Solving Environment for Data Assimilation Applied for Hydrodynamical Modeling.


Articles with similar content:

AN ADAPTIVE MULTIFIDELITY PC-BASED ENSEMBLE KALMAN INVERSION FOR INVERSE PROBLEMS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Tao Zhou, Liang Yan
REDUCED ORDER MODELING FOR NONLINEAR MULTI-COMPONENT MODELS
International Journal for Uncertainty Quantification, Vol.2, 2012, issue 4
Hany S. Abdel-Khalik, Christopher Kennedy, Jason Hite, Youngsuk Bang
Minimax Approach to Magnetic Storms Forecasting (Dst-index Forecasting)
Journal of Automation and Information Sciences, Vol.43, 2011, issue 3
Nikolay N. Salnikov, Igor A. Kremenetskiy
INCORPORATING PRIOR KNOWLEDGE FOR QUANTIFYING AND REDUCING MODEL-FORM UNCERTAINTY IN RANS SIMULATIONS
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 2
Heng Xiao, Jin-Long Wu, Jianxun Wang
AN ENSEMBLE KALMAN FILTER USING THE CONJUGATE GRADIENT SAMPLER
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 4
Heikki Haario, Antti Solonen, Albert Parker, Marylesa Howard, Johnathan M. Bardsley